Frédéric Beau

Paco Bustamante

Bruno Michaud

François Brischoux

Environmental causes and reproductive correlates of mercury contamination in European pond turtles (Emys orbicularis)

Keywords: aquaculture, bioindicator, Emydidae, freshwater, mercury, reproduction, turtles, wetlands

Assessing Hg contamination in aquatic ecosystems is difficult because wetlands are part of large and complex networks, and potential sources of Hg contamination are highly diverse. To investigate environmental determinants of Hg contamination, we studied one of the largest continental French wetlands structured as a dense network of artificial ponds. Such context allows to investigate the influence of pond characteristics on Hg contamination in an area relatively disconnected from direct sources of pollution. We relied on a bioindicator organism, the European pond turtle (Emys orbicularis) to assess Hg contamination in a relatively large number of sites (N>255 turtles from 15 ponds sampled in 2016 and 2017). Non-invasive sampling in the claws of turtles show that Hg concentrations were not related to their sex or size, but we found an effect of age (1.62±0.20 in juveniles and 2.21±0.06 µg.g -1 dw in adults), suggesting that turtles do bioaccumulate Hg through their life. Turtle Hg was different between pond, and we found that pond age and pond usage (draining events linked to pond maintenance) were the main environmental determinants of Hg concentrations in turtles. Finally, and more importantly, our dataset allowed us to highlight potential negative effect of Hg concentration on the proportion of reproductive females, suggesting an influence of Hg on reproductive mechanisms in this species. This result indicates that Hg contamination, even in absence of direct and strong sources of pollution, may have a critical impact on reproduction and thus the persistence of a long-lived vertebrate.

Introduction

Mercury (Hg) is one of the most (in)famous environmental contaminants [START_REF] Wiener | Ecotoxicology of mercury[END_REF]. Through various transport processes, Hg tends to concentrate in aquatic environments, which are considered as sinks of Hg [START_REF] Mason | Mercury biogeochemical cycling in the ocean and policy implications[END_REF]Driscoll et al. 2013). Assessing the sources of Hg contamination in aquatic ecosystems is difficult because wetlands are part of large and complex networks composed of both surface and underground waters. Contaminants can enter aquatic environments through various pathways such as atmospheric deposition, erosion or anthropogenic sources including agricultural drainage, mining, or industrial effluents (Förstner and Wittman;[START_REF] Depew | Toxicity of dietary methylmercury to fish: derivation Förstner U[END_REF][START_REF] Wiener | Ecotoxicology of mercury[END_REF][START_REF] Wang | Sources and remediation for mercury contamination in aquatic systems-a literature review[END_REF]). Cryptic sources can further complicate our understanding of the extent of Hg contamination. For instance, it has recently been shown that fish farming is responsible for the transfer of marine Hg to areas that superficially appear unaffected from other sources of pollution [START_REF] Hansson | Transfer of marine mercury to mountain lakes[END_REF] see also [START_REF] Lemaire | Determinants of mercury contamination in viperine snakes, Natrix maura, in Western Europe[END_REF][START_REF] Guillot | Trace Element Concentrations in European Pond Turtles (Emys orbicularis) from Brenne Natural Park, France[END_REF].

Aquatic environments are important sources of methyl-Hg (MeHg) [START_REF] Ackerman | Avian mercury exposure and toxicological risk across western North America: A synthesis[END_REF]2016;Eagles Smith et al. 2018;[START_REF] Gilmour | Sulfate stimulation of mercury methylation in freshwater sediments[END_REF][START_REF] Hsu-Kim | Mechanisms regulating mercury bioavailability for methylating microorganisms in the aquatic environment: a critical review[END_REF], a form of Hg responsible for toxic effects on humans and wildlife (e.g. [START_REF] Tan | The endocrine effects of mercury in humans and wildlife[END_REF][START_REF] Scheuhammer | Relationships among mercury, selenium, and neurochemical parameters in common loons (Gavia immer) and bald eagles (Haliaeetus leucocephalus)[END_REF][START_REF] Crump | Mercury-induced reproductive impairment in fish[END_REF][START_REF] Green | Mercury contamination in turtles and implications for human health[END_REF][START_REF] Rutkiewicz | Mercury exposure and neurochemical impacts in bald eagles across several Great Lakes states[END_REF][START_REF] Wolfe | Effects of mercury on wildlife: a comprehensive review[END_REF][START_REF] Tartu | To breed or not to breed: endocrine response to mercury contamination by an Arctic seabird[END_REF][START_REF] Schneider | Mercury contamination in reptiles: an emerging problem with consequences for wild life and human health. Mercury: Sources, Applications and Health Impacts[END_REF]. Several processes, relatively specific to wetlands, are known to influence the rates at which inorganic Hg can be biotransformed to MeHg (Eagles Smith et al. 2018;[START_REF] Hsu-Kim | Challenges and opportunities for managing aquatic mercury pollution in altered landscapes[END_REF]. Such factors involve sedimentation and biomethylation by microorganisms, which depends on physical (e.g., anoxia in slow moving water bodies) and biological (e.g., development of periphytic biofilm on algae and macrophytes) processes (see [START_REF] Hsu-Kim | Challenges and opportunities for managing aquatic mercury pollution in altered landscapes[END_REF] for a review, [START_REF] Gochfeld | Cases of mercury exposure, bioavailability, and absorption[END_REF]. Once methylated, Hg becomes readily bioavailable, is bioaccumulated within organisms and biomagnified through the food chain [START_REF] Lavoie | Biomagnification of mercury in aquatic food webs: a worldwide meta-analysis[END_REF]. In turn, these processes can also be influenced by several ecological factors such as primary productivity, habitat structure, bioenergetics, and food web structure (Eagle-Smith et al. 2018).

In complex aquatic networks, monitoring Hg contamination is logistically complicated.

