C Deledalle

L Denis

G Poggi

F Tupin

L Verdoliva

Exploiting patch similarity for SAR image processing: the nonlocal paradigm

Most current SAR systems offer high-resolution images featuring polarimetric, interferometric, multi-frequency, multi-angle, or multi-date information. SAR images however suffer from strong fluctuations due to the speckle phenomenon inherent to coherent imagery. Hence, all derived parameters display strong signal-dependent variance, preventing the full exploitation of such a wealth of information. Even with the abundance of despeckling techniques proposed these last three decades, there is still a pressing need for new methods that can handle this variety of SAR products and efficiently eliminate speckle without sacrificing the spatial resolution. Recently, patchbased filtering has emerged as a highly successful concept in image processing. By exploiting the redundancy between similar patches, it succeeds in suppressing most of the noise with good preservation of texture and thin structures. Extensions of patch-based methods to speckle reduction and joint exploitation of multi-channel SAR images (interferometric, polarimetric, or PolInSAR data) have led to the best denoising performance in radar imaging to date. We give a comprehensive survey of patchbased nonlocal filtering of SAR images, focusing on the two main ingredients of the methods: measuring patch similarity, and estimating the parameters of interest from a collection of similar patches.

I. INTRODUCTION

Current SAR systems share two common characteristics: they provide a wealth of information thanks to polarimetric, wavelength or angle diversity, and they offer very high spatial resolutions that give access to the shape of man-made structures. In radar images, however, parameters of interest, like interferometric phase, coherence, polarimetric properties, or radiometry, are not directly accessible but must be estimated from unreliable data. It is essential that the estimation procedure be robust to the strong fluctuations in the measurements due to speckle without trading off the spatial resolution.

The simplest way to reduce speckle noise 1 is to average pixels in a rectangular window around the target pixel, socalled spatial multilooking. This process, already present in the first ERS satellite images and still widely used for interferometric or polarimetric data, leads to a uniform reduction of speckle in homogeneous areas, with a residual variance inversely proportional to the number of pixels averaged. However, by potentially mixing different signals, it also impairs such important signal features as region edges, man-made structures, and fine textures. The point is that multilooking is just a basic non-adaptive form of parameter estimation: to remove speckle without degrading fine features, local image content must be taken into account.

The design of efficient despeckling filters is a long-standing problem that has been the object of intense research since the advent of SAR technology [START_REF] Touzi | A review of speckle filtering in the context of estimation theory[END_REF], with first contributions dating back to the 80s [START_REF] Lee | Digital image enhancement and noise filtering by use of local statistics[END_REF]. However, research activity has accelerated significantly in recent years, reflecting both the success of SAR remote sensing in general and the lack of satisfactory methods for resolution-preserving speckle reduction. Some of the most successful methods proposed in the recent past for locally adaptive estimation are based on image models that enforce strong regularity constraints, either in the original domain (e.g., Markov random fields [START_REF] Denis | Joint Regularization of Phase and Amplitude of InSAR Data: Application to 3D reconstruction[END_REF]), or in some transform domain (e.g., wavelet-based sparse representations [START_REF] Achim | SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling[END_REF]).

Very recently, patches, i.e., small rectangular image regions (typically squares of size between 3 × 3 and 11 × 11), have emerged as a powerful representation on which to build rich and flexible statistical models of natural images. Patches capture richer neighborhood configurations than first-order Markov random fields and are better localized than wavelets. Patch-based models do not enforce the solution to belong to a restricted class of signals, such as signals with bounded variations or with sparse transform coefficients. They exploit the self-similarity, typical of natural scenes, and look for similar patches not just in the immediate neighborhood of the target pixel but in an extended search area. Unlike a local method like [START_REF] Vasile | Intensity-Driven Adaptive-Neighborhood Technique for Polarimetric and Interferometric SAR Parameters Estimation[END_REF] that considers only connected pixels, far apart pixels can be combined, thereby justifying the widespread nonlocal appellative. The evolution from explicit image models to the concept of patch redundancy corresponds to a true methodological shift in image processing. In particular, recent denoising methods most often rely on the notion of a patch.

