Anne Ventura
email: anne.ventura@lcpc.fr

Classification of chemicals into emissionbased impact categories: a first approach for equiprobable and site specific conceptual frames

Keywords: classification, life cycle impact assessment, emission-based impact categories, site specific lca

Classification of chemicals into emission-based impact categories: a first approach for equiprobable and site specific conceptual frames

Introduction

The Life Cycle Impact Assessment is a step of the Life Cycle Assessment that is dedicated to translate a huge amount of environmental inventory flows into their expected environmental effects using a reduced number of indicators. According to [START_REF] Consoli | Guidelines for life cycle assessment. A code of practice[END_REF], the first step that consists of distributing pollutants into various impact categories is called "classification". This classification step is systematically neglected in the calculation of LCIA indicators (equation ( 1)):

for several direct contribution of one pollutant to several impact categories, the distribution between these impact categories is not accounted.

∑ = i i i m C I . ( 1
)
where I is the environmental indicator (kg equivalent to the reference substance), i C is the contribution coefficient of the inventory flow i to the impact category as an equivalent to the reference substance, and i m is the mass of the inventory flow i .

As one mass of pollutant is entirely affected to each of the direct impact categories, this comes down to multiply the mass of one pollutant by the number of impact categories, and thus overestimating the actual indicator value. Furthermore, if one pollutant indirectly contributes to an impact category because it is chemically transformed, it is not included into indicators calculation.

In that case, the indicator value is underestimated. This classification problem has recently been highlighted as still unresolved by [START_REF] Reap | A survey of unresolved problems in life cycle assessment. Part II: impact assessment and interpretation[END_REF].

Udo de [START_REF] Udo De Haes | Part I -Discussion of general principles and guidelines for practical use in Towards a methodology for life cycle impact assessment[END_REF] had already discussed of this classification step and defined the notions of parallel, serial, indirect and combined impacts. Based on this initial approach (Udo de [START_REF] Udo De Haes | Part I -Discussion of general principles and guidelines for practical use in Towards a methodology for life cycle impact assessment[END_REF], the present study aims at defining a methodological frame for non-redundant classification, based on the probability that an emitted substance and its chemically degraded forms are involved into several environmental impacts. Two types of repartitions are examined in this paper: i) one, called equiprobable classification, based on identical probability of contributions to several impact categories, and ii) and one, called zone classification, that has already been studied in a first attempt (Ventura et al, 2007) and [START_REF] Sayagh | Sensitivity of the LCA allocation procedure for BFS recycled into pavement structures[END_REF], based on territorial conditions and that is formalized in this paper.

General principles of classification

Compared to the classical LCA indicator, an additional classification coefficient i α for the inventory flow i is defined (see equation ( 2)). This coefficient yields, for a given inventory flow, the mass proportion contributing to a given impact category. The new indicator equation including the i α coefficient is detailed below:

∑ = i i i i m C I . . α (2)
where i α is the classification coefficient of the inventory flow i to the impact category (no unit).

A Distribution coefficient is defined by the equation below:

∑ = i i i D α (3)
Several types of contributions of one pollutant to an impact category are defined and schematized on Figure 1. The contribution of the pollutant i to one impact category is defined as reactive when the contribution implies that the pollutant i is transformed by a chemical reaction.

The contribution of the pollutant i to one impact category is defined as suspensive when the contribution does not imply the chemical transformation of the molecule.

The contribution of the pollutant i to one impact category is defined as direct when the contribution is directly issued from the pollutant i .

The contribution does not imply the chemical transformation of the molecule. The contribution of the pollutant i to one impact category is defined as indirect, when the impact is due to a new pollutant j produced after a first contribution being reactive or suspensive. For example, the contribution of methane to photochemical ozone formation is reactive because CH 4 is chemically degraded, whereas its contribution to the greenhouse effect is suspensive because it is not chemically degraded. In that case, the CH 4 molecule is still available for a chemical reaction, i.e. CH 4 can react with another organic compound under the action of ultraviolet rays, and produce photochemical ozone. This contribution can be considered as successive to the first one.

Another example is airborne emitted NH 3 : it contributes to odour and toxicity as direct contributions, it is chemically transformed in HNO 3 in the atmosphere and thus successively contributes to acidification, and once in soil and water, contributes to eutrophication, successively to acidification.

Several rules need to be respected for the i D values, depending on the chemical behaviour of pollutant i when contributing to each impact category.

Generalizing this concept conducts to the following rules:

-for direct and reactive contributions of pollutant i to several impact categories 1 , ,

∑ = = i direct reactive i direct reactive i D α -If there is any indirect or suspensive contributions issued from pollutant i : 1 , , > + = indirect suspensive i direct reactive i total i D D D
The following parts of the paper will examine various procedures for calculating i α values.

Equiprobable classification

The purpose the equiprobability classification procedure is to avoid multiple counting of pollutants.

Let's consider that pollutant i has direct reactive contributions to one or several impact categories numbered 1 to n , and direct suspensive contributions to one or several impact categories numbered 1 + n to m . With the equiprobable procedure, direct i α has the same value whatever is the impact category. It is calculated by the following equation:

n direct i 1 = α (4)
And then, the Distribution coefficient is calculated by:

n n m D direct i ) ( 1 - + = (5)
In that case of indirect contributions, the "no impact" contribution is considered equiprobable and one is added to the denominator. If pollutant i is degraded in pollutants k to j 1 for k indirect impact categories, then:

1 + = → k direct i indirect j i α α (6)
To show an application of the method, let's take again the example of methane. Thus, CH 4 is still available for chemical reaction, and can contribute to produce photochemical ozone. However, the contribution to photochemical oxidation is considered successive to the contribution to the greenhouse effect. According to equation (6), and with

1 = k , then 2 1 1 ) ( ) ( 4 4 = + = k GWP direct CH POCP indirect CH α α . Using 1 = k
at the denominator in equation ( 6), means that the whole mass of methane is not classified in the photochemical oxidation. This indeed takes into account that the fate and transport of the methane is not known, and thus may not undergo photochemical oxidation.

Zone classification

Another methodology can be proposed to calculate these coefficients accounting local conditions parameters. The zone classification method is based on two steps: i) the first step requires defining an impacted zone around the source, inside which the emitted chemicals are expected to majorly diffuse or spread; ii) in the second step, the score of the chemical is set according to the occurrence of the chemical target inside the impacted zone. The chemical target is defined as the event that will simultaneously provoke the degradation of a pollutant and the environmental effect. Thus, the chemical target does not exist for suspensive contributions, but only for reactive contributions.

The following parts detail the method for calculating classification coefficients. Values are suggested to show the application of the method: for impacted zones in relationship with the type emission (Table 1), and for chemical targets inside impacted zone (Table 2). The choices of impacted zones and chemical targets are however very rough, and are further examined in the discussion part of this article.

Case of direct and reactive contributions

For each emitted pollutant that has a direct contribution to several environmental impacts, the emissions conditions are analyzed by filling Table 1. The local emission conditions will gather rough information concerning the transport of the pollutant and the probability to reach the chemical target concerned by each impact category.

A score, noted k i, σ , is affected to each case (Table 1). The value of k i, σ can be defined as -

k k k i N n = , σ (7) if the number of chemical targets is k k N n <
in the impacted zone.

For the impact category k , with K k < < 1

, and the pollutant i , the total score is defined as:

∑ = ts compartmen all k i k i s , , σ (8)
the emission compartments being those defined in Table 1.

Then the classification coefficient

direct k i,
α can be calculated as follows:

∑ = = K k k i k i direct k i s s 1 , , , α (9)

Case of indirect or suspensive contributions

The calculation of classification coefficients for indirect contributions will follow the same rule as for the direct ones, but they will be calculated from the corresponding

direct k i, α .
Let's consider the contribution of pollutant j to the several impact categories

2 2 1 K k < <
, after being initially produced by pollutant i through a reactive contribution to the impact category 1 k

(route A on Figure 1). The score of pollutant j is calculated as a direct contribution to impact categories 2 k but considering the zone of the impact category 1 k initially affected by pollutant i .

2 2 1 2 . , , k k k i k j N n σ σ = (10)
Then, the total score is calculated by:

∑ = ts compartmen all k j k j s 2 2 , , σ (11)
Then the indirect contribution of pollutant i is calculated as follows:

2 1 2 , , , . k j direct k i indirect k j i s α α = → (12)
The case of direct but suspensive contribution concerns environmental impacts caused by a molecule but not by a chemical reaction, therefore there is no chemical target. The greenhouse gases have such a contribution to the climate change impact category. Whatever is the type of air emission (Table 1) greenhouse gases will contribute to the climate change impact category. In that case, the score 1 , = CCI j σ .

Suggestions for chemical targets

Table 2 presents possible reference values for chemical targets that can be used to calculate scores (see equations ( 8) and ( 11)).

For toxicity, the involved pollutant is degraded by human metabolism. Thus, the indicator for chemical target has been chosen as the presence of human being in the impacted zone. Then, population density is proposed as a reference. The maximal existing value is the population density of Cairo city: 35,420 people/km².

For ecotoxicity, the involved pollutant is degraded when in contact with any living being. Thus, the percentage of natural or cultivated surface area in the impacted zone, have been chosen as the chemical target indicator.

For photochemical ozone formation, the involved pollutant is degraded under the action of ultraviolet rays, and sometimes only if simultaneously in contact with other chemical species (synergistic effect). However, sunrays are necessary and are thus the limiting factor. Therefore, the sunshine duration appears to be a quite acceptable indicator of the chemical target. The maximal existing value is the number of hours in a year: 8,760 hr/yr. Values concerning impacted zones of Table 2 have been collected from (Meteo France, 2009).