To circumvent these difficulties, the use of biological indicators is often required and allows spatiotemporal biomonitoring of the contaminant. Traditionally, freshwater fish have been intensively investigated for Hg contamination (e.g., [START_REF] Depew | Toxicity of dietary methylmercury to fish: derivation Förstner U[END_REF][START_REF] Åkerblom | Half a century of changing mercury levels in Swedish freshwater fish[END_REF][START_REF] Scheuhammer | Recent progress on our understanding of the biological effects of mercury in fish and wildlife in the Canadian Arctic[END_REF]Eagles-Smith et al., 2016), because fish are widely used as a food source by many human populations [START_REF] Futsaeter | The UNEP global mercury assessment: sources, emissions and transport[END_REF]Dong et al., 2015;[START_REF] Lepak | Assessing potential health risks to fish and humans using mercury concentrations in inland fish from across western Canada and the United States[END_REF]Fliedner et al.;2016). More recently, aquatic reptiles (mainly turtles and snakes) have been shown to be particularly useful to monitor Hg in freshwater habitats [START_REF] Bergeron | Influence of feeding ecology on blood mercury concentrations in four species of turtles[END_REF]Burger et al., 2009;[START_REF] Schneider | Mercury bioacumulation in four tissues of Podocnemis erythrocephala (Podocnemididae: Testudines) as a function of water parameters[END_REF][START_REF] Schneider | Mercury levels in muscle of six species of turtles eaten by people along the Rio Negro of the Amazon basin[END_REF][START_REF] Turnquist | Mercury concentrations in snapping turtles (Chelydra serpentina) correlate with environmental and landscape characteristics[END_REF]Hopkins et al. 2013a;[START_REF] Schneider | Mercury contamination in reptiles: an emerging problem with consequences for wild life and human health. Mercury: Sources, Applications and Health Impacts[END_REF]Eggins et al 2015;[START_REF] Adel | Mercury, lead, and cadmium in tissues of the Caspian Pond Turtle (Mauremys caspica) from the southern basin of Caspian Sea[END_REF]. Because of their relatively limited dispersal capacity and their high degree of philopatry, Hg concentrations found in their tissues should be closely linked to those of their small home-ranges, thereby allowing a spatially explicit sampling. In addition, reptiles are considered as meso-or apex-predators thereby allowing to integrate information from the underlying levels of the trophic web. Contrarily to endothermic vertebrates, their relatively lower metabolic rates and relatively higher tissue conversion rates allow a greater capacity to integrate long-term Hg contamination in their organism [START_REF] Slimani | Large-scale geographic patterns of mercury contamination in Morocco revealed by freshwater turtles[END_REF][START_REF] Lemaire | Determinants of mercury contamination in viperine snakes, Natrix maura, in Western Europe[END_REF]. Finally, recent developments of non-invasive techniques to assess individual Hg contamination allow sampling of relatively large sample sizes while respecting important ethical considerations. For instance, easily accessible tissues such as scales or claws in which Hg bioaccumulates due to its binding to keratins [START_REF] Schneider | Assessment of non-invasive techniques for monitoring mercury concentrations in species of Amazon turtles[END_REF][START_REF] Bezerra | Monitoring mercury in green sea turtles using keratinized carapace fragments (scutes)[END_REF][START_REF] Hopkins | Non-destructive techniques for biomonitoring of spatial, temporal, and demographic patterns of mercury bioaccumulation and maternal transfer in turtles[END_REF]) allow the use of such a non-invasive technique to quantify Hg contamination in these models (Hopkins et al. 2013a;[START_REF] Lemaire | Determinants of mercury contamination in viperine snakes, Natrix maura, in Western Europe[END_REF][START_REF] Slimani | Large-scale geographic patterns of mercury contamination in Morocco revealed by freshwater turtles[END_REF].

Using the European pond turtle Emys orbicularis as a bioindicator of Hg, we took advantage of a natural, semi-experimental context in one of the largest continental French wetlands: the Brenne region. In this area, each pond harbours a faithful turtle population and is characterized by a suite of features (age, size, usage;[START_REF] Beau | Tendance démographique, fécondité et état sanitaire des populations de Cistudes de la Réserve Naturelle Nationale de Chérine et des propriétés conventionnées. Bilan[END_REF]. Based on a relatively large sample size (255 turtles from 15 ponds), the goals of our study were three-fold. First, we investigated the individual determinants of Hg concentrations (i.e., sex, age and body size). Second, we aimed at assessing the environmental determinants of Hg contamination based on each site's unique combination of physical features (i.e., age of the pond, its size and usage). Finally, we investigated the potential deleterious consequences of such contamination in our study species by examining relationships between Hg concentration and body-condition and reproduction.

Material and methods

Study species and study sites

The European pond turtle Emys orbicularis is a small European freshwater turtle species. Our study took place in 2016 and 2017 in the Brenne Natural Park (hereafter "Brenne").

Brenne spreads over 1700 km² and is characterized by a matrix of ~4000 large artificial ponds created since the Middle-Age in order to raise fish [START_REF] Beau | Tendance démographique, fécondité et état sanitaire des populations de Cistudes de la Réserve Naturelle Nationale de Chérine et des propriétés conventionnées. Bilan[END_REF].

Sampling (see below) took place on 15 ponds, mainly located in the vicinity of the Réserve Naturelle Nationale de Chérine (46°47′25.23″N, 1°12′3.54″E, Figure 1). Sites were sampled either in 2016 (May to September, N=9 sites and N=148 turtles) or in 2017 (April to June, N=6 sites and N=107 turtles). Because each pond is characterized by a unique suite of features, those were assessed as follow. We measured the size of each pond (ha) using QGIS (QGIS Development Team (2017). QGIS Geographic

Information

System. Open Source Geospatial Foundation Project.

http://qgis.osgeo.org). We recorded the age of each pond from local archives (Benarrous, 2007). Because local usage is characterized by a full draining of each pond during a whole year (for pond maintenance) at a variable frequency (typically once every 7-25 years), the elapsed time since the last draining event was also recorded (hereafter latency since last draining "LSLD"). Finally, we created two categories of local management: ponds located in protected areas (or managed by the Natural Reserve staff) were classified as "reserves", while ponds not submitted to any regulations were classified as "not protected". The combination of this detailed information for various sites distributed across a relatively similar environmental context and over a relatively small spatial scale represents a powerful opportunity to investigate of the environmental determinants of Hg contamination in a typical continental wetland.

Field procedures and sampling

Turtles were captured with baited funnel traps from April to July usually during three 4 days-long capture sessions per site. Funnel traps were visited every day in order to avoid long-term disturbance for captured individuals.

Upon capture, each turtle was individually and permanently marked with notches in the marginal dorsal and ventral scutes. The straight carapace length (SCL) was measured with a calliper (±0.01mm) and body mass was measured with a digital scale (±1g).

Most individuals were sexed based on the morphology of the plastron (concave in males, [START_REF] Zuffi | Sexual dimorphism of the European pond terrapin, Emys orbicularis (L., 1758) from Italy[END_REF]. Sexing was not possible in a few juvenile individuals and these individuals were kept as "unsexed" in our analyses. Individuals were classified as juveniles when a large growth ring was visible on the ventral scutes, while individuals lacking this growth mark were classified as adults [START_REF] Olivier | Ecologie, traits d'histoire de vie et conservation d'une population de cistude d'Europe, Emys orbicularis, en Camargue[END_REF]. Gravidity of adult females was systematically assessed using manual pelvic palpation (Duguy & Baron 1998;[START_REF] Olivier | Ecologie, traits d'histoire de vie et conservation d'une population de cistude d'Europe, Emys orbicularis, en Camargue[END_REF].

Finally, the distal extremities of 2 claws from each leg per individual were collected with a nail clipper for further Hg measurements. Such non-invasive technique has been successfully used in several freshwater species (e.g., Hopkins et al. 2013a;[START_REF] Slimani | Large-scale geographic patterns of mercury contamination in Morocco revealed by freshwater turtles[END_REF]) and validated in Emys orbicularis from the Brenne area [START_REF] Guillot | Trace Element Concentrations in European Pond Turtles (Emys orbicularis) from Brenne Natural Park, France[END_REF].

Importantly, each turtle is relatively faithful to its home-pond [START_REF] Owen-Jones | La Cistude d'Europe (Emys orbicularis) en Brenne : démographie, Reproduction, déplacements et impacts des pratiques piscicoles[END_REF] thereby allowing for a precise determination of the Hg contamination level for each site.

When possible, we aimed at collecting claws from 10 males and 10 females per site.

Overall, we collected claw samples from 255 individuals (232 adults and 23 juveniles), representing 126 females, 122 males and 7 unsexed individuals.

Each individual was released at the location of capture, usually within an hour after capture.