Interestingly, the concept of nonlocal filtering originally emerged in image processing after the pioneering work of Lee [START_REF] Lee | Digital image smoothing and the sigma filter[END_REF] for SAR despeckling. However, it was only with the development of patch-based methods, following the seminal work [START_REF] Buades | A Review of Image Denoising Algorithms, with a New One[END_REF] in the 2000s, and the definition of highly discriminative patch-based similarity measures, that nonlocal filtering could be successfully applied to the low-SNR specklecorrupted SAR images. The paradigm of patch-based nonlocal estimation is particularly interesting for SAR image processing given the poor fit of classical models to SAR scenes, characterized by many very strong punctual targets and high-contrast structures that are poorly modeled with piecewise constants or wavelets.

SAR IMAGING MODALITIES

Synthetic Aperture Radar systems are based on the emission of an electromagnetic wave which is then back-scattered by the ground level features, and finally recorded by the receiving antenna. Several modalities are used in SAR imaging (see [START_REF] Moreira | A tutorial on Synthetic Aperture Radar[END_REF] for a comprehensive survey): amplitude: The simplest configuration provides, after SAR synthesis, an image of scattering coefficients k that are complex values with a magnitude (i.e., amplitude) that is representative of the radar crosssection. The square magnitude (i.e., intensity) is also often considered. polarimetric: The use of different polarizations at emission and reception of the radar wave provides a deeper insight into the backscattering mechanisms inside the resolution cell. The scattering vector k is formed by the complex values corresponding to each combination of emission / reception polarizations. Usually, horizontal (H) and vertical (V) polarizations are used for emission and reception providing the The potential of this new paradigm for SAR imaging has quickly been recognized, with more than 30 papers published since 2009 that describe patch-based methods applied to SAR, including most state-of-the-art despeckling techniques [START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF], [START_REF] Zhong | SAR Image Despeckling Using Bayesian Nonlocal Means Filter With Sigma Preselection[END_REF], [START_REF] Parrilli | A Nonlocal SAR Image Denoising Algorithm Based on LLMMSE Wavelet Shrinkage[END_REF]. In addition, nonlocal patch-based methods are very flexible and can readily be extended to different SAR modalities [START_REF] Chen | Nonlocal filtering for polarimetric SAR data: A pretest approach[END_REF], [START_REF] Deledalle | NL-InSAR: Nonlocal interferogram estimation[END_REF], [START_REF] Deledalle | NL-SAR: a unified Non-Local framework for resolution-preserving (Pol)(In)SAR denoising[END_REF].

scattering vector k = [z HH , z HV , z V H , z V V ] t (or, by reciprocity, k = [z HH , z HV , z V V ] t ).
This paper reviews the underlying ideas and principles of nonlocal estimation methods proposed in SAR imaging. We consider despeckling as a familiar and important case study, but we also address the more general point of view of parameter estimation, looking ahead at extensions to more challenging SAR modalities and estimation problems. Before diving into the core of patch-based methods, we begin by describing the classical speckle model in SAR imaging and the major families of estimation methods that have emerged these last 3 decades.

II. A SHORT OVERVIEW OF SAR DESPECKLING

Depending on the modality, SAR systems can record up to 6 channels of complex valued signals (see box "SAR imaging modalities"). All these signals present highly varying fluctuations because SAR is a coherent imaging system (see box "Speckle fluctuations in radar images"). The simplest way to reduce these fluctuations and estimate the values of the physical parameters is to average several independent samples from the data. This operation, called multi-looking, was applied in various forms from the very beginning of the SAR era. However, such simple averaging that applies equally to every region of the image, regardless of the local heterogeneity, strongly degrades the spatial resolution.