For acidification, the involved pollutant is expected to release H + ions mainly when in contact with water molecules in the atmosphere. This corresponds to inverse conditions compared to the occurrence of photochemical ozone formation. Thus, hours without sunshine can be taken as a reference. The maximal existing value is again the number of hours in a year: 8,760 hr/yr. For aquatic eutrophication, the pollutants are consumed by plants and microorganisms that will proliferate in surface waters. Thus, the percentage of surface water area in the impacted zone can be chosen as an indicator for the chemical target. The maximum value is therefore 100%, and the values concerning impacted zones of Table 2 have been crossed from several sources [START_REF] Ose | Ressources en eaux -eaux de surface[END_REF], [START_REF] Ose | Observatoire national des zones humides -les zones humides en France[END_REF] and (Wikipedia, 2009).

Application example on NOx emissions

As an example, both classification methods are applied to stack and diffuse emissions of nitrogen oxides NOx, occurring in Paris.

Figure 2 presents the nitrogen biogeochemical paths, and contributions of human activities.

NOx are mainly produced by human activities, and especially by combustion processes, where N 2 is oxidized into NO and NO 2 .mainly by thermal decomposition of N 2 [START_REF] Miller | Mechanism and modelling of nitrogen chemistry in combustion[END_REF]:

N 2 + O • → N • + NO (13a) N • + O 2 → NO + O • (13b) N • + • OH → NO + H • (13c)
Other chemical pathways (not detailed in this paper) can also produce NO: fuel NO [START_REF] Tomita | Suppression of nitrogen oxides emission by carbonaceous reductants[END_REF] or prompt NO [START_REF] Fenimore | Formation of nitric oxide in premixed hydrocarbon flames[END_REF]. Whatever the pathway is, NO is rapidly converted in NO 2 in the atmosphere:

NO + RO 2 → NO 2 + ½HO 2 + R (14)
NO 2 can directly contribute to several impact categories.

In presence of water in the atmosphere, NO 2 will form nitric acid, and cause an acidification impact:

3NO 2 + H 2 O → 2HNO 3 + NO (15)
In the presence of ultraviolet rays, NO 2 can lead to photochemical ozone formation:

NO 2 + uv O • + NO • (16a) O • + O 2 O 3 (16b)
NO 2 also directly contributes to toxicity when breathed by human population.

NO 2 can also indirectly contribute to several impact categories: HNO 3 produced by equation (15)

will produce NO 3 -in contact with water, and thus contribute to terrestrial and aquatic eutrophication.

HNO 3 + H 2 O → H + + NO 3 - ( 17
)
Furthermore, O 3 produced by equations ( 16a) and (16b) will contribute to toxicity.

Results shown in Table 3 highlight that big differences of final indicators value would be found when using or not the classification coefficient. With an equiprobable classification, the contributions of NOx molecules to photochemical ozone formation, acidification and toxicity is respectively 33%, 33% and 47% of an actual value without classification.

The coefficients calculated using equiprobable or zone classifications are in the same order of magnitude except for indirect contributions, where the equiprobable method leads to an overestimated result.

Discussion

The discussion is organized in three parts. In a first part, the zone classification is compared with existing LCA localised approaches. In the second part, the two steps of zone classification are discussed. In a third part, the feasibility of both equiprobable and zone classifications is examined.

Zone classification and existing LCA-localised approaches

In the literature, various sets of impact categories were defined corresponding to midpoints, endpoints, and damages for each generic areas of protection [START_REF] Bare | Environmental impact assessment taxonomy providing comprehensive coverage of midpoints, endpoints, damages, and areas of protection[END_REF].

Some authors have been interested by assessing spatial differentiated indicators for resources issues [START_REF] Brent | A life cycle impact assessment procedure with resource groups as areas of protection[END_REF]) and [START_REF] Raugei | A novel approach to the problem of geographic allocation of environmental impact in Life Cycle Assessment and Material Flow Analysis[END_REF]. Concerning emissions of chemical substances, other studies have been conducted in order to integrate spatial differentiation in LCA methods with the aim of calculating endpoint indicators. They all require transports models of pollutants in the various compartments of the environment; these have been reviewed by [START_REF] Mackay | Local and distant residence times of contaminants in multicompartment models. Part I: A review of the theoretical basis[END_REF].

These models are often completed by the inclusion of chemical fate of pollutants, especially to account for pollutants involved into human toxicity and ecosystem toxicity [START_REF] Huijbregts | Priority assessment of toxic substances in life cycle assessment. Part I: Calculation of toxicity potentials for 181 substances with the nested multi-media fate, exposure and effects model USES-LCA[END_REF], [START_REF] Huijbregts | Human population intake fractions and environmental fate factors of toxic pollutants in life cycle impact assessment[END_REF]. A scientific consensus between modellers has raised from the UNEP/SETAC Life Cycle initiative [START_REF] Rosenbaum | USEtox -the UNEP/SETAC toxicity model: recommended characterisation factors for human toxicity and freshwater ecotoxicity in life cycle impact assessment[END_REF] leading to the USEtox model. Some general remarks can be made concerning these various models:

-they are all focused on long term distribution of pollutant in the environment, -thus, they are all focused on persistent pollutants, and their effect on toxicity and ecotoxicity, -they deeply examine the distribution of one pollutant in the different compartments of the environment,

-the complexity of those methods mainly relies upon the number of considered compartments [START_REF] Mackay | Local and distant residence times of contaminants in multicompartment models. Part I: A review of the theoretical basis[END_REF].

However, many pollutants do no enter these models because they are not persistent: they are more or less rapidly chemically transformed, and, because of their chemical transformation, they can indirectly contribute to several other impact categories.

The inclusion of geographical specified data has already been proposed by several authors [START_REF] Potting | Spatial Differentation in Life Cycle Impact Assessment[END_REF], [START_REF] Huijbregts | Priority assessment of toxic substances in life cycle assessment. Part I: Calculation of toxicity potentials for 181 substances with the nested multi-media fate, exposure and effects model USES-LCA[END_REF], [START_REF] Huijbregts | Geographical scenario uncertainty in generic fate and exposure factors of toxic pollutants for life-cycle impact assessment[END_REF], [START_REF] Webster | Regional differences in chemical fate model outcome[END_REF], [START_REF] Mackay | Local and distant residence times of contaminants in multicompartment models. Part I: A review of the theoretical basis[END_REF]. The main difference between those methods and the zone classification are schematised on Figure 3 and Figure 4.

For existing methods (Figure 3), indicators calculations are performed from a pollutant mass that is aggregated for the whole environmental system, wherever is the emission spot. Then, the distribution of pollutant is considered between environmental compartments, they will depend on transport scenarios. However, the environmental compartments are not geographically defined (air, water, soil, sediments…). The aggregation of one pollutant mass over the whole system before classification indeed conducts to lose the specificity of the geographical details.

For the zone allocation method (Figure 4), although the transport of pollutant presented in this paper is roughly integrated, by considering a perimeter of impacted zone, the geographical specificities are kept until the ending step of impact characterisation. In case of specific needs, the level of accuracy for the transport of pollutants can be increased. Furthermore, territorial environmental issues are considered in the indicator calculation. [START_REF] Potting | Background for spatial differentiation in LCA impact assessment -The EDIP2003 methodology[END_REF] introduced the notion of site factor that characterizes the sensitivity of an impacted zone area to a given environmental impact, because they mention that "…it is commonly recognised that the calculated contributions, except for the global impacts, could be in poor accordance with the expected occurrence of actual impacts". Although site specific data are required, the objective of zone classification is different: it is dedicated to assess the occurrence of chemical targets in an impacted zone, as a previous step to the indicator calculation.

The two steps of zone classification

The use of site specific data in LCA is a particularly paradoxical challenge.

Defining the impacted zone

Table 1 gives suggestions for emission compartments that could be related to the dimension, and size of the impacted zone. For airborne emissions, two types of emissions are distinguished:

"stack" and "other" emissions. This distinction between stack emissions and others is linked to the design principles of industrial exhaust equipments (ASHRAE, 2007). Industrial stacks (height and diameter) are designed to ensure large dispersions of pollutants: it must be sufficient to avoid exposure of immediate neighbourhood to high concentrations of toxic compounds. The geometrical characteristics of industrial stacks are generally defined according to the expected gas flue (average velocity), the analysis of surrounding environment (presence of other stacks, buildings or natural obstacles), and of prevailing wind (main directions and velocity). General design rules are generally incorporated into environmental regulations, i.e. (JORF 2008) in France.

Thus, one can consider that stack emissions will preferentially be dispersed and transported on long distances. The term "other" emissions correspond to emissions sources that are not designed for large dispersions. They can be engine exhausts, diffuse, fugitive emissions… The emitted pollutants can be considered to be dispersed and transported on short distances, although in some particular cases, it could also be transported on long distances, i.e. favourable physical and wind configurations and/or persistent pollutants [START_REF] Bennett | Predicting long-range transport: a systematic evaluation of two multimedia transport models[END_REF].

For water emissions, the pollutant transport zone will depend on the type of receiving water. For stagnant water, the dispersion can be considered limited to the pool or lake surface area. The depth could also be considered, as well as sediments. For quick current water, the dispersion can be considered to follow the stream bed on a distance mainly depending on the rate of flow. For ocean water, the dispersion can be considered on a surface (or depth) depending on the tide amplitude.

For soil emissions, the pollutant can be estimated to almost not disperse.