Mercury analysis

Prior to chemical analysis, claws were cleaned three times with a mixture of 2:1 chloroform/methanol solution in an ultrasonic cleaner and rinsed in milli-Q quality water, and dried for 48 h [START_REF] Guillot | Trace Element Concentrations in European Pond Turtles (Emys orbicularis) from Brenne Natural Park, France[END_REF]. Total Hg concentrations were measured using and atomic absorption spectrophotometer (Advanced Mercury Analyser-254, Altec) on dried tissue aliquots (ranging from 0.5 to 3 mg) as described by [START_REF] Chouvelon | Hg concentrations and related risk assessment in coral reef crustaceans, molluscs and fish from New Caledonia[END_REF]. The analytical quality (i.e. accuracy and reproducibility) of the Hg measurements was assessed by the analyses of blanks and certified reference material (CRM) TORT-2 Lobster Hepatopancreas (NRC, Canada; certified Hg concentration: 0.27 ± 0.06 µg.g -1 dw). The CRM were analysed at the beginning and at the end of the analytical cycle, and by running controls for every 10 samples [START_REF] Bustamante | Total and organic Hg concentrations in cephalopods from the North East Atlantic waters: influence of geographical origin and feeding ecology[END_REF]. Mass of the CRM was adjusted to represent an amount of Hg similar to that in turtle samples. Our measured values for the CRM were 0.255 ± 0.014 µg.g -1 dw (N = 38) showing a recovery of 94%. Blanks were analysed at the beginning of each set of samples and the quantification limit of the method was 0.05 ng. Data for Hg concentrations are presented as µg.g -1 relative to the dry weight (dw).

Statistical analyses

We used general linear models to investigate individual determinants of Hg concentration, with Hg concentration as the dependent variable and individual characteristics as the factors (sex [unsexed, female, male], age class [juvenile, adult] and size [SCL]).

We also used general linear models to investigate environmental determinants of Hg concentration, with Hg concentration as the dependent variable, and pond characteristics as the factors (pond size, pond age, LSLD, and management category).

To explore the potential correlates of Hg concentration, we relied on two proxies of turtle state. First, we computed a body-condition index (calculated as the residuals of the regression of log-transformed body mass against SCL) separately for males and females. The relationship between body-condition index and Hg concentration assessed with linear regressions.

Second, for each site, we assessed the proportion of gravid females. It was calculated as the number of gravid females divided by the total number of females restricted to those captured during the reproductive period solely (defined as period between the date of capture of the first gravid females and the date of capture of the last gravid female). Gravidity can be influenced by environmental conditions (e.g., temperature, precipitation, food availability). Indeed, both years show strong variation of the proportion of gravid females (i.e., 0%-18% for the sites sampled in 2016 versus 0%-53% for the sites sampled in 2017, see results). As a consequence, both years were analyzed separately. Because there was only one value per site (and per year) for the proportion of gravid females (see above for our calculations of this proportion), relationships between this metric and mean Hg concentration (restricted to adult females with SCL > 133 mm)) were assessed with Spearman rank correlations.

Importantly, both estimates should be relatively independent as the proportion of gravid females was calculated for each site's captured individuals (i.e., including individuals not sampled for Hg) while the mean Hg concentration for adult females was calculated on a sub-sample of the captured population.

All analyses were performed with Statistica 12.

Results

Mean Hg concentrations (±SD) for each site and sex are presented in Table 1.

Hg concentration was not linked to turtle size (F1,250=2.35, p=0.13) nor to turtle sex (F2,250=1.79, p=0.17) but was influenced by turtle age classes (F1,250=10.10, p=0.001)

with juveniles having lower Hg concentration than adults (mean Hg 1.62±0.20 for juveniles and 2.21±0.06 µg.g -1 dw for adults, Figure 2).

Hg concentrations diverged strongly between sites (F14,240=7.27, p<0.0001; range 1.44±0.18 -3.17±0.25 µg.g -1 dw, Table 1). Hg concentration was not linked to management category (F1,127=0.02, p=0.87) or pond size (F1,127=0.06, p=0.81) but it was positively related to pond age (F1,127=7.17, p=0.008) and negatively related to LSLD (F1,127=4.43, p=0.03, Figure 3).

We did not find a significant influence of Hg concentrations on the body condition of males (F1,117=1.31, p=0.25) or females (F1,123=0.007, p=0.93). Similar results were found when the analyses were restricted to adult individuals (all p>0.32).

We found significant negative relationships between the proportion of gravid female per pond and the Hg concentrations of adult females for both 2016 (Spearman rank correlation, rs=-0.50, p<0.0001, Figure 4) and 2017 (Spearman rank correlation, rs=-0.39, p=0.004, Figure 4.).

Discussion

Overall, the results we found on the individual determinants of Hg concentrations in E.

orbicularis support the use of freshwater turtles as bioindicators of environmental contamination, as already demonstrated in other studies [START_REF] Bergeron | Influence of feeding ecology on blood mercury concentrations in four species of turtles[END_REF][START_REF] Burger | Arsenic, cadmium, chromium, lead, mercury, and selenium levels in blood of four species of turtles from the Amazon in Brazil[END_REF][START_REF] Schneider | Mercury bioacumulation in four tissues of Podocnemis erythrocephala (Podocnemididae: Testudines) as a function of water parameters[END_REF][START_REF] Schneider | Mercury levels in muscle of six species of turtles eaten by people along the Rio Negro of the Amazon basin[END_REF][START_REF] Turnquist | Mercury concentrations in snapping turtles (Chelydra serpentina) correlate with environmental and landscape characteristics[END_REF][START_REF] Hopkins | Mercury exposure is associated with negative effects on turtle reproduction[END_REF][START_REF] Slimani | Large-scale geographic patterns of mercury contamination in Morocco revealed by freshwater turtles[END_REF]. Importantly, the semi-experimental context of our field sites allowed to highlight several environmental variables (other than direct anthropogenic contamination) that appear to influence Hg bioavailability to turtles.

Finally, the concentrations of Hg we found in E. orbicularis from our study site appear related to their propensity to reproduce and thus may bear consequences for the persistence of this population. All of these findings are discussed sequentially below.

Individual determinants of Hg concentrations

The usefulness of freshwater turtles as bioindicators of Hg contamination has already been demonstrated in this species [START_REF] Guillot | Trace Element Concentrations in European Pond Turtles (Emys orbicularis) from Brenne Natural Park, France[END_REF]) and others [START_REF] Bergeron | Influence of feeding ecology on blood mercury concentrations in four species of turtles[END_REF][START_REF] Burger | Arsenic, cadmium, chromium, lead, mercury, and selenium levels in blood of four species of turtles from the Amazon in Brazil[END_REF][START_REF] Schneider | Mercury bioacumulation in four tissues of Podocnemis erythrocephala (Podocnemididae: Testudines) as a function of water parameters[END_REF][START_REF] Schneider | Mercury levels in muscle of six species of turtles eaten by people along the Rio Negro of the Amazon basin[END_REF][START_REF] Turnquist | Mercury concentrations in snapping turtles (Chelydra serpentina) correlate with environmental and landscape characteristics[END_REF][START_REF] Hopkins | Mercury exposure is associated with negative effects on turtle reproduction[END_REF][START_REF] Slimani | Large-scale geographic patterns of mercury contamination in Morocco revealed by freshwater turtles[END_REF]. Consistent with these studies, our investigations also indicate that analysis of the claws of E. orbicularis is a useful noninvasive technique to monitor Hg contamination in a large number of individuals. We found that juvenile individuals had lower Hg concentrations in their claws than older adult turtles indicating that Hg bioaccumulates during the life of E. orbicularis [START_REF] Guillot | Trace Element Concentrations in European Pond Turtles (Emys orbicularis) from Brenne Natural Park, France[END_REF]. Despite this difference between age classes (juveniles versus adults), we did not find any relationship between turtle size and Hg concentration, while such correlation has been previously recorded [START_REF] Guillot | Trace Element Concentrations in European Pond Turtles (Emys orbicularis) from Brenne Natural Park, France[END_REF]Hopkins et al, 2013a).