Improved approaches have long been proposed to enhance this basic estimation method by better taking into account the image information. Many efforts have been devoted to the case of amplitude images, corresponding to the modulus of single polarization data. Most of these "filtering" methods are described in the review paper [START_REF] Touzi | A review of speckle filtering in the context of estimation theory[END_REF], and the very recent tutorial [START_REF] Argenti | A tutorial on Speckle Reduction in Synthetic Aperture Radar Images[END_REF]. The first attempts were derived according to estimation theory: Lee [START_REF] Lee | Digital image enhancement and noise filtering by use of local statistics[END_REF] proposed a minimum mean square error estimator in the class of linear filters, while Lopes et al. [START_REF] Lopes | Adaptative speckle filters and scene heterogeneity[END_REF] considered the maximum a posteriori estimator. Both works used a statistical model limited to local distributions, and it is worth noting that these two filters were popular because of the clever analysis of the local context, using window splitting, or edge and target detection [START_REF] Lopes | Adaptative speckle filters and scene heterogeneity[END_REF]. The idea of selecting the most relevant samples in the window has been further developed in [START_REF] Vasile | Intensity-Driven Adaptive-Neighborhood Technique for Polarimetric and Interferometric SAR Parameters Estimation[END_REF] and is the main motivation of patch-based approaches. The following generation of filtering approaches introduced stronger priors to guide the solution.

A first family includes Markovian and variational approaches which impose smoothness or regularity constraints on the solution through a suitable prior model. These approaches usually lead to minimizing an energy function composed of two terms. The first term reflects the data distribution and is related to statistical models of speckle (see the box "Speckle fluctuations in radar images"). Due to the heavy tail of the distributions of speckle-corrupted images, classical least-squares data fitting must be replaced by a more relevant criterion derived from speckle distributions. The second term relies on some prior on the solution. Although regularization models such as gradient sparsity have been investigated [START_REF] Denis | Joint Regularization of Phase and Amplitude of InSAR Data: Application to 3D reconstruction[END_REF], they do not fit well SAR signal properties. The Markovian formalism can be easily extended to deal with different SAR modalities like interferometric data. However, the specific nature of SAR signals is poorly captured by simple models and more complex ones lead to very hard optimization problems.

A second large family of approaches is based on wavelet transforms. Thanks to their spatially localized and multiresolution basis functions, wavelets yield sparse yet accurate representations of natural images in the transform domain. Sharp discontinuities and point-like features, so common in SAR images, are well described by a small number of basis functions, just like the large homogeneous regions between them. This compact representation was quickly recognized as a powerful tool for denoising. In fact, while the signal is projected on a relatively small number of large wavelet coefficients, the white noise remains white after the transform, and hence evenly distributed on all coefficients. Signal and noise can be, therefore, efficiently separated by means of an appropriate non-linear processing, such as hard/soft thresholding or more sophisticated shrinkages. The encouraging results provided by early SAR despeckling techniques spawned an intense research to overcome the shortfalls of soft/hard thresholding. A popular approach considered wavelet shrinkage as a Bayesian estimation problem, possibly expressed after application of a homomorphic transform in order to reduce speckle to an independent additive perturbation. The major problem in this context becomes the modeling of signal and noise by suitable distributions, and a number of parametric models have indeed been proposed [START_REF] Achim | SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling[END_REF], [START_REF] Argenti | Multiresolution MAP Despeckling of SAR Images Based on Locally Adaptive Generalized Gaussian pdf Modeling[END_REF]. Further improvements come from joint modeling of wavelet coefficients in and across subbands, like in [START_REF] Xie | SAR speckle reduction using wavelet denoising and Markov random field modeling[END_REF]. Despite its potential, the wavelet transform cannot deal by itself with the high heterogeneity of SAR scenes. A number of spatially adaptive techniques were therefore proposed, based on some prior classification of the image, typically in homogeneous,

SPECKLE FLUCTUATIONS IN RADAR IMAGES

Coherent signals like SAR data present strong fluctuations. The waves backscattered by elementary scatterers inside each resolution cell are not "in phase" but arbitrarily "out-of-phase", which results in constructive and destructive interferences. In a SAR intensity image, fluctuations due to speckle follow a heavy tail distribution (large deviations occur often) and are signal dependent (standard deviation is proportional to the radiometry), which departs from the usual additive Gaussian noise model: Measured SAR intensity I > 0 in untextured areas deviates from the radiometry R > 0 according to an exponential distribution:

p(I|R) = 1 R exp(- I R ) . (1)
Multi-look SAR images, obtained by averaging L intensity images, follow a gamma distribution:

p(I|R) = L R L I L-1 Γ(L) exp -L I R . (2)
In the more general case of a K-dimensional scattering vector as encountered in polarimetric and interferometric modalities k = [z 1 , . . . , z K ] t , the observed complex vector k follows a K-dimensional circular complex Gaussian distribution under Goodman's fully developped speckle model (valid for untextured areas with physically homogeneous and rough surfaces):

p(k|Σ) = 1 π K |Σ| exp -k † Σ -1 k (3)
where Σ = E{kk † } is a K × K complex covariance matrix characteristic of the imaged surface, E is the expectation, and † the hermitian transpose. Some radar images are not available in the form of scattering vectors, but rather as empirical covariance matrices:

C = 1 L L i=1 k i k † i , (4)
where the sum is carried over several scattering vectors for each pixel. In the case of amplitude images, k is a scalar and C corresponds to an L-looks intensity image.

The empirical covariance C follows a Wishart distribution given by:

p(C|Σ, L) = L LK |C| L-K Γ K (L)|Σ| L exp -L Tr(Σ -1 C) , (5)
where Tr(•) is the matrix trace. The equivalent number of looks L acts as the shape parameter of the Wishart distribution.

heterogeneous (e.g., textures) and highly heterogeneous (e.g., point targets) regions, in order to tune filtering parameters or strategies to the different regions [START_REF] Foucher | Multiscale MAP filtering of SAR images[END_REF]. The approaches reviewed above generally try to estimate the signal at a certain pixel from the noisy observations at pixels close to it. However, with plenty of data to estimate the signal, that is, the observations over the whole image, why restricting attention only to a small neighborhood of the target? The obvious answer is that not all image pixels carry valuable information on the target, and only close pixels are used because they are expected to be more similar to it, and hence, better estimators. The above consideration makes clear that the image denoising problem may be performed in two separate steps: i) selecting good predictors, which carry useful information on the target, and then ii) using them to perform the actual estimate. Lacking any other hints, spatial closeness is taken as a surrogate of signal similarity relying heavily on the fact that natural images are predominantly lowpass. Needless to say, sophisticated filters go much beyond a simple distance-based weighting of contributions, but this basic criterion remains a founding paradigm of local filters.

The patch-based nonlocal approach avoids the potentially dangerous identification between closeness and similarity and goes back to the original problem, trying to identify the pixels more similar to the target, irrespective (to a certain extent) of their spatial distance from it. In next Section we explore in more depth the fundamental steps involved in nonlocal SAR despeckling and review the current state of the art.

III. NONLOCAL APPROACHES: EXPLOITING PATCH

REDUNDANCY

At the core of the nonlocal approach stands the selection of suitable predictors based on their similarity with the target.

This idea began to gain some popularity with the bilateral filter, proposed for additive white Gaussian noise (AWGN) denoising, with predictor weights depending not only on their spatial distance from the target, but also on their similarity with it, measured by the difference between observed values. Despite its simplicity, this filter gave a surprisingly good denoising performance, reducing the annoying edge smearing phenomenon. However, the pixel-wise estimation of similarity was very rough, and happened to reinforce observed values affected by strong noise, justifying the need for the spatialdistance term. The fundamental step towards nonlocal filtering was then the introduction, in NL-means [START_REF] Buades | A Review of Image Denoising Algorithms, with a New One[END_REF], of a reliable patchwise measure of similarity. When a relatively large patch is taken into account, it is very unlikely that pixels characterized by a signal much different from the target be accepted as good predictors. Thanks to the improved reliability, predictors can be weighted based only on similarity, with no reference to spatial information. Unlike local filters, non-local ones do not impose any specific structure (connectivity, shape) or smoothness, but only exploit that patches recur more or less frequently, a self-similarity property common to most images. Recurring patches are easily found in smooth regions, but just as well around region boundaries, textures, artificial structures, etc., as shown in Fig. 1. Hence, for most patches, several other patches can be found with similar content. This form of stationarity in the space of patches is central to nonlocal approaches.