In actual environmental impacts of chemical pollution, environmental transport distances and transfers between compartments, is much more complex. Suggestions featuring in Table 1 could be refined using existing transport models like the one suggested by [START_REF] Mckone | Chemical-specific representation of air-soil exchange and soil penetration in regional multimedia models[END_REF], if a good knowledge of local parameters is available. This degree of complexity could especially be relevant for persistent chemicals: complexity of their transport is partly linked to the amount of time between the emission into the environment and the chemical reaction.

Choice of the chemical target

Table 2 suggests chemical targets to account inside the impact zone, in relationship with the emission-based impact categories.

The population density has been chosen as the chemical target for toxicity.

For ecotoxicity, the chemical target has been chosen as the percentage of wild nature or cultivated surface area inside the impacted zone. Actually, the presence of any living thing does not indicate an effect because some ecotoxicants are very specific to certain types of species but not others. If suitable data are available chemical targets could be refined using more detailed data on specific ecosystems, i.e. in accordance with the ones used by [START_REF] Huijbregts | Priority assessment of toxic substances in life cycle assessment. Part I: Calculation of toxicity potentials for 181 substances with the nested multi-media fate, exposure and effects model USES-LCA[END_REF]: fresh water, marine and terrestrial.

For photochemical ozone creation, the annual hours of sunshine duration have been chosen as the chemical target, because it is the limiting factor, without which the chemical reaction would not occur.

For acidification, the choice of annual duration hours without sunshine for a chemical target is disputable: acidification can occur during sunshine by means of dry deposition followed by reaction with any humid surfaces. In fact, this chemical target is only relevant for airborne emissions, for which acid molecules can be in competition with photochemical oxidation. For water compartment, the score is logically maximal, and it can also be considered maximum for soil in most of the cases, as the acid molecule will release H + ions whenever in contact with living organisms or rainwater.

Feasibility of both classification methods

The equiprobable classification only requires knowing the conditions of emissions for each substance (see Table1): in the available ILCD guidance for life cycle inventories [START_REF] Eplca | European Platform on LCA, International Reference Life Cycle Data System (ILCD) Handbook, ILCD reference elementary flows table[END_REF], sufficient details about emission conditions are already forecasted. This method is thus well adapted to general LCA studies, where pollutants are aggregated upon their emission spots. It is mainly useful to avoid multiple counting of one pollutant mass and can rapidly be included in existing tools. However, this first approach can not be entirely satisfying because it is not justified by physical and chemical backgrounds.

The zone classification is more satisfying from this last requirement, but the method needs several types of specific data: emission compartments, the knowledge of emission sites, and the occurrence of chemical targets.

In existing databases, the inventory data in LCA are usually expressed in amounts per functional unit and, in principle, nothing is known about the source. When examining SPOLD exchange format [START_REF] Singhofen | Life Cycle Inventory Data: Development of a common format[END_REF]

D D

)? In fact, this possibility changes the limit of the system. Although there can be no general answer to be give to this question, for the moment, one iteration seams a reasonable track to explore, as the example dealt in Table 3, shows very weak values of the classification coefficient for indirect impacts.

Conclusion

The principle of using a classification coefficient for distributing a mass of pollutant between several impact categories appears relatively simple and is scientifically justified. This conceptual frame suggests classification as a previous step to indicator calculations. It can thus be combined with any type of emission-based indicators for LCIA, from midpoint to endpoint or damage indicators.

Two different methods, based on a classification coefficient, are presented to solve this problem.

Both proposed methods require for the calculation of the coefficient value, a categorization of chemical pathways (reactive, suspensive, direct, indirect). The first method, the equiprobable classification, is a quick method that allows avoiding multiple counting of pollutants and is well adapted to general LCA studies, where pollutants are aggregated upon their emission spots. It could rapidly be included in existing tools.

The second method, the zone classification method, is related to territorial aspects. This method requires the definition of a chemical target. It appears helpful by accounting the effect of pollutants in the territory they are emitted, whereas actual methods consider environmental compartments wherever the pollution occurs. Applying this new method drives to gather detailed information about each location spots of involved producing processes. The classification method is dedicated to differentiate environmental pressures between varying places all over the world, but it does not contribute to assess actual environmental impacts. Udo de Haes (1996) defined LCA as "…primarily a tool for resource conservation and pollution prevention", and for this reason "....all emissions are regarded as relevant on the basis of their intrinsic hazard characteristics". Although using geographical parameters, the classification step only allows differentiating, by a probabilistic approach, environmental pressures from one place to another. The conceptual frame for classification is still in accordance with the general LCA philosophy promoted by ISO 14040/44 that the impacts in LCIA are potential, not real ones.

However, the choice of the impacted zone is important and it is thus necessary to find general rules that are scientifically relevant in the majority of cases. The suggested rules (Table 1) are still to refine, especially in the case of persistent pollutants. In the same manner, chemical targets are suggested in the present article but may be refined; this essentially depends on the availability of geo-localised data. For example, in practice it could be difficult in an LCA to include the population density since so many different locations would be included. However, some similar approaches have been recently suggested, using GIS and dynamic map gridding tools, concerning toxic pollutant sources and population density targets [START_REF] Jolliet | Multiscale, Multimedia modelling to compare local and global life cycle impacts on human health[END_REF].

The possibility to include indirect impacts can conduct to shift away the environmental system boundaries, taking into account the chemical fate of pollutants.

Finally, another important consequence of such a method is that indicators are not anymore mathematically independent from one another, although it reflects a chemical reality. The further use of indicators results into a multicriteria decision aiding process should take this new fact into consideration.

The feasibility of zone classification as for other region-specific methods will depend on the specific LCA study and has to be decided in the "Goal & Scope". It is clearly not applicable in the case of generic LCA, where production processes are not related to sites and suppliers of one product are interchangeable. The feasibility is also related to availability of data. In most databases, it is in general not possible to trace back the sites, data are most frequently averages. In comparative LCAs, the question of potential asymmetries between compared cases will be an important one.

The

  are at their maximum known value k N in the impacted zone or if the impacted zone is the Earth (i.e. global impacts such as climate change or stratospheric ozone layer depletion).

  geographical information is already available, although not very accurate (only the country code is required), but this type of information could be completed by geographical coordinates. The ILCD guidance[START_REF] Eplca | European Platform on LCA, International Reference Life Cycle Data System (ILCD) Handbook, ILCD reference elementary flows table[END_REF] for inventories seams also appropriate to integrate the information.Concerning emission compartments, the knowledge does exist at the very first step of data collection: measurement methods are very different considering the emission compartment. As an example for airborne emissions, stack emissions require particular measurements systems whereas diffuse emissions from a stockpile require emission models (US-EPA, 2010). Thus, inventory data could contain suitable information, if producers care to collect and properly aggregate them.The question of indirect contributions, accounting for chemical transformation of pollutants is also important, because it introduces a new complexity in the impact assessment. In the case of one pollutant leading several successive chemical reactions, each product being itself a pollutant, how far the number of iterations should be conducted? In the same manner, in the case of an emitted chemical i that has not direct and reactive contribution, but that is chemically transformed into a pollutant j , having itself a contribution, should the indirect or suspensive contributions be

	accounted (in this particular case:	total i	=	suspensive i	, indirect	≤	1


Cécilia Damon

Antoine Liutkus

Alexandre Gramfort

Slim Essid

NON-NEGATIVE TENSOR FACTORIZATION FOR SINGLE-CHANNEL EEG ARTIFACT REJECTION

Keywords: EEG, artifact removal, nonnegative matrix/tensor factorization, source separation, Gaussian model

New applications of Electroencephalographic recording (EEG) require light and easy-to-handle equipment and free of constraints experiments involving powerful algorithms of artifact removal. In our work, we target informed source separation methods for artifact removal in the extreme case of singlechannel EEG recordings by exploiting prior knowledge from auxiliary lightweight sensors capturing artifactual signals. To achieve this, we propose a method using Non-negative Tensor Factorization (NTF) in a Gaussian source separation framework that proves competitive against the classic Independent Component Analysis (ICA) technique. Additionally the both NTF and ICA methods are used in an original scheme that jointly processes the EEG and auxiliary signals. The adopted NTF strategy is shown to improve the source estimates accuracy in comparison with the usual multi-channel ICA approach.

INTRODUCTION

Electroencephalographic (EEG) recordings may be strongly disturbed by endogenous brain activities and extraneous environmental and physiological artifacts such as power grid noise, eye movements, heart beat or muscle activities. Therefore, the cerebral signal of interest mixed to these artifacts could be difficult to identify and analyse in the EEG data given the overlapping of signals [START_REF] O G Lins | Ocular artifacts in EEG and event-related potentials I: Scalp topography[END_REF].

Moreover, new applications of EEG recording, for instance brain-computer interfaces or human-activity monitoring, pose new challenges in terms of artifact removal as they call for fully automatic techniques, that would be additionally amenable to real-time processing. Among these applications, we are interested in the general public applications where the EEG setup is to be maintained as light as possible and ideally be limited to a single electrode, while allowing the use of other types of lightweight sensors, for example Electromyographic (EMG), Electrocardiographic (ECG), or inertial measurement sensors. This paper extends our previous study [START_REF] Damon | Nonnegative matrix factorization for single-channel EEG artifact rejection[END_REF] focusing on ocular artifacts to multiple artifact removal. In the latter, it was shown that single-channel EEG Non-negative Matrix Factorization (NMF) performs as well as multi-channel EEG Independent Component Analysis (ICA). Both methods properly exploit prior knowledge on artifactual signals from auxiliary channels recording, introduced in the learning process through the initialization of the matrix decomposition, to guide the artifact rejection and hence the identification of the cerebral signal of interest.