We suggest two complementary, non-mutually exclusive hypotheses to explain this result. First, the range of size available in our study is restricted to relatively large individuals (e.g. all SCL> 96.5 mm corresponding to large juveniles and adults), while a previous study included neonates and very small individuals (see [START_REF] Guillot | Trace Element Concentrations in European Pond Turtles (Emys orbicularis) from Brenne Natural Park, France[END_REF] As already suggested for this species [START_REF] Guillot | Trace Element Concentrations in European Pond Turtles (Emys orbicularis) from Brenne Natural Park, France[END_REF], and for other freshwater turtles (Adel et al. 2005;[START_REF] Bergeron | Influence of feeding ecology on blood mercury concentrations in four species of turtles[END_REF][START_REF] Schneider | Mercury bioacumulation in four tissues of Podocnemis erythrocephala (Podocnemididae: Testudines) as a function of water parameters[END_REF][START_REF] Turnquist | Mercury concentrations in snapping turtles (Chelydra serpentina) correlate with environmental and landscape characteristics[END_REF]Hopkins et al. 2013a;[START_REF] Slimani | Large-scale geographic patterns of mercury contamination in Morocco revealed by freshwater turtles[END_REF]) sex did not influence Hg concentrations. This suggests that feeding, metabolism and/or growth rates are presumably fairly similar for both sexes [START_REF] Allender | Select metal and metalloid surveillance of free-ranging Eastern box turtles from Illinois and Tennessee (Terrapene carolina carolina)[END_REF]Yu et al. 2011), contrarily to what has been found in another species of freshwater turtle [START_REF] Nagle | Accumulation and selective maternal transfer of contaminants in the turtle Trachemys scripta associated with coal ash deposition[END_REF]) and in seaturtles [START_REF] Guirlet | Maternal transfer of trace elements in leatherback turtles (Dermochelys coriacea) of French Guiana[END_REF]. In addition, this further suggests that reproduction (egg production and laying) does not represent a major excretion pathway in female E. orbicularis (but see [START_REF] Burger | Trace Elements in Egg Contents and Egg Shells of Slider Turtles (Trachemys scripta) from the Savannah River Site Arch[END_REF][START_REF] Hopkins | Mercury exposure is associated with negative effects on turtle reproduction[END_REF]). Yet, mechanisms through which female E. orbicularis would limit Hg deposition in their eggs remain puzzling, and future studies should usefully investigate this question.

Environmental determinants of Hg concentrations

Our study highlights the role of several environmental factors affecting the concentrations of Hg in the claws of E. orbicularis. Importantly, these determinants are not related to direct sources of pollution due to anthropogenic activities (e.g., industrial effluents, [START_REF] Wang | Sources and remediation for mercury contamination in aquatic systems-a literature review[END_REF]), but instead indicate subtler sources of Hg bioavailability in the wild (Driscoll et al. 2013). First, the management category of each pond does not seem to significantly influence Hg concentrations in turtles. This suggests that, in Brenne, intensive fish farming (in unprotected ponds) may not be responsible for the transfer of marine mercury through fish food as shown in trout farming systems [START_REF] Hansson | Transfer of marine mercury to mountain lakes[END_REF][START_REF] Lemaire | Determinants of mercury contamination in viperine snakes, Natrix maura, in Western Europe[END_REF]. Indeed, in our study area, fish farming is mainly dedicated to omnivorous species (i.e., carps) for which food supplementation is represented by corn, rather than commercial pellets based on proteins from fishery products of marine origin [START_REF] Hansson | Transfer of marine mercury to mountain lakes[END_REF]. Second, our results show that E.

orbicularis inhabiting older ponds display relatively higher Hg concentrations. This result suggests that Hg concentrations, and thus its bioavailability, increase with the age of the water body. Because natural sources of Hg include both hydrologic and atmospheric deposition (e.g., [START_REF] Mason | Mercury biogeochemical cycling in the ocean and policy implications[END_REF], older water body have been subjected to these natural processes for a longer time period, and may thus display naturally higher Hg concentrations (Eagles-Smith et al. 2018). Although it may be complicated to assess such parameter in other geographic areas, we believe that this natural source of variation of Hg concentration is a major issue to take into account.

Finally, we found an influence of the latency since the last draining event of the ponds on the Hg concentrations of E. orbicularis. Periodic year-long draining of each pond has been ancestrally used in Brenne to maintain pond and associated structures (e.g., pond drain). During such a year-long draining event, the organic matter contained in the mud is mineralized. As a consequence, the years following such draining episode are usually characterised by a significant bloom of aquatic vegetation both in terms of density and species richness [START_REF] Richier | Connaissances des facteurs influençant la biodiversité des étangs piscicoles : quelques principes de gestion issus des travaux de l'ONCFS[END_REF]. Such process can influence Hg bioavailability (i.e., the methylation of inorganic Hg) by promoting growth of bacterial biofilm on algae and macrophytes all of which play a role in Hg methylation and thus in the increase of its bioavailability [START_REF] Gentès | Incidence of invasive macrophytes on methylmercury budget in temperate lakes: Central role of bacterial periphytic communities[END_REF][START_REF] Gentès | Bacterial periphytic communities related to mercury methylation within aquatic plant roots from a temperate freshwater lake (South-Western France)[END_REF].

Furthermore, the macrophytic rhizosphere is involved in Hg methylation, and may therefore increase Hg bioavailability to local fauna [START_REF] Gentès | Incidence of invasive macrophytes on methylmercury budget in temperate lakes: Central role of bacterial periphytic communities[END_REF]). Such process is likely to explain the negative and significant relationship we found between the latency since the last draining event and the Hg concentration in E. orbicularis.

Although draining events are no doubt favourable to promote aquatic vegetation blooming [START_REF] Richier | Connaissances des facteurs influençant la biodiversité des étangs piscicoles : quelques principes de gestion issus des travaux de l'ONCFS[END_REF], our results suggest that if they are too frequent, they may provoke an increase of Hg bioavailability. Future management policies should take this result into account, and should aim at a finely tuned balance between the required periodical blooms of aquatic vegetation and the associated increased bioavailability of Hg.

Reproductive correlates of Hg concentrations

Finally, our study allowed to highlight potential negative effects of Hg concentrations on the reproduction in E. orbicularis. Specifically, we found negative relationships between mean Hg concentrations of adult females and the proportion of reproductive females for a given site. Importantly, this negative trend was repeatedly detectable during the two consecutive years of our study. Although Hg has been shown to negatively influence hatching success in another species of freshwater turtle [START_REF] Hopkins | Mercury exposure is associated with negative effects on turtle reproduction[END_REF], to our knowledge our study is the first to document a negative relationship between Hg concentrations and the propensity of adult females to reproduce. Such negative relationship may be attributable to endocrine disruptive properties of Hg.