Nonlocal estimation methods generally follow a three-step scheme, summarized in the box "Nonlocal estimation in action", with many possible variations at each step and, possibly, pre-processing steps and/or iterative refinement of results by repeated nonlocal estimations. The first step identifies similar patches (patch size is generally set from 3×3 to 11×11 pixels). It must reliably find, within an extended search window (typically 21 × 21 to 39 × 39), patches that are close to the reference central patch. Once several patches have been selected (from a few tens to all the hundreds of patches within

NONLOCAL ESTIMATION IN ACTION: PROCESSING AT PIXEL x
the search window), they are assigned relative weights. The second step combines patches, according to their weights, to form an estimate of either the central pixel, the central patch, or all selected patches. The estimates computed from all possible reference patches are then merged in a last step to produce the final image.

We now illustrate these steps for the special case of NLmeans [START_REF] Buades | A Review of Image Denoising Algorithms, with a New One[END_REF], indicating by v(x) and v(x), respectively, the at pixel x, and the image patch centered on x in the observed image. In NL-means, each pixel x ′ in a large search area around the target pixel x is considered and a similarity measure ∆(x, x ′ ) is computed by comparing the two patches centered on x and x ′ . Under AWGN, the sum of squared differences is a natural criterion to evaluate similarity:

∆(x, x ′ ) = v(x ′ ) -v(x) 2 . ( 6
)
This measure is used to compute the weight for each predictor pixel x ′ , with large weights associated with similar patches and negligible weights with dissimilar ones. An exponential kernel is used to this end:

w(x, x ′ ) = exp (-∆(x, x ′ )/h) , (7)
with the bandwidth parameter h governing the weight distribution. Finally, the target pixel x is estimated through the weighted average of all pixels within the search area:

u NL (x) = x ′ w(x, x ′ )v(x ′ ) x ′ w(x, x ′ ) , (8)
where u denotes an estimate of the unknown signal value u.

In the NL-means, therefore, only one estimate is obtained for each pixel x, which corresponds to the top branch depicted in the box "Nonlocal estimation in action". Generalizations provide several estimates for each pixel that must be properly combined in the last step.

The NL-means filter and its numerous variants are known to perform well under AWGN. However, the extension to SAR imaging, and in particular to speckle, is by no means trivial, and has been the object of several recent papers. One has to understand the foundation of such filters, and provide a flexible formulation suitable for different modalities and models of noise. In the following, we focus on the main concepts that have been proposed in SAR imaging, and try to provide some insight into the problems that emerge when noise departs from the Gaussian distribution, and possible solutions to them. The key point of all these extensions is the consideration of the specific distributions of radar data.

Step 1: Defining patch similarities -The first step of nonlocal estimation methods is the identification of similar patches through a (dis)similarity criterion ∆(x, x ′ ). This criterion quantifies, in a principled manner, by how much the unknown patches u(x) and u(x ′ ) differ. Based on the similarity to the reference patch at x, predictor patches at x ′ can be either softassigned or hard-assigned to the set of similar patches. In the case of soft-assignment, a weight reflecting the level of similarity is associated to each patch within the search area, otherwise the most similar patches are included and used to perform the prediction.

Under AWG noise, ( 6) is a natural criterion to evaluate similarity between two patches. Fluctuations created by speckle are multiplicative and non-Gaussian, see the box "Speckle fluctuations in radar images". Specific criteria must be derived for the comparison of patches in SAR imaging.

The similarity between two patches is generally defined as the sum of the similarity δ of each pair of corresponding pixels in the two noisy patches: ∆(x, x ′ ) = τ δ(v(x + τ ), v(x ′ + τ )). In order to improve the discrimination power of the similarity criterion, several authors suggest using a pre-estimate u computed either over the whole patch [START_REF] Torres | Speckle reduction in polarimetric SAR imagery with stochastic distances and nonlocal means[END_REF], obtained after a first iteration [START_REF] Parrilli | A Nonlocal SAR Image Denoising Algorithm Based on LLMMSE Wavelet Shrinkage[END_REF] or at the previous iteration [START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF] of the nonlocal method. The similarity then takes the form: ∆(x, x ′ ) = τ δ( u(x + τ ), u(x ′ + τ )). The following paragraphs describe possible approaches to derive the pixelwise similarity δ.