Significant improvements to the previous scheme are introduced in this paper as we propose a novel artifact removal scheme that jointly processes single-channel EEG and artifact auxiliary signals using Non-negative Tensor Factorization (NTF). This is motivated by the fact that the single-channel EEG observations may be considered as a linear mixture of the cerebral sources of interest and the various artifactual sources.

Given our data configuration, single-channel EEG and artifact auxiliary signals are processed under a parallel factorization analysis where each spectrogram represents a slice of a third order tensor. We additionally challenge this method with a particular ICA approach, similar in spirit to our NTF scheme, where the single-channel EEG data is processed jointly with multiple auxiliary channels.

To our knowledge, EEG artifact removal within a joint processing framework of single-channel EEG and auxiliary recordings is completely novel. Also, while NTF has already been used for EEG-feature extraction [START_REF] Lee | Nonnegative tensor factorization for continuous eeg classification[END_REF], its use for EEG artifact removal within a Gaussian source separation framework is novel.

In Section 2, we briefly recall the statistical NTF approach and we describe our algorithm aiming at recovering both cerebral and artifactual sources in single-channel EEG recordings. Section 3 assesses and compares the four studied algorithms : single-channel EEG NMF, multiple-channel EEG ICA, and NTF and ICA based on single-channel EEG and multiple auxiliary channels. Note that we use the Itakura-Saito divergence for the NMF and NTF since this cost function has proven effective in our previous study [START_REF] Damon | Nonnegative matrix factorization for single-channel EEG artifact rejection[END_REF].

A further extension to our previous study consists of conducting our experimental validation with multiple artifacts on simulated datasets. This study focuses on three kinds of physiological artifacts, namely ocular, cardiac and facialmovement artifacts and investigates the quality of the source estimates depending on the position of the electrode used to record the EEG signals, considering that the intensity of the artifactual disturbances on the cerebral activities changes through the brain surface.

NTF-BASED ARTIFACT REJECTION

For a complete description of how informed NMF/NTF is used in order to perform EEG artifact rejection following a probabilistic source separation paradigm, we refer the reader to [START_REF] Damon | Nonnegative matrix factorization for single-channel EEG artifact rejection[END_REF]. We use Itakura-Saito divergence (IS) given its link with maximum likelihood estimation in a Gaussian context and since successful results have been previously obtained with this cost function [START_REF] Damon | Nonnegative matrix factorization for single-channel EEG artifact rejection[END_REF]. We hereafter, first, briefly recall the general principle of the Itakura-Saito-based NTF decomposition. Then, we describe the algorithm applied to our particular data configuration, that is single-channel EEG accompanied with auxiliary signals describing the sources of artifacts.

IS-based NTF-decomposition

Consider I observable time-series x (t, i), each x ( • , i) corresponding to one of the EEG sensors. For a given sensor i, we assume that each x ( • , i) is the sum of J underlying signals ỹ ( • , i, 1) , . . . , ỹ ( • , i, J) which are called latent variables in this study.

The NTF technique operates in the Time-Frequency (TF) domain of the signals considered. More specifically, x ( • , • , i) will denote the Short Term Fourier Transform (STFT) of the mixture x ( • , i), so that x (f, n, i) ∈ C is its spectrum at frequency bin f for frame index n. Similarly, y (f, n, i, j) denotes the STFT of the i th channel of latent component j at TF bin (f, n). All signals are supposed to have the same number F of frequency indices and the same number N of frames.

The IS-NTF model approximates the power spectrograms |x ( • , • , i)

2 | by a linear combination of non-negative rank-1 elementary spectrograms W j Q ij H T j , corresponding to one given spectral template W j modulated by a time-varying activation gain H j up to a nonnegative scaling factor Q ij . W j and H j have been gathered as the J columns of matrices W and H of respective dimensions F × J and N × J. At TF bin (f, n), the Power Spectral Density (PSD) of the i th channel is modeled by :

|x (f, n, i) 2 | ≈ ṽ (f, n, i) = j W f j H nj Q ij , (1)
Learning such a model (1) through maximum likelihood estimation is equivalent to minimizing the Itakura-Saito divergence 1 between the power spectrogram of the observations and the model [START_REF] Bertin | Nonnegative Matrix Factorization with the Itakura-Saito Divergence. With Application to Music Analysis[END_REF][START_REF] Liutkus | Gaussian processes for underdetermined source separation[END_REF] :

Ŵ , Ĥ, Q = argmin W,H,Q f,n,i d IS |x (f, n, i)| 2 ṽ (f, n, i) (2)
To ensure that the latent components obtained that way correspond to the latent components we are looking for, we initialize the model parameters as described hereafter.

Informed NTF initialization

To aid the rejection of artifacts in single-channel EEG analysis, we inform the learning process by initializing the model parameters with the results of the IS-NMF decomposition of such auxiliary signals [START_REF] Cichocki | Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation[END_REF].

The algorithm proceeds in three steps :

1. for each auxiliary signal r, representing a potential artifactual source in EEG signal, we perform a IS-NMF decomposition :

ṽr (f, n) = j W r f j H r nj , (3)
2. a) we recall that the third order tensor to approximate is composed of the single-channel EEG and auxiliary spectrograms. Before learning the IS-NTF model, we initialize the corresponding subparts of the spectral and activation gain matrices with the K r artifactual components W r j H r j estimated in step 1. We use both the basis spectra W r and activation gain H r matrices for initialization to improve, during the learning process, the identification of the artifactual components both in auxiliary and single-channel EEG signals. The remaining Kr K r components of the EEG NTF decomposition are randomly initialized with K being the total number of sources, cerebral and artifactual b) we perform the learning process of the IS-NTF model 3. the artifacts and decontaminated EEG signals are reconstructed through WIENER filtering : .

ŷ (f, n, i, j) = W f j H nj Q ij J j=1 W f j H nj Q ij x (f, n, i) . (4)

EXPERIMENTS AND RESULTS

We now present results on EEG signals corrupted by three kinds of artifacts : ocular, cardiac and motion artifacts. As in our previous study, we aim at proving the efficiency of NMF in removing these artifacts in single channel EEG analysis comparing to 4-channel based ICA source separation since the minimum number of EEG channels that need to be used to handle L sources of artifacts must be L + 1 (one channel per artifact component plus one for EEG useful information).

We are also interested in proving the performance gain of a IS-NTF and ICA approaches analysing conjointly EEG and auxiliary signals.

Simulations

The EEG and artifactual auxiliary signals are simulated from the public DEAP dataset2 , a database for emotion analysis using a wide-range of physiological signals [START_REF] Koelstra | Deap: A database for emotion analysis using physiological signals[END_REF]. The EEG and 13 peripheral physiological signals of 32 participants were recorded at a sampling rate of 512 Hz during the viewing of 40 one-minute long music videos preceded by 3-second baselines. Raw EEG data were recorded with 32 active AgCI electrodes placed according to the international 10-20 system. In order to be able to objectively evaluate our systems we create contaminated EEG signals in a controlled manner in such a way to simulate realistic recordings. Thus, we first extract from the DEAP dataset each type of signal, i.e. EEG and artifacts, each from a different subject, so as to avoid unwanted correlated signals. Then, we process these signals in order to remove artifacts from the EEG recordings and potential cerebral or noisy activities in auxiliary physiological recordings. The raw EEG signals have actually already been preprocessed in the public DEAP dataset (downsampled to 128 Hz) removing in particular ocular and motion artifacts3 [START_REF] De Clercq | Canonical correlation analysis applied to remove muscle artifacts from the electroencephalogram[END_REF][START_REF] Gómez-Herrero | Automatic removal of ocular artifacts in the eeg without a reference eog channel[END_REF]. We further process these signals to correct for other sources of artifacts such as cardiac artifacts or drifts discovered by visual inspection of the ICA component signals obtained using the artifact removal procedure provided by the EEGlab toolbox 4 .

Among the different peripheral nervous system signals (available at a sampling rate of 128 Hz in the DEAP dataset), we choose those recorded by the plethysmograph, the electromyogram of the Zygomaticus muscle and the electroocculogram sensors. The plethysmograph sensor measures indirectly the heart rate through the blood volume variations in the participant's thumb. The electromyogram sensor of the Zygomaticus major monitors the participant laughs or smiles during music listening. The electroocculogram sensor captures eye movements and blinks. We also filter the auxiliary signals with a 3-order Butterworth filter in order to isolate the artifact electrical signature by removing brain signal relative to the artifact. All signals are scaled between -50µV and +50µV .

The simulated contaminated EEG signal is then obtained by applying a mixing matrix to the previous signals. We have decided to simulate four situations corresponding to four EEG sensor locations : temporal (T7 electrode), frontal (Fp2 electrode), occipital (02 electrode) and central (Cz electrode). The impact of each artifact on each EEG channel location are presented in the table below under the form of noise-to-signal ratios, that is the ratio between the amplitudes of the EEG and artifactual signals. Given the length of the signals, we build 10 simulated datasets, each one including the EEG and auxiliary signals of four 63-second long videos.

❳ ❳ ❳ ❳ ❳ ❳ ❳ ❳ ❳ ❳

Validation procedure

As in our previous study [START_REF] Damon | Nonnegative matrix factorization for single-channel EEG artifact rejection[END_REF], multiple EEG channel FastICA and single EEG channel NMF methods integrate prior information on artifacts by initializing a part of the mixture model with the given auxiliary signals to guide the source learning process. For FastICA, this merely consists in initializing each dedicated artifact component of the mixing matrix with the corresponding auxiliary signal and the other components are generated randomly. For NMF, the initialization is done as described in [START_REF] Damon | Nonnegative matrix factorization for single-channel EEG artifact rejection[END_REF].