Indeed, Hg has been shown to affect thyroid hormones in freshwater turtles [START_REF] Meyer | Mercury exposure associated with altered plasma thyroid hormones in the declining western pond turtle (Emys marmorata) from California mountain streams[END_REF]. Our results on body condition (i.e. no effect of Hg on turtles' body condition)

do not support an influence of Hg on feeding, growth or indeed, metabolism. Our results rather suggest an influence of Hg on reproductive mechanisms. For instance, Hg and especially MeHg is known to disrupt reproductive hormones [START_REF] Frederick | Altered pairing behaviour and reproductive success in white ibises exposed to environmentally relevant concentrations of methylmercury[END_REF][START_REF] Tan | The endocrine effects of mercury in humans and wildlife[END_REF][START_REF] Zhu | The endocrine disruptive effects of mercury[END_REF] and have been shown to influence reproductive probability in other long-lived vertebrates [START_REF] Tartu | To breed or not to breed: endocrine response to mercury contamination by an Arctic seabird[END_REF][START_REF] Goutte | Demographic consequences of heavy metals and persistent organic pollutants in a vulnerable long-lived bird, the wandering albatross[END_REF]. Our dataset does not allow teasing apart causation and our conclusion needs to be taken with caution. Despite the lack of evidences of direct causation, Hg concentrations found in E. orbicularis (up to 7 µg.g -1 dw) are coherent with those known to provoke reproductive failure in other study systems (e.g., 1 µg.g -1 in blood and from 2.4 to 40 µg.g -1 in feathers in birds for instance, Burger andGochfeld 1997, Evers et al. 2008), suggesting the relationships we found may not be trivial for E. orbicularis.

Figure 1 .

 1 Figure 1. Map of the study sites and general situation of the Brenne area in France.

Figure 2 .Figure 3 .Figure 4 .

 234 Figure 2. Relationship between turtle straight shell length (SCL) and Hg concentration

  .

	Such restricted range of size inevitably obscured any relationship between Hg
	concentration and turtle size. Second, E. orbicularis has a relatively determinate
	growth. Indeed, although young adults can continue to grow, most older individuals
	have nearly ceased growing. As a result, individuals having a similar SCL can differ in

age (i.e., mixing young and very old adults). Because Hg bioaccumulates with age, individuals having a similar size can display highly different Hg concentrations. Again, such phenomena would obscure any relationship between Hg concentrations and size among adult individuals. Future studies should investigate such hypotheses, notably by sampling individuals of known age from long-term mark-recapture studies.

Table 1 .

 1 Future studies should investigate reproductive hormone levels and Hg concentrations in female E. orbicularis in order to test for this hypothesis. Interestingly, although the Brenne population of E. orbicularis is thought to be one of the largest in France, the Jim, R. C., Hatley, E. L., Backus, A. S., Shine, J. P., Spengler, J. D., & Schaider, L. A.(2015). A longitudinal study of mercury exposure associated with consumption of freshwater fish from a reservoir in rural south central USA. Summary of the characteristics of the study sites (15 ponds) and associated sampled turtles. "Number" refers to the number displayed in Fig.1. "Management" indicates management type (R: reserves, NP: not-protected). "Age" indicates the age of the pond in years. "LSLD" stands for "latency since last draining" in years. "Sex" indicates the sex of the sampled turtles (U: unsexed individuals, F: females, M: males). "SCL" stands for straight shell length (mean ±SD, mm). Hg levels are given as the mean ± SD (μg.g -1 dw). See text for details.

	proportion of neonates is among the lowest (Beau 2015). Clearly the negative
	relationship between Hg concentrations and the proportion of reproductive female we
	detected suggest that Hg contamination, even in absence of direct and strong sources
	of pollution, may have a critical impact on reproduction and thus the persistence of
	population in a long-lived vertebrate.

Eagles-Smith, C. A., Ackerman, J. T., Willacker, J. J., Tate, M. T., Lutz, M. A., Fleck, J. A., Stewart, A.R.,

Wiener, J.G., Evers, D.C., Lepak, J.M., Davis, J.A., Pritz, C.F., (2016)

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Spatial and temporal patterns of mercury concentrations in freshwater fish across the Western United States and Canada. Science of the Total Environment, 568, 1171-1184. Eagles-Smith, C. A., Silbergeld, E. K., Basu, N., Bustamante, P., Diaz-Barriga, F., Hopkins, W. A., Kidd KA & Nyland, J. F. (2018). Modulators of mercury risk to wildlife and humans in the context of rapid global change. Ambio, 47(2), 170-197.

Eggins, S.,

Schneider, L., Krikowa, F., Vogt, R. C., Silveira, R. D., & Maher, W. (2015)

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(2016)

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Acknowledgments

We thank all the volunteers and the staff from the Réserve Naturelle Nationale de Chérine for their help during field work and especially J. Lemaire and J. Morgnieux.

We thank M. Brault-Favrou and C. Churlaud from the plateforme Analyses Elementaires of the laboratory LIENSs for their assistance in mercury analyses. The drawing for the graphical abstract was made by F. Desbordes. The CPER (Contrat de Projet Etat-Région) and the FEDER (European Regional Development Fund) are acknowledged for funding the AMA. Funding was provided by the CNRS, the Agence de l'Eau Loire-Bretagne, the WWF (World Wide Fund) and the Réserve Naturelle Nationale de Chérine. The IUF (Institut Universitaire de France) is also acknowledged for its support to PB as a Senior Member.


by the same LED with and without SL is roughly the same than before irradiation.

While Fig. 5 A#2 is a direct emitting AlInGaP LED, Fig. 5 A#3 LED is a 450 nm emitting InGaN device, which Fig. 5. Amber LED A#1-3 normalized spectral output powers at different doses. The normalization consists in dividing by the maximum value of the before radiation spectrum. Fig. 6. Flux ratio between the same LED with and without an SL before and after irradiations for W#5. employs a phosphor-conversion layer to convert its 450 nm emission into an "amber" spectrum around 600 nm. Our results show that Fig. 5 A#3 is less degraded (-5.34%) in the range of dose investigated than Fig. 5 A#1 (-39.12%) and Fig. 5 A#2 (-59.29%). This agrees with [19] that concluded that (In,Ga)N-based materials and devices are more radiation resistant than those exploiting (Al,Ga,In)P materials.

Different behaviors are observed for the white LEDs. Fig. 4 W#1 is almost unaffected by radiations (-4.5% after 1.1 MGy). Fig. 4 W#3 exhibits a decrease of its emission, both in the blue part of the spectrum and in the phosphorconverted region. Last case Fig. 4 W#5 shows a decrease only in the converted part of the spectrum, suggesting a degradation of the phosphor conversion. Interestingly, the most radiation tolerant device Fig. 4 W#1 is a high-power device, while all the others are mid-power LEDs. However, in the absence of more details from LED manufacturers, it is difficult to analysis in detail this discrepancy. LEDs W#3, A#1, A#2 (Figs. 3 and4), either amber or white, also present a minor increase (+20% at best) of their emitted powers at the first dose level (0.1 MGy). To the best of our knowledge, this phenomenon has never been observed by other authors, either with gamma or other type of radiations and its origin deserves further experiments.

InGaN blue emitting LEDs are known to be affected by the phenomena of "efficiency droop," i.e., a decrease of quantum

B. Results on Bulk Glasses

Fig. 9 illustrates the RIA spectral dependences at the various doses for BK7, SF6G05, BK7G18, K5G20, and SUPRASIL glass, respectively. The RIA above 500 nm remains limited for SCHOTT Ltd RH glasses (Fig. 9(b)-(d)) and very low for the pure silica glass (Fig. 9(e)), whereas it is larger for BK7. To better highlight the good resistance of these glasses in terms of permanent damages at RT, we compared RIA of SF6G05 and K5G20 glasses to their non-RH counterparts (SF6 and K5), in Fig. 10, exposed to low-radiation doses of a few kGy [12].

Fig. 10 shows that the Ce doping is efficient to decrease for all these glasses even if it seems less efficient to improve the SF6G05 glass under 500 nm. For a monochromatic system operating around 600 nm, the RIA should be acceptable for the various OS designs, whereas for color systems, a more in-depth study has to be conducted to see how radiations will affect the colorimetry of the recorded images, especially at lower wavelengths where the photometry budget possesses the smallest margins and the radiation effects are the larger.

We measured also the RIRIC after the second (up to 0.4 MGy) and the third (up to 1.1 MGy) irradiation run. Obtained results are given in Fig. 11(a)-(c) for the two RH glasses exhibiting RIRIC higher than 2 × 10 -4 . For the SUPRASIL glass, the RIRIC is larger than 5 × 10 -4 .

We selected our wavelengths to be able to calculate the Abbe number that is a measure of the refractive index variation versus wavelength and use it for future simulations. For the BK7 there is nearly no more RIRIC increase after a total dose between 0.4 and 1.1 MGy, as observed for the RIA that tends to saturation at larger doses [START_REF] Meeten | Refractive index errors in the critical-angle and the Brewster-angle methods applied to absorbing and heterogeneous materials[END_REF]. For K5G20, the RIRIC modification between 0.4 and 1.1 MGy appears more important. For the SUPRASIL with really a low RIA, this modification of the refractive index may rather be attributed to a slight modification of the glass density rather than to absorption. RIRIC is usually considered as the result of two modifications: density change [START_REF] Poumellec | The UV-induced refractive index grating in Ge:SiO 2 preforms: Additional CW experiments and the macroscopic origin of the change in index[END_REF] and RIA [15] (through Kramer-Krönig relation). These two modifications are linked and there are no consensus about the leading one in our dose range, in both cases refractive-index modification may be positive or negative [START_REF] Ruller | The effect of gamma-irradiation on the density of various types of silica[END_REF] and [START_REF] Bishay | Radiation induced color centers in multicomponent glasses[END_REF]. To be able to give a full understanding of the RIRIC, it will be necessary to measure the density change and the RIA in the UV part of the spectrum with a great accuracy. For the cerium-doped glasses such measurement is prevented by the cerium-induced attenuation below 500 nm and for the BK7 case, the numerous impurity prevents also this measurement. Gusarov et al. [15] attribute the existence of a positive variation of refractive index to a side effect of Ce. Average composition of BK7 and other none pure silica glasses are globally known [27]- [30] but remains quite complex to allow an easy identification of the point defects responsible for the RIA and RIRIC. In term of OS design, the RIRIC effects have to be considered. To make the OS tolerant by design, it is possible to use the simulation tools [START_REF] Muller | Extrapolated degradation of optical systems at MGy levels due to radiation-induced refractive index change[END_REF] to design an OS architecture more robust against RIRIC of its lenses. Glass with a high RIA could not be used in an radiation tolerant OS but for low RIA glasses with known RIRIC values before starting the conception phase it will be possible to enhance the design quality, even maybe compensate the RIRIC of the lenses made with different materials.

C. Results on the Illumination System

The whole photometry budget for the camera has been done again after irradiation by including in our calculations,

Fig. 4 .

 4 Fig. 4. White LED W#1-6 normalized spectral output powers at different doses. The normalization consists in dividing by the maximum value of the before radiation spectrum.

Fig. 10 .

 10 Fig. 10. Comparison between RIA of non-RH glass and there RH version. (a) SF6 and SF6G05. (b) K5 and K5G20. For SF6 and K5 RIA were calculated from [12].

Fig. 11 .

 11 Fig. 11. RIRIC spectral dependence at the various doses. (a) BK7, (b) K5G20, and (c) SUPRASIL glasses.

Fig. 12 .

 12 Fig. 12. Evolution of the contrast at various doses. Error bars are representing the dispersion originating from the measurements repetitions. Squares mark the median value.

TABLE III EVOLUTION

 III OF THE LED EMISSION PROPERTIES WITH DOSE


J F P J Abascal
email: juan.abascal@creatis.insa-lyon.fr

P Douek

F Peyrin
email: peyrin@esrf.fr

A sparse and prior based method for 3D image denoising

Keywords: image denoising, total variation, split Bregman, spectral CT

Denoising algorithms via sparse representation are among the state-of-the art for 2D image restoration. In this work, we propose a novel sparse and prior-based algorithm for 3D image denoising (SPADE). SPADE is a modification of total variation (TV) problem with an additional functional that promotes sparsity with respect to a prior image. The prior is obtained from the noisy image by combining information from neighbor slices. The functional is minimized using the split Bregman method, which leads to an efficient method for large scale 3D denoising, with computational cost given by three FFT per iteration. SPADE is compared to TV and dictionary learning on the Shepp-Logan phantom and on human knee data acquired on a spectral computerized tomography scanner. SPADE converges in approximately ten iterations and provides comparable or better results than the other methods. In addition, the exploitation of the prior image avoids the patchy, cartoon-like images provided by TV and provides a more natural texture.

I. INTRODUCTION

Sparse methods are among the state-of-the art denoising methods. Total variation (TV) preserves edges and was termed as a "proper norm" for images [START_REF] Rudin | Nonlinear total variation based noise removal algorithms[END_REF]. Other L1-norm methods exploited sparsity using wavelet transform or frames and also provided competitive results [START_REF] Cai | Split Bregman Methods and Frame Based Image Restoration[END_REF]. However, TV leads to the so called "staircase artefacts" when images are highly corrupted by noise. To mitigate these effects generalizations of TV, such as total generalized variation [START_REF] Bredies | Total Generalized Variation[END_REF] and nonlocal TV [START_REF] Zhang | Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction[END_REF], were proposed. Similarly to nonlocal TV, patchbased [START_REF] Schaeffer | A Low Patch-Rank Interpretation of Texture[END_REF] and dictionary learning (DL) [START_REF] Aharon | K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation[END_REF] methods exploit redundancy across patches at different locations on the image. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement N • 701915. It was also performed within the framework of the LabEx PRIMES (ANR-11-LABX-0063) of University de Lyon and under the support of the ANR project SALTO (ANR-17-CE19-0011-01). The project has also received funding from the European Union's Horizon 2020 research and innovation programme under the grant agreement N 668142.

This adds an extra dimension along which images have a sparser representation.

Exploiting sparsity in a high dimensional space is common in compressed sensing applications where data redundancy is present along temporal or other higher dimensions [START_REF] Abascal | A novel prior-and motion-based compressed sensing method for small-animal respiratory gated CT[END_REF], [START_REF] Chen | Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets[END_REF], [START_REF] Abascal | Incorporation of prior knowledge of the signal behavior into the reconstruction to accelerate the acquisition of MR diffusion data[END_REF]. In these applications, prior-based methods exploit sparsity by subtracting the unknown image to a prior image that is built from data in the high dimensional space. When restricted to 2D or 3D, the best is to use patch-based or similar strategies.

The goal of this work is to present a new paradigm to exploit sparsity in 3D and, in specific, to propose a novel sparse and prior-based algorithm for 3D image denoising (SPADE), with the additional benefit of being computationally efficient for application to experimental clinical images. SPADE minimizes both a TV functional and an additional functional that promotes sparsity with respect to a prior image. The prior is obtained from the noisy image by combining information from neighbor slices. In this study, we used a running average to provide a specific prior image for each slice. The functional is minimized using the split Bregman method, which is an efficient method for L1-norm problems [START_REF] Goldstein | The Split Bregman Method for L1-Regularized Problems[END_REF]. SPADE is compared to TV and to DL method. The comparison with TV shows the improvement of adding the proposed priorbased regularization functional to a given algorithm. Although the DL method is a 2D-denoising algorithm, it allows to compare the recovery of image texture with a more complex algorithm than TV. Methods are assessed on Shepp-Logan phantom and on human knee experimental data acquired on a spectral computerized tomography (SCT) scanner. SCT is a new imaging modality with the potential of improving conventional CT but reconstructed images are affected by noise [START_REF] Heismann | Spectral computed tomography[END_REF], [START_REF] Ducros | Regularization of nonlinear decomposition of spectral x-ray projection images[END_REF], [START_REF] Abascal | Nonlinear material decomposition using a regularized iterative scheme based on the Bregman distance[END_REF]. In particular, we are interested in using SCT for knee osteoarthritis, as SCT may provide sufficient soft-tissue contrast to visualize and quantify cartilage tissue. Quantification requires image segmentation and improvement in image quality is thus essential.