Single EEG channel FastICA and NTF methods embed additional prior knowledge of the artifacts by jointly processing the EEG and the auxiliary data with a matrix decomposition in the temporal domain for the former and a tensor decomposition in the spectral domain for the latter as described in section 2.2.

The validation procedure includes two steps : a training step during which the hyperparameters of each source separation method are learned on one half of the datasets and a test step during which the best hyperparameter is tested on the other half of the datasets. Ten models (each with 100 multiplicative-update iterations), each of them with a different initialization, have been learned on both EEG-and artifactbased NMF/NTF models and only those yielding the smallest cost-function value have been selected.

While we necessarily estimated only 4 components for ICA, we have been able to test a range of hyperparameters for NMF/NTF by varying the number of components associated to the artifact on the one hand (i.e. 2, 5, 8, 10, 13), and the total number of components on the other hand (i.e. 16, 24, 32, 40, 48) thus defining, by subtraction, the number of EEG sources.

To compare the results of the different methods, we used the correlation similarity measures between each estimated signal and the true signal used to simulate the mixture.

In order to solve the ambiguity in the order of the source signals estimated by FastICA, we rely on the the mutual information similarity measure, which is the assessment measure of the ICA, between each estimated source signal and the different recorded signals (EEG and auxiliary).

Results

In figure 1, we present the results of the four methods on datasets simulated with EEG data coming from three different subjects to study the robustness of our methods.

Multiple EEG channel ICA achieves poor signal recovery except in the frontal location case where the denoised EEG signal is well recovered (see Figure 1(a)). In this situation, the problem is easier since the EEG recordings are mainly disturbed by a single artifact relating to the EMG signal. Single EEG channel NMF significantly outperforms the denoised EEG signals recovery obtained with multiple EEG channel ICA, which is probably induced by a slightly better artifact signal recovery, particularly with respect to the ECG-based artifact (see Figure 1(b)).

The results of single EEG channel ICA (using auxiliary artifact signals) are comparatively good with respect to the previous methods and stable across the different brain locations, around 0.6 correlation for the EOG-and EMG-related artifact estimations and 0.8 for the denoised EEG and ECGbased artifact estimations (see Figure 1(c)). Single EEG channel NTF proves to be the best strategy to recover the denoised EEG signal, with a cross-correlation close to 1, arising from the accurate estimations of the dominating artifactual signals (having an amplitude greater or equal to the EEG source signal amplitude.

For all the methods except single EEG channel ICA, we note that the quality of the artifactual signal recovery depends both on the artifact-to-EEG amplitude ratio and the complexity of the mixture linked to the number and the intensity of the artifacts. For instance, in the temporal case, the three artifacts noticeably impact the cerebral activity while in the central case, only the EMG-based artifact significantly impacts the EEG recordings (see Table 1). The scale invariance property of the Itakura-Saito cost function in NMF/NTF approaches is useful when analyzing signals of different scales, however it is here found to reach its limits as it fails to decompose some of the source signals that are weakly present in the mixture.

All the methods are robust to the inter-subject variance leading to similar results for the three subjects except for EOG-related artifacts and more specifically with the first subject. This inter-subject variability may be explained by inter-subject differences in the ocular artifact processing of EEG recordings performed with a blind automatic EOGrelated artifact rejection method [START_REF] De Clercq | Canonical correlation analysis applied to remove muscle artifacts from the electroencephalogram[END_REF]. This study shows that this blind method is less acurate than an informed method using individual EOG reference signal.

Below, the figure 3.3 provides a visual insight into the signal recovery quality of all the studied informed source separation methods. The resulting signal decompositions on two pieces of a single EEG channel recording located in the temporal cerebral area improve our understanding of the previous numerical results.

The temporal case is particularly relevant to compare the methods since it best represents all the artifacts. The first recording piece is an example of good recovery while the second is a more difficult example.

In the former case, we outline three highlights : first, the estimates of EOG-and ECG-based artifacts become more accurate in the order of appearance of the methods, that is multiple EEG channel ICA, single EEG channel NMF, single EEG channel ICA and single EEG channel NTF. Second, the EMG-related artifact is well recovered by NMF and NTF approaches contrary to ICA methods that completely fail. On the other hand, the NMF and NTF approaches seem to capture a part of the EMG-based artifact in the EOG-based artifact estimate. This is particularly visible at the end of the recording piece. In the latter case, none of the methods manages to recover EMG-and EOG-related artifacts. No signal is captured for the EMG-related artifact whereas false estimates are achieved for the EOG-related artifact. However, the estimates of the ECG-related artifact become more accurate in the order of appearance of the methods.

Finally, we analyze the impact of the hyperparameters, i.e. number of components associated to each source, on the source-estimation accuracy. Figure 3.3 shows the variations of the average cross-correlation measure with respect to the hyperparameters on the training datasets for single EEG channel NTF. For each source, the average cross-correlation measures remains quite steady through the different set of hyperparameters. Trying other sets of hyperparameters around the best learned set with different number of components for each type of artifact does not change the performance.

CONCLUSION

In this study, we have focused on the improvement of artifact rejection in single EEG channel recordings by incorporating the NTF approach has the attractive feature of allowing the use of different types of physical auxiliary signals giving a great flexibility in the kind of prior knowledge to be introduced in the spectral domain. From this point of view, our experimental results on simulated datasets can be seen as a proof of concept.Therefore, future work will consider other kinds of physical auxiliary recordings such as head and body motion through 3D positions and acceleration measures.

Fig. 1 .

 1 Fig. 1. Average cross-correlation measures obtained with the different techniques trough the 10 datasets for each subject and on each brain location. It represents the recovery quality of ocular (in red line), motion (in blue line), cardiac (in black line) artifacts-and denoised EEG based signals respectively noted EOG, EMG, ECG and DEN in the legend.

Fig. 2 .

 2 Fig.2. Signal decomposition on two pieces of a single EEG channel recordings located in the temporal brain area for each separation source method. In order of appearance, the blue signal is the original signal, the red signal is the denoised signal and the last three signals respectively include the EMG, ECG and EOG signal in black dotted line and the estimated artifact signal in red solid line.

Fig. 3 .

 3 Fig. 3. Average cross-correlation measures for a range of hyperparemeters obtained with single EEG channel NTF on temporal training datasets for each source. The hyperparameters are noted as a couple

Table 1 .

 1 Artifact

	Location	Artifacts Ocular Motion Cardiac
	Temporal	1.5	4.5	1.0
	Frontal	3.0	4.0	0.1
	Central	0.1	3.0	0.1
	Occipital	0.1	4.0	0.1

-to-EEG ratio for ocular, motion and cardiac artifacts in four brain locations: left temporal, right frontal, central and right occipital electrodes.

The Itakura-Saito divergence between two nonnegative scalars a and b is defined as d IS (a | b) = a b -log a b -1.

http://www.eecs.qmul.ac.uk/mmv/datasets/deap/

http://kasku.org/projects/eeg/aar.htm

http://sccn.ucsd.edu/eeglab/

* Thanks to the DGA and the DGCIS for funding under the MEEGAPERF project.


Antoine Liutkus
email: antoine.liutkus@telecom-paristech.fr

Pierre Leveau
email: pierre.leveau@audionamix.com

Separation of Music+Effects sound track from several international versions of the same movie

This article concerns the separation of the music+effects (ME) track from a movie sountrack, given the observation of several international versions of the same movie. The approach chosen is strongly inspired from existing stereo audio source separation and especially from spatial filtering algorithms such as DUET that can extract a constant panned source from a mixture very efficiently. The problem is indeed similar for we aim here at separating the ME track, which is the common background of all international versions of the movie soundtrack. The algorithm has been adapted to a number of channels greater than 2. Preprocessing techniques have also been proposed to adapt the algorithm to realistic cases. The performances of the algorithm have been evaluated on realistic and synthetic cases. * Antoine Liutkus performed this study when he was working at Audionamix. one side, and voices on the other side. Creating the version of the content adapted to a language consists in mixing the voices track of the correct language with a generic ME track.

Sometimes, the music and effects track is not available. In that case, releasing a new version of the content in another language is not possible, unless

INTRODUCTION

The movie and broadcast industries are interested in producing content available in as many languages as possible. For that purpose, they generally have at hand separated tracks for music and effects (ME) on this track is recorded another time.

In this paper, a method to extract the ME and voices track using several international versions of the content is proposed. It addresses the case when several localized versions of the content exist with a good quality, while the separated tracks (voices, and music and effects) are not available. For example, given a French, an American and a Japanese version of the mixed content, it enables to extract the music and effects track and the voice track for each version.

Given a localized version, this problem can be restated as a voice extraction problem. This problem has been adressed using a number of approaches, first with sinusoidal model [START_REF] Mcaulay | Speech analysis/Synthesis based on a sinusoidal representation[END_REF] or more recently, using a source-filter model in a Non-Negative Matrix Factorization context [START_REF] Durrieu | Source/filter model for main melody extraction from polyphonic audio signals[END_REF]. Both of these models were extended recently in the source-separation community to allow voice extractions within mixtures. Unfortunately, most of the work achieved in this direction so far relies on parametric models whose optimization requires very heavy computational ressources, which is prohibitive for the desired applications that ought to perform well and rapidly on very limited computing devices.

The method relies on methods inspired from stereo audio source separation, like DUET [START_REF] Yilmaz | Blind separation of speech mixtures via time-frequency masking[END_REF]. In this class of source separation methods, each channel is represented in the time-frequency domain, then each time-frequency point is allocated to a source according to the value of its left and right channel components. In this stereo case, the panpot parameter (angle between 0 and 90 degrees) can be computed from the amplitudes of the time-frequency point on each channel. The time-frequency point is then allocated to the source that has the closest angle. For example, if one wants to extract the signal of the voice in a song, the angle of the source to extract is set to 45 degrees. The voice separation is here equivalent to the extraction of the signal which is common between the two channels.