II. METHODS

A. TV denoising

Let ũ be the 3D noisy image and u the 3D denoised image, the constrained total variation denoising problem is posed as follows:

min u ∇u 1 such that u -ũ 2 2 ≤ σ 2 , (1)
where the first term is 3D TV functional and the second term constrains the denoised image to lie close to the noisy image. We assume that noise follows a Gaussian distribution. The TV functional is nonlinear and nondifferentiable, so it requires stable and efficient iterative algorithms. It is common to approximate TV functional but this can lead to slow convergence or non optimal results [START_REF] Burger | A Guide to the TV Zoo[END_REF]. The split Bregman method provides a framework for efficient minimization of convex nondifferentiable functional [START_REF] Goldstein | The Split Bregman Method for L1-Regularized Problems[END_REF] (see section II-C).

B. SPADE denoising

SPADE imposes both spatial regularization and sparsity with respect to a prior image by solving the following problem:

min u (1 -α) Ψu 1 + α Φ(u -u p ) 1 such that u -ũ 2 2 ≤ σ 2 , (2)
where u p is a prior image that is assumed to be known. Operators Ψ and Φ are chosen to be equal to ∇ in order to compare to TV denoising and for computational purposes, as described in section II-C. With this choice, SPADE minimizes a combination of T V (u) and TV(u -u p ).

The prior image should be a good estimate of the unknown image in most but not in all pixels and should have low noise. In this study, the prior is obtained by combining information from neighbor slices by using a running average to provide a specific prior image for each slice, that is, u p = (u 1 p , . . . , u N p ), where u i p represents the ith slice and N is the number of slices along the z-dimension in the image. Each prior slice u i p is built from the 3D noisy image ũ as follows

u i p = j β ij ũj , (3)
where β ij = exp(-γ|j -i|), j = 1, . . . , N is the index of the slice, and γ = 0.04, which was set empirically in order to provide slow decaying coefficients. The prior image, which is a low-pass filtered version of the noisy image, has low noise but it is obviously blurred. This methodology provides an easy way to exploit structure similarity across slices. The further away from the current slice the lower the similarity. Thus, we propose a stack based denoising approach where a given number of slices are denoised at each time. We used stack of ten slices (N = 10).

C. Split Bregman formulation to solve SPADE and TV problems

We implemented SPADE and TV methods using the Split Bregman method, which is an efficient method for L1regularization problems [START_REF] Goldstein | The Split Bregman Method for L1-Regularized Problems[END_REF], [START_REF] Abascal | Fluorescence diffuse optical tomography using the split Bregman method[END_REF], [START_REF] Abascal | A novel prior-and motion-based compressed sensing method for small-animal respiratory gated CT[END_REF]. The nondifferentiability of TV is handled by introducing 3D auxiliary variables d i and e i , i = x, y, z, such that problem (2) becomes

arg min u,di,ei (1 -α) (e x , e y , e z ) 1 + α (d x , d y , d z ) 1 such that u -ũ 2 2 ≤ σ 2 , d i = ∇ i (u -u p ), e i = ∇ i u, i = x, y, z, (4)
adopting isotropic TV [START_REF] Goldstein | The Split Bregman Method for L1-Regularized Problems[END_REF]. Constrained problem ( 4) is easily managed using an iterative regularization scheme where constraints are imposed by adding Bregman iterations b i , c i :

(u k+1 , d k+1 i , e k+1 i ) = arg min u,di,ei α (d x , d y , d z ) 1 + (1 -α) (e x , e y , e z ) 1 + µ 2 u -ũk 2 2 + i λ 2 d i - ∇ i (u -u p ) -b i 2 2 + i λ 2 e i -∇ i u -c i 2 2 , (5a)
ũk+1 = ũk + ũ -u k+1 , (5b)
b k+1 i = b k i + ∇ i (u k+1 -u p ) -d k+1 i (5c) c k+1 i = c k i + ∇ i u k+1 -e k+1 i ( 5d
)
Variables u, d i , and e i are decoupled so they can be solved in alternating steps. Solution of u that leads to a linear system is efficiently solved in the Fourier domain and auxiliary variables are solved using shrinkage formulas. This leads to an efficient method for large scale 3D denoising, with computational cost given by three FFT per iteration. In addition, it can be parallelized across stacks, which provides additional computational efficiency. We remark that the linear system can be solved in the Fourier domain as Φ Φ and Ψ Ψ have Fourier representation. Other choices for Φ or Ψ that meet this criterion are unitary operators such as the wavelet transform.

A previous work proposed a Gauss-Seidel method for efficient resolution of the linear system for a banded Hessian matrix that arises in a Bregmanized nonlocal TV formulation [START_REF] Zhang | Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction[END_REF].

For methods hyperparameters, we used µ = λ = 1 for both TV and SPADE. This parameter selection does not affect convergence, only convergence speed (see [START_REF] Goldstein | The Split Bregman Method for L1-Regularized Problems[END_REF], [START_REF] Abascal | Fluorescence diffuse optical tomography using the split Bregman method[END_REF], [START_REF] Abascal | Investigation of different sparsity transforms for the PICCS algorithm in small-animal respiratory gated CT[END_REF] for further details). The effect of α is analyzed in section III-A.

D. Dictionary learning denoising

For the DL method [START_REF] Aharon | K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation[END_REF] we used the KSVD toolbox downloaded from http://www.cs.technion.ac.il/ elad/software/ with the following parameters: block size b = 8, redundancy factor R = 4, number of atoms in the dictionary Rb 2 , estimate of noise SD σ and ten KSVD iterations. Number of iterations could be made smaller to accelerate convergence but did not affect results. We checked varying parameter σ in the range from 5 to 20 and present best results. We remark that while TV and SPADE are 3D-denoising methods, the DL code used is a 2D-denoising method.

E. Methods analysis and image evaluation

The proposed method SPADE (2) is a modification of TV, so convergence and solution error at different iteration numbers are shown for both methods. Then, SPADE, TV and DL methods are compared in terms of mean-squared error (MSE) with respect to the ground truth image, streak artefact measure (SAM), and noise. SAM is the total variation of the denoised image subtracted to the ground truth image, so it provides an estimate of how well edges are recovered [START_REF] Abascal | A novel prior-and motion-based compressed sensing method for small-animal respiratory gated CT[END_REF]. SAM accounts for noise, artefacts and texture recovery. Noise is computed as the standard deviation (SD) on a small homogeneous region. As DL is a 2D method, we also provide metrics for TV method in 2D (TV-2D), for comparison.