In our case, the situation is similar: the ME track is a signal which is common between several signals (assumed mono), the international versions. The proposed method extends the principle of the spatial source separation that have more than two channels, and takes into account the sparsity of the voice sig-nals in the time-frequency domain. The use of simple statistical filtering is tried to extract the common signal. To address the realistic cases, track synchronization and filtering are also performed.

In Section 2, the problem of extracting a common ME track from several international version is detailed. Then in Section 3, the algorithm to address this problem is described. Section 4 depicts the results of the algorithm on synthetic and realistic situations.

PROBLEM STATEMENT

Naive modelling

The signals considered are movie soundtracks, that consist in the superposition of a ME track and a voice track. Let us call these signals mixtures and furthermore assume that N international versions of the same movie are available. Let m i (t) be the soundtrack of the international version i. We have :

∀i ∈ [1 : N ], m i (t) = b i (t) + v i (t) (1)
With b i (t) and v i (t) being the ME (background) and voice track respectively for international version i.

The main difference between different international versions of a movie soundtrack is the voice track. If the ME tracks are strictly identical on all versions

(∀i ∈ [1 : N ], b i (t) = b(t)), a first idealized model is: ∀i ∈ [1 : N ], M i (t) = b(t) + v i (t) (2)
This model can be cast into the spectral domain using a Short Time Fourier Transform (STFT) F :

∀i ∈ [1 : N ], F {m i } = F {b} + F {v i } (3)
Still, even if it may be adequate in some cases, experience shows that model ( 2) is very unrealistic most of the time, for two main reasons :

• It is not realistic to consider that the ME signals are exactly synchronized among the localized versions. We have observed delays up to almost half a second in real international versions sold on DVDs on the market.

• The different international versions may come from different mixing processes, possibly even involving different mixing hardware or artistic choices such as dynamics or equalization.

Hence, the naive model ( 2) is most likely to be wrong in real world usecases. However, it will still be useful in this study as an idealized case and most of our effort on real data will be spent processing it so that it may be compatible with the naive model.

A more realistic model

As has been discussed in the previous section, it is not realistic to consider that the several localized versions of a movie share exactly the same ME track. Real international versions are notably not perfectly synchronized and are mixed differently with the voice tracks. Their level and spectral equalizations may vary between the versions. In this study, non linear effects will be put aside and differences between the different ME tracks will be modelled as coming from 1) a temporal delay between the tracks and 2) a different equalization on each of the ME tracks1 .

Hence, the naive model ( 2) is replaced here by :

∀i ∈ [1 : N ], m i (t) = h i * (d τi b) + v i (t) (4)
where h i is a linear filter, * is the convolution operator and d τi denotes a delay operator. The more realistic model (4) thus assumes that there is a single ME track, which is filtered differently for each international version. Furthermore, the different versions are no more assumed to be perfectly synchronized. Note that τ i can be positive or negative.

The ME track of a movie soundtrack may contain highly varying material comprising very different sorts of music, noises, bursts of sounds and complex sound effects. Thus, the a priori information available on the signal b(t) is very weak and the model ( 4) encodes all we can say doubtlessly about it. For convienence, (4) can also be cast into the spectral domain to become :

∀i ∈ [1 : N ], F {m i } n = F {h i }.F {d τi b} n +F {v i (t)} n ( 5
)
Where n is a frame index of the STFT and . denotes element-wise multiplication.

Indeterminacies and equalizing inversion

One can guess here that there are indeterminacies in the equivalent models (4) and [START_REF] Fox | Modeling perceptual similarity of audio signals for blind source separation evaluation[END_REF]. Indeed, let g be an inversible linear filter, then h i * g -1 and g * b instead of h i and b lead to the same model. Likewise, if τ i is replaced by τ iτ 0 and b(t) by b(t + τ 0 ), the same model is found again.

In order to fix these indeterminacies, we can arbitrarily choose one i 0 from [1 : N ] that will be denoted the target version. Then, we will set h i0 to the identity and τ i0 to 0. This way, we will have

m i0 (t) = b(t) + v i0 (t)
This can be interpreted saying that the ME track that will be estimated is the particular version found in mixture i 0 .

An important remark must be made here with respect to the choice of the target version, for an important issue was actually raised choosing i 0 .

When considering old movies or resampled soundtracks, it is possible and was indeed observed in practice that some international versions may be of limited bandwith compared to others even for the same movie. In this situation, it is actually impossible to consider that the ME tracks with the largest bandwith can be obtained from the damaged ones using a linear filter. Indeed, this would involve infinite gains in the frequency domain for the corresponding filters F {h i } which cannot be allowed. Hence, the target version needs to be one with the largest bandwidth. Still, the separation process will imply the inversion of the equalizing filter h i in order to estimate so-called alignment filters h -1 i . This cannot be achieved correctly if some of the filters h i are destructive in the frequency domain as may occur in case of different bandwiths. We will nevertheless consider that all the filters h i are invertible, which basically means that there was no destructive equalization process and that all international versions roughly have the same bandwidth, which may not always be a realistic assumption. Still, we will see in 3.2.2 that the chosen method to estimate filters actually handles this instability issue even when real data does contain damaged mixes.

Sparse voice signals

In [START_REF] Mcaulay | Speech analysis/Synthesis based on a sinusoidal representation[END_REF], we have modelled the mixtures as the sum of two components called respectively the background (ME) and voice tracks. The first one of these components has been modelled in (4) as the filtered and delayed version of a common underlying and unknown signal of interest. It is extremely difficult to make any complementary realistic assumptions about this background signal as it may contain very different sorts of audio material. On the contrary, we will show here that it is possible to highlight important general properties of the additive voice signals v i (t). Indeed, even in realistic usecases, the additive signals mainly consist of voice sounds, whether they be sung or spoken. It would be possible to add strong a priori information on the signals v i (t) using all the litterature concerning models of voice signals (see Section 1), but it is out of the scope of the paper.

The property that will be particularly interesting in the scope of this paper is the generally observed sparsity of the voice signals in the time-frequency domain. Except in the case of whispered or cracky voiced sounds, voice signals can indeed be modelled as the sum of a limited number of sinusoids, typically 50 per time frame or less. In order to test for the empirical validity of assessing spectral sparsity of realistic voice signals, we computed the distribution of the element-wise ratio between ||F {m i }|| and ||F {b i }|| computed on a 30s excerpt of a real movie soundtrack2 . Figure 1 shows the result of this experiment and it can be seen that this distribution is very strongly peaked on 1, indicating that most of the time-frequency bins of the mixture actually correspond to their value in the desired background signal. As can be seen on this The sparsity of the voice track in the time frequency domain induces the sparsity of the voice track activation for a given time-frequency point across the version signals. There is a low probability that a timefrequency point has a voice activity for any version. This property will be used in a method described in Section 2.5.1.

Derived extraction methods

Median filtering

The extraction methods used in this study will mainly involve the naive model ( 2) and (3). There will indeed be a first processing step called alignment that is reviewed in 3.2 and that will allow to transform real data in order for it to be correctly modelled by the naive model. We thus suppose here that the observed (transformed) signals are the superposition of the same desired background signal with different additive voice signals that are sparse in the frequency domain. As mentioned in previous Section, Figure 1 showed that if one considers a random time-frequency bin from the STFT of the mixture, there is a high probability for its value to correspond to the value of the desired background signal at that bin. If this is not the case, there is a low probability that the voice is active on that bin for several versions since the voice signals are strongly independant.

The distribution of the amplitudes of a given timefrequency point among the channels is thus strongly peaky around the background value, with sometimes outliers when the voice is active on that point. To estimate the amplitude of the background from this distribution, the median value of the set is a clever choice because the set size is very small.

As we have seen in 2.2, it is actually very unrealistic to suppose that the different voices of a movie soundtrack are perfectly synchronized (words, pitch contours are different across the languages). The fact that the additive voice signals are far from being perfectly synchronized in real situations makes the independance assumption between them less unrealistic, even if the general acoustic properties of voice signals across the different versions are similar (with respect to the gender of the speaker in particular).

Min filtering

The rationale behind median filtering was explained in the previous section 2.5.1. Another point of view can be adopted. It is rather common in the source separation litterature to consider that the power spectra of the different sources simply add to produce the power density spectrum of the resulting mixture, which is equivalent to consider that the sources are independent. This can be written :

∀i ∈ [1 : N ], ||F {m i }|| 2 = ||F {b}|| 2 + ||F {v i }|| 2 (6)
This assumption amounts to considering that an additive signal can only increase the energy of all frequency bins. Another filtering strategy can very simply be deduced from this expression. Given several observations of some time-frequency bin, the most likely to correspond to the common underlying ME track will necessarily be the one whose energy is smaller according to model 6. This idea leads to estimating the background by simply chosing the observation that has the minimal energy at each timefrequency point. As it simply boils down to neglecting phase effects which is actually a rather coarse assumption, we will see that when N gets large, the ME track estimation performed this way will actually become very poor. This can be interpreted stating that the more different versions there are, the more probable it is that phase has a non negligible role in one of the version for some given time-frequency bin. Still, the min filtering will be actually useful in situations where only a few observations are available. Indeed, the median filtering in this case will lead to the addition of systematic noise in the estimation of every time-frequency bin. We will also see in 4 that it is also very interesting to apply the min filter after having applied the median filter in order to guarantee that the estimated ME track does not have higher energy than the target ME track on any time-frequency bin.

Mean filtering

One may wonder why only median and min operators were considered in the preceding instead of some simple mean between the different observations for every time-frequency bin. As we will see in 4, taking the mean is actually a very bad idea, since the data is intrinsically very likely to contain outliers that can have a strong influence on this estimation. Figure 1 shows that the ME and mixture tracks very often share the same value, it also strongly suggests that when they do not, they actually differ greatly, a property to which the mean would be actually very sensitive to since the sample set is small, contrarily to the median filtering.

ALGORITHM

In section 2 we have stated the main assumptions of the proposed method, namely • The different observed mixtures consist in the sum of a differently-filtered and delayed common underlying signal of interest. This is summed up in model ( 4) as well as in its spectral counterpart (5).

• The additive voice signal can be considered as being sparse in the time-frequency domain.

Both of these assumptions will be used extensively in the following. We will here present a complete extraction system that can very rapidly extract the ME track with decent performance. We will first give an overview of the proposed system and will then linger on the main two problems it has to solve : alignment and statistical filtering.

Overview

The general structure of the proposed separation method is outlined in Figure 2. The extraction procedure involves four important steps that will be reviewed now :

•

Step A : First, some user needs to identify manually some section of the movie soundtrack on which there is no voice and on which there is a significant spectral richness of the ME track. Such a configuration is typically very easily found on the musical parts of a soundtrack. In our experiments, a minute-long excerpt was fine to process one whole movie. It would of course be possible to automatically detect such an excerpt, but we have not lingered on this task here.

• Step B : Given some isolated excerpt on which we know that no voice signal is present, we can estimate the alignment parameters that consist in the inverse filters h -1 i and delays τ i from model (4).

•

Step C : With these alignment parameters, we will be able to easily transform the data so that the naive model ( 2) is adequate. This is explained in section 3.2.

•

Step D : The naive model (2) now being realistic on the transformed data, we will be able to derive a simple statistical filtering scheme (as detailed in 2.5) in order to estimate the desired ME track from the mixtures. This is explained in section 3.3

Alignment

In section 2, we saw that the different available international versions, called mixtures, can be modelled in several ways. The most simple model simply stated in (2) that each mixture m i (t) was the sum of a common background signal of interest, b(t), with a voice signal v i (t). We saw that for several reasons, this model can in no way be called realistic. On the contrary, we derived in (4) and ( 5) another model which accounts for most obvious discrepancies observed between the ME tracks of real international versions of the same movie, namely a time delay and a different equalization. Supposing that we knew all the mixing filters h i , that they were invertible and that we knew all the delays τ i , we would have :

∀i ∈ [1 : N ], h -1 * m i (t + τ i ) = b(t) + h -1 * v i (t + τ i ) (7) Which can be recast in the spectral domain as fol- lows : ∀i ∈ [1 : N ] F {h -1 i }.F {d -τi m i } n = F {b(t)} n +F {h -1 i }.F {d -τi v i } n (8)
These expressions mean that we could process the data so as to be able to consider the naive model ( 2) as valid on this processed data. As we will see in 3.3, the naive model ( 2) along with the sparsity assumption found in 2.4 will allow us to derive very efficient extraction method. This is why estimating the delays and filters will be of special interest to us. We saw in 3.1 that a first step of the system consists in selecting an excerpt of the soundtrack on which there is no voice signals, which can easily be found in practical situations. On such an instrument excerpt T = [t 1 : t 2 ] we have :

∀t ∈ T, ∀i = i 0 , m i (t) = u h i (u)b(t -τ i -u) m i0 (t) = b(t) (9
) We will first review methods to estimate delays in 3.2.1 and then methods to estimate alignment filters h -1 i in 3.2.2.

Temporal alignment

We noted in 2.2 that delays between tracks can actually be quite large and we observed values up to almost half a second in practical situations. As was suggested in 2.3, some mixture may be taken as a reference and if we have identified an instrumental excerpt T on which no additive voice signal is present, relations (9) hold. Let R bb be the autocorrelation of b, i.e :

R bb (τ ) = E t∈T [b(t)b(t + τ )]
Let us furthermore define R i0i as the correlation on T between the target track i 0 and track i, i.e :

R i0i (τ ) = E t∈T [m i0 (t)m i (t + τ )]
We readily see that R i0i can be expressed slightly differently as :

R i0i (τ ) = (h i * R bb ) (τ -τ i ) (10)
Thus, we see that the correlation between the target track and another international version on some instrumental excerpt T corresponds to the delayed convolution of the autocorrelation of b by the equalizing filter h i .

In theory, if the autocorrelation of the background signal on the instrumental excerpt T, R bb , is very peaky (this is the case for wide band signals), i.e R bb (τ ) ≈ δ τ and if the impulse response of the mixing filter h i is centered on zero, the maximum of R i0i will be observed for τ = τ i , which gives a very simple procedure to estimate τ i . Annoying perturbations were nevertheless observed in cases where the mixing filters were complicated and when the autocorrelation R bb of the background signal was very different from the idealized case. Indeed, both of these effects can interact and translate the maximum of R i0i far from the desired delay.

In order to address this issue, different strategies were tried and a practical and efficient solution was found that consists in computing the correlations on the squared signals instead of the raw data. Indeed, the autocorrelation R2 bb of b 2 (t) computed on an instrumental excerpt shows much less perturbations than R bb as can be seen in Figure 3.

It was thus decided to compute the correlations between the squared signals in order to estimate the delays between the different versions. The expression of the correlation of these squared signals is indeed given by :

R2 i0i (τ ) = E t∈T [m 2 i0 (t)m 2 i (t + τ )] (11)
Which is readily shown to be :

Fig. 3: Normal and energy autocorrelations for the ME track computed on a 30s excerpt.

R2 i0i (τ ) = h i . 2 * R2 bb (τ -τ i ) (12)
This expression shows that the correlation between m 2 i0 and m 2 i can also be interpreted as the convolution between a filter and a correlation function. Still, the correlation function R2 bb is much smoother that R bb and h 2 i is centered on nearly the same point as h i anyway.

Figure 4 shows the differences between R i0i and R2 i0i whereas Figure 5 shows the delays computed using these two different methods on a realistic example. We can first see that the correlation function computed on squared signals is indeed much smoother and then that the delays computed this way are much more adequate than those computed using plain correlations functions. Intuitively, this correlation scheme may be far less sensitive to phase shifts and may thus concentrate on energy correlations, which seems to be a good feature for our particular purpose.

Spectral alignment : equalization

When the delays between the different versions have been estimated, we can readily translate accordingly the different versions on the instrumental excerpt so as to obtain :

∀t ∈ T, ∀i ∈ [1 : N ], m i (t + τ i ) = (h i * b) (t)
Which can be cast into the spectral domain using some STFT F on T to get:

F {d -τi m i } n = F {b} n .F {h i } ( 13
)
Where n is a frame number. If we suppose as was suggested in 2.3 that filters h i are invertible, we can write (13) as :

1 F {h i } = F {b} n F {d -τi m i } n
Where a b denotes element-wise division. This is equivalent to :

F {h -1 i } = F {b} n F {d -τi m i } n (14)
Theoretically, this expression allows us to compute F {h -1 i } which can then be injected in (8) in order to be able to consider the naive model (3) as valid on the processed data F {h -1 i }.F {d -τi m i }. Still, in practice we cannot assume that expressions such as (14) are indeed perfectly verified for real data in the sense that the ratio F {b}n F {d -τ i mi}n is never observed as being constant over the frames n, which can be explained stating that real mixing filters h i may be non-linear or even non-invertible. However, we can go on and nevertheless estimate F {h -1 i } from the observation of the different F {b}n F {d -τ i mi}n , i.e one for each frame of the instrumental excerpt. Several estimation schemes were tried, some of which are listed now :

• The first naive idea would be to simply take F {h -1 i } as the expectation of the absolute value of these ratios over n, i.e :

F {h -1 i } = E n [ ||F {b} n || ||F {d -τi m i } n || ] (15)
This strategy was called the non weighted real scheme for the resulting filters are considered to be gains only and because every time-frequency bin is taken into account the same way. An example of filters computed this way is given in Figure 6 upper-left.

• Another strategy was to try to weight the different time-frequency bins according to their value, i.e :

F {h -1 i } = n ||F {b} n ||.||F {d -τi m i } n ||. F {b}n F {d -τ i mi}n n ||F {b} n ||.||F {d -τi m i } n || (16
) This strategy was called the weighted complex scheme because the resulting filters are complex and because every time-frequency bin is taken into account accordingly to its amplitude. An example of filters computed this way is given in Figure 6 upper-right.

• We also tried to weight each time-frequency ratio

||F {b}n||

||F {d -τ i mi}n|| accordingle to the magnitude squared coherence C bm between the two signals b and d -τi m i . This quantity is given as

[C bm ] n = |[P bm ] n | 2 [P bb ] n [P mm ] n
Where [P bb ] n and [P mm ] n are the power spectral densities of b and d -τi m i for frame n respectively and [P bm ] n is the cross power spectral density of these two signals. Inverse filters were then computed by :

F {h -1 i } = n [C bm ] n . F {b}n F {d -τ i mi}n n [C bm ] n (17)
This strategy was called was called the coherence scheme. Examples of filters computed this way can be found in Figure 6 lower-left.