F. Data sets

Methods were tested on a numerical phantom and experimental data (figure 1). The phantom was built from the Shepp-Logan phantom where a slice was replicated along zdimension and 5% additive Gaussian noise was added. Experimental data consisted of a excised human knee image acquired at Philips prototype SCT scanner, at CERMEP, Lyon [START_REF] Si-Mohamed | Review of an initial experience with an experimental spectral photon-counting computed tomography system[END_REF]. Knee sample was taken from the Institut d'Anatomie Paris Descartes and provided by B2OA (Bioingénierie et Bioimagerie ostéo-articulaire) CNRS 7052, Paris Diderot University. The study was approved by the ethics committee of Descartes University, Paris. Two levels of noise were considered: the original image and a second noisier data set with 5% additive Gaussian noise. For the latter the image provided by the scanner was adopted as ground truth. Images were 640 × 640 pixels and we worked with one stack of 10 slices.

III. RESULTS

A. Shepp-Logan phantom

SPADE is first analyzed in comparison to TV method on the Shepp-Logan phantom. Figure 2 shows solution error norm versus the number of iterations for TV and for SPADE for different values of α. Both methods converged in less than 10 iterations. SPADE presented lowest errors and more stable convergence for intermediate values of α (0.2 ≤ α ≤ 0.4); solution error was 34% lower than TV error. Very low or large values of α resulted more unstable. We emphasize that TV becomes unstable after few iterations because of high noise. On the other hand, SPADE had smoother convergence for a wide range of values of α. From now onwards we use α = 0.4. Figure 3 shows denoised images by TV and SPADE for different number of Bregman iterations k and the prior image used by SPADE. TV presented the lowest MSE for k = 3 but edges were not well recovered. Higher number of iterations allowed to recover edges at the expense of noise and "staircase artefacts". SPADE had the lowest MSE for k = 16, for which most edges were recovered. Increasing the iteration number recovered edges without detrimental noise.

DL reduced noise considerably but it did not recover edges as efficiently as SPADE and presented less natural texture. Best results for DL were obtained for 10 ≤ σ ≤ 12, where 10 provided sharper objects but also more artefacts, and 12 led to larger noise reduction but blurred edges. Using the simulated noise SD, (σ = 12.75 for gray-level scale images), would have led to a excessively blurred image.

Table I (left) presents MSE, SAM and noise for TV (k = 3), SPADE (k = 16), prior image used by SPADE, TV-2D (k = 3) and DL (10 iterations, σ = 12). SPADE led to the lowest MSE among all methods and DL led to the lowest noise reduction and SAM. SPADE improved all metrics with respect to TV except to noise, which was similar.

-----------

B. Experimental data

Figure 4 shows denoised images for the knee experimental data set with higher noise (5% additive Gaussian noise). TV and DL were quite efficient in removing noise but they presented less natural image texture than SPADE, which Table I (right) shows MSE, SAM and noise metrics for knee data. SPADE led to lower reduction in MSE than other methods. TV and DL provided the largest noise reduction but all methods presented similar SAM, as it accounts for both noise and artefacts.

Codes were run on a Windows computer with a 64-bit operating system, Intel Xeon(R) E5-1650 v4 3.60 GHz CPU and 128 GB RAM. We provide in table II algorithm computation times with codes ran in MATLAB. We also give the average time per iteration as most codes can be tuned to achieve faster convergence. Time for denoising the whole volume was computed only for SPADE; times for other methods were extrapolated. Computation times for SPADE can be further reduced by parallelization and exploiting GPU, as heaviest computation time is the FFT.

Figure 5 shows denoising of the original image provided by the spectral CT scanner (figure 4-a), which has lower noise than previous data set (figure 4-b). SPADE improved image quality both in terms of reduced noise and increased tissue contrast. Cartilage tissue is clearly seen and better

IV. DISCUSSION AND CONCLUSION

We have presented a new methodology for 3D image denoising, in specific, we proposed SPADE method and compared it to TV and DL methods. Results show that adding a prior-based functional avoids artefacts that appeared in TV and provides a more natural image texture than TV and DL methods. We note that while the prior image is not actually set a priori, as it is learned from the data, it guides the denoising algorithm to reduce noise and maintain texture. In addition, the prior makes SPADE to be more robust to the iteration number than TV method, where both methods were solved using the split Bregman formulation [START_REF] Abascal | A novel prior-and motion-based compressed sensing method for small-animal respiratory gated CT[END_REF], [START_REF] Goldstein | The Split Bregman Method for L1-Regularized Problems[END_REF], [START_REF] Abascal | Fluorescence diffuse optical tomography using the split Bregman method[END_REF]. SPADE also provided competitive results in terms of computation time, allowing to denoise the whole volume in few minutes. We found that a higher iteration number led to improved results for the less noisy data. We remark that SPADE can further benefit from GPU implementation and that the possibility of processing the 3D volume in stacks allows for further parallelization.

This work is subject to few limitations. The comparison of SPADE, which is intrinsically a 3D-denoising method, to DL is not fair, as DL is a 2D-denoising method. However, we showed the improvement of adding a prior-based regularization functional to TV method, so we could expect similar improvement by applying this approach to DL or other methods such as total generalized variation. In addition, the use of DL for 3D images should be time consuming which could be a severe restriction for clinical applications. With regard to the Shepp-Logan phantom, it was built from a 2D slice, which makes it an ideal situation for the prior image as it is less blurred than in practice. On the contrary, results on knee data show the feasibility of the proposed methodology on clinical data.

Several generalizations of the proposed method can be designed. For instance, one may think of more general transforms that combine neighbor slices.

In conclusion, we have presented a new paradigm for 3D image denoising that allows to exploit sparsity in a easy and efficient manner. From the results shown on experimental data, we expect SPADE to be widely used for 3D image processing.

Fig. 1 .

 1 Fig. 1. Left: Slice of Shepp-Logan phantom. Right: Slice of experimental SCT image of human knee.

Fig. 2 .

 2 Fig. 2. Solution error norm versus the iteration number for TV and SPADE for different values of α.

12 Fig. 3 .

 123 Fig. 3. a) Detail of Shepp-Logan image, b) noisy image with 5% Gaussian noise, and denoised images by c-d) TV, e-f) SPADE for α = 0.4, and h-i) DL. g) Prior image used by SPADE.

  (a) Original image (b) Noisy image (c) TV (k = 5) (d) TV (k = 7) (e) Prior image (f) SPADE k = 15 (g) SPADE k = 23 (h) SPADE k = 30 (i) DL σ = 10 (j) DL σ = 12

Fig. 4 .

 4 Fig. 4. Detail of a) original image, b) noisy image with 5% Gaussian noise, and denoised images by c-d) TV, f-h) SPADE and i-j) DL. e) Prior image used by SPADE.

Fig. 5 .

 5 Fig. 5. Denoising on experimental knee image (figure 4-a) by SPADE for different iteration number.

TABLE I METRICS

 I FOR DENOISING OF SHEPP-LOGAN PHANTOM (LEFT) AND EXPERIMENTAL KNEE DATA (RIGHT).

		MSE % SAM	SD	MSE % SAM	SD
	TV	6.5	4.1	0.010	6.7	2.7	45.2
	SPADE	4.3	3.8	0.011	6.4	2.7	57.4
	Prior	4.4	5.8	0.016	8.3	3.3	68.7
	DL	4.8	3.2	0.008	6.8	2.7	48.0
	TV-2D	8.9	6.3	0.017	7.6	3.0	57.0

TABLE II COMPUTATION

 II TIME FOR THE KNEE DATA. the original image, which is the goal for the medical application. Images are shown at two different iteration numbers. We can see that SPADE already provides high quality image after 10 iterations and larger number of iterations are needed to recover all fine details.

		Iteration (s) Slice (s) Volume (min)
	TV	0.05	0.4	2
	SPADE	0.08	1.1	5.2
	DL	2.4	29	192
	delineated than in