• Finally, a last strategy was to try to use the same idea as in the weighted complex scheme but computing real filters only, i.e :

F {h -1 i } = ... n ||F {b} n ||.||F {d -τi m i } n ||. ||F {b}n|| ||F {d -τ i mi}n|| n ||F {b} n ||.||F {d -τi m i } n ||.
Which can be simplified to :

F {h -1 i } = n ||F {b} n || 2 n ||F {b} n ||.||F {d -τi m i } n ||.
(18) This strategy was called the weighted real scheme because the resulting filters are real and because every time-frequency bin is taken into account accordingly to its amplitude. An example of filters computed this way is given in Figure 6 lower-right.

A first thing to notice here is that weighted schemes (16) and (18) allow to handle the non-stability issues that might occur in (15) and that were raised in 2.3 as caused because of some bins in ||F {d -τi m i } n || that may be very close to zero. Indeed, if such is the case, a weighted scheme will end up not taking such damaged bins into account thus preventing non realistic inverse filters to be estimated. Indeed, it can be seen in 6 that the non weighted (15) and coherence (17) schemes both are very unrealistic as the estimated filters involve amplification gains reaching 80dB, which is totally unacceptable. The weighted complex scheme (16), even if theoretically could estimate a more realistic filter, is actually lost for high frequencies due to phase incoherence between the different versions, that could not properly be modelled as a simple linear effect. On the contrary, the weighted linear scheme (18) seems to produce filters that do not seem to show all these weaknesses and that indeed look very smooth and realistic as to the range of their amplification gains. It was hence decided to proceed to spectral alignment using the weighted real scheme (18).

Alignment results

Figure 7 gives qualitative results of the overall alignment procedure. An instrumental excerpt of 30s was selected from a real movie soundtrack for which N = 5 to be used as the instrumental excerpt T. Then, track 4 was chosen arbitrarily as a target track and the alignment parameters were computed. Delays were estimated using the squared correlation strategy (11) and alignment filters were estimated using the weighted real scheme (18). After this alignment estimation, and for the sake of illustration, another instrumental excerpt T 2 was chosen from the original soundtrack, that is displayed as is in the upper part of Figure 7. Alignment parameters estimated on T were then used to compute the h -1 i * d -τi m i signals on T 2 , and these signals are displayed in the lower part of the Figure .  As can be seen, the dynamics of the different versions look much more similar that before alignment. The proposed system is then able to provide a descent estimation of the alignment parameters τ i and h -1 i for further processing.

Statistical filtering

In the previous section 3.2 about alignment, we saw that we may estimate some alignment parameters, namely delays τ i and alignment filters h -1 i that allow us to consider the naive model 3 to be valid on some

′ i : ∀i ∈ [1 : N ], m ′ i (t) = b i (t) + v ′ i (t)
with :

F {m ′ i } n = F {h -1 i }.F {d -τi m i } n and F {v ′ i } n = F {h -1 i }.F {d -τi v i } n
Thus, the different extraction methods described in 2.5 can be applied on the transformed signals to obtain the desired ME track. Several quantitative results will be given in the following section, but in order to test the exprimental validity of the method quickly, Figure 8 shows the distribution of the ratio between the amplitude of the STFT points of the estimated ME track amplitudes and the amplitude of the STFT points of the target ME track using the median filter described in 2.5.1 on aligned real data. The Figure shows a very pronounced peak on 1, which shows that the estimator is unbiased.

RESULTS

Performance metrics

The metric used to evaluate the source separation is the Source to Distortion Ratio (SDR), defined in the BSS EVAL toolbox [START_REF] Vincent | Performance measurement in blind audio source separation[END_REF]. Among all the measurements proposed in this toolbox, SDR is the most correlated to the human assessment [START_REF] Fox | Modeling perceptual similarity of audio signals for blind source separation evaluation[END_REF].

We recall here the definition of this measurement:

The Signal-to-Distortion Ratio is:

SDR = 10 log 10 ||s target || 2 ||s target -s estimated || 2 (19)
where s target is the target source signal, s estimated is the estimated source signal.

Synthetic experiment

In order to validate the extraction method, a first experiment was conducted in which perfect alignment was simulated. In order to do this, we chose an excerpt of the movie on which no voice signal was present and chose arbitrarily one of the versions that was then simply duplicated. Then, an excerpt of the same length was chosen on which no ME signal was AES 128 th Convention, London, UK, 2010 May 22-25 present. These signals were then mixed together so as to obtain data on which real voice signals from different international versions were separately mixed down on exactly the same ME signal. The naive model ( 2) is thus known to be perfectly appropriate for this synthetic data. Median filtering was then performed along with min filtering between the result of the median filter with one of the mixtures to obtain the estimated ME track. Perceptually, the separation was extremely good. Quantitative results are given in table 1 for 5 different versions and confirm that performance are very good when the naive model is adequate (SDR and SAR around 12dB, SIR around 30dB). The audible noise on some resulting signals are often related to the voice parts that are non sparse, namely the noise present in consonants when they occur simultaneously in the versions.

Realistic experiments

In the following experiments, alignment data was estimated on an excerpt from a movie soundtrack on which no voice signal was present, and the mixtures artificially produced from two excerpts of the same length, the first of which only contains ME signal and the second of which only contains dialogues. We tried to make the mix realistic, in the sense that voice signals were slightly overmixed compared to The extracted ME track did sound much better than with the MEAN filter, even if it was not as good as in the idealized case. Still, the resulting tracks did perceptually sound good nonetheless, and were anyways a good basis for building another international version of the movie using some further audio engineering. In any cases, the resulting estimated ME track did not contain understandable voice signals.

The quantitative results given in tables and show that the extraction method does give very reasonable performance, when considering its extreme efficiency : one whole movie could be processed in less than 15 minutes, which is remarkable considering the computing time of state-of-the-art systems (around 10 times real-time). Performance actually seems quite similar with 3 or 5 international versions. However, experience showed that the more international versions, the better in general.

Performance of the MIN filter

A last experiment was conducted for which only two international versions were provided. As suggested in 2.5.2, the chosen strategy in this case was the MIN filtering whose results are given in table 5. These results are actually quite good and show that the system can already provide some interesting results in cases where only two international version of the movie are available.

CONCLUSION

In this paper, we proposed a method to address the problem of the extraction of a common signal between several tracks, with an application on the extraction of the Music and Effects track from several localized versions. Preprocessing strategies have been proposed to synchronize the localized versions, and to equalize the music and effect tracks. Results have been computed on artificially mixed localized versions when the ME track is known to be exactly the same in the different versions. In this case, the results have a good quality. When the test signals are not aligned nor equalized, the imperfection of the preprocessing step yields lower performances. However, they can be used in most realistic cases, and they use far less processing time than other source separation techniques. The perspective of this work is to investigate multi-resolution analysis to improve the sparseness of the sources to separate. Indeed, using a sparser sound representation improves the source separation performance in this kind of context, as for stereo source separation [START_REF]Sparse decomposition of stereo signals with matching pursuit and application to blind separation of more than two sources from a stereo mixture[END_REF].

  Figure, even if most of the time-frequency bins are the same in both background and mixture signals, differing bins due to the voice signal are extremely different, which is highlighted by the very strong difference between the mean and median values of the ratios. The back and front tails of the distribution represent time-frequency bins where the voice is present.

Fig. 1 :

 1 Fig. 1: Distribution of the ratio between Mixture and ME tracks TF points amplitudes .

Fig. 2 :

 2 Fig. 2: General structure of the proposed separation method.

Fig. 5 :

 5 Fig. 5: Zoom for temporal alignment. Original tracks (above). Alignment with correlation (middle). Alignment with energy correlation (below).

Fig. 4 :

 4 Fig. 4: Two different strategies for temporal alignment. Left : correlation. Right : energy correlation. See text in 3.2.1.

Fig. 6 :Fig. 7 :

 67 Fig. 6: Different spectral alignment designs'.

Fig. 8 :

 8 Fig. 8: Distribution of the ratio between estimated and original ME track with the MEDIAN filter.

Table 1 :

 1 Averaged

	Targetted ME SDR ME (dB)
	1	12.3153
	2	12.2399
	3	11.9619
	4	11.6382
	5	11.9122
		ME Extraction results for an
	idealized test case using the MEDIAN filter for 5
	available international versions. Experimental setup
	detailed in 4.2
	the ME track, in order for them to be very clearly
	understandable on the mixtures.
	4.3.1. Performance of the MEAN filter
	In order to verify what was explained in 2.5.3 con-
	cerning the poor expected performance of the mean
	filter, an experiment was conducted using this filter.
	Performance is shown in Figure 2 and are not good.
	Perceptually, the resulting ME track did sound re-
	ally damaged or blurred compared to the original
	version.
	4.3.2. Performance of the MEDIAN filter
	Performance of the method was of course tested us-

Table 3 :

 3 ME Extraction results for a real world test case using the MEDIAN filter for 5 available international versions. Experimental setup detailed in 4.3.2

	Targetted ME SDR ME (dB)
	1	3.9355
	2	1.5180
	3	2.7493
	4	0.4616
	5	2.1307
	Targetted ME SDR ME (dB)
	1	3.3700
	2	0.9421
	3	3.1034

Table 4 :

 4 ME Extraction results for a real world test case using the MEDIAN filter for 3 available international versions. Experimental setup detailed in 4.3.2

	Targetted ME SDR ME (dB)
	1	2.2242
	2	-0.0801

Table 5 :

 5 ME Extraction results for a real world test case using the MIN filter for 2 available international versions. Experimental setup detailed in 4.3.3

As movie soundtracks are not often hardly compressed, neglecting non-linear effects may not be such an extreme approximation.

In order to build such signals, an excerpt with no voice has been added to an excerpt with voices only to allow both signals b i and v i to be known as well as to consider a realistic situation for experiments.