Detection approach -Dissimilarity can be defined based on the detection of the difference between the underlying values u 1 and u 2 [START_REF] Deledalle | How to compare noisy patches? Patch similarity beyond Gaussian noise[END_REF]. This detection problem can be formulated as an hypothesis test where the null hypothesis corresponds to no difference (H 0 : u 1 = u 2 = u 12 ) and the alternative one to a difference (H 1 : u 1 = u 2 ). Among several criteria considered in [START_REF] Deledalle | How to compare noisy patches? Patch similarity beyond Gaussian noise[END_REF], the generalized likelihood ratio (GLR) is shown to perform best and fullfil several invariance properties:

δ GLR (v 1 , v 2 ) = -log sup u12 [ p(v 1 |u 12 ) p(v 2 |u 12 ) ] sup u1 [ p(v 1 |u 1 ) ] sup u2 [ p(v 2 |u 2 ) ] . (9)
Criteria specific to SAR imaging can be derived from ( 9) by using the statistical speckle models recalled in the box "Speckle fluctuations in radar images". Both single channel (intensity) and multi-channel (polarimetric and/or interferometric) configurations lead to a criterion defined as the log of the ratio between arithmetic and geometric means [START_REF] Conradsen | A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data[END_REF]:

δ GLR (C 1 , C 2 ) = 2L log 1 2 |C 1 + C 2 | |C 1 | • |C 2 | , ( 10
)
where C may represent either the L-looks intensity (singlechannel images) or the L-looks empirical covariance matrices (multi-channel images). This is a natural criterion to compare patches corrupted by a multiplicative noise such as speckle since the criterion is invariant to a multiplicative change of contrast. It has been successfully used in nonlocal filtering of intensity, interferometric and polarimetric SAR images [START_REF] Chen | Nonlocal filtering for polarimetric SAR data: A pretest approach[END_REF], [START_REF] Deledalle | NL-SAR: a unified Non-Local framework for resolution-preserving (Pol)(In)SAR denoising[END_REF]. Detection-based criteria using similar expressions are also at the heart of [START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF], [START_REF] Deledalle | NL-InSAR: Nonlocal interferogram estimation[END_REF], [START_REF] Poggi | Nonlocal methods for filtering interferometric SAR datasets[END_REF], [START_REF] Liu | Nonlocal Means Filter for Polarimetric SAR Data Despeckling Based on Discriminative Similarity Measure[END_REF].

Information approach -In line with the detection approach, the authors of [START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF], [START_REF] Torres | Speckle reduction in polarimetric SAR imagery with stochastic distances and nonlocal means[END_REF] consider a similar hypothesis test involving pre-estimates of the parameters. Good criteria to perform such a hypothesis test are provided by the h-φ divergences where h and φ refer to pre-defined functions. The h-φ divergences measure the quantity of information shared by the distributions parametrized by u 1 and u 2 : they evaluate the proportion of samples from one distribution that can be explained by the other. Specific choices of h and φ lead for instance to the Hellinger divergence or the Kullback-Leibler divergence. Again, taking into account specific SAR distributions provides well-founded criteria. The symmetrical version of Kullback-Leibler divergence (sKL) gives, in the case of Wishart-distributed empirical covariance matrices: 11) again involving ratios, as customary in SAR imagery.

δ sKL ( 1 , Σ 2 ) = L Tr( Σ -1 1 Σ 2 + Σ -1 2 Σ 1 ) + const. (
Geometric approach -The similarity can be defined by deriving a metric suitable to the specificities of SAR data. D'Hondt et al [START_REF] Hondt | Iterative Bilateral Filtering of Polarimetric SAR Data[END_REF] suggest using Hermitian semi-definite positive matrices and propose a metric connected to geodesic and Riemannian distances:

δ Geo ( Σ 1 , Σ 2 ) = log( Σ -1/2 2 Σ 1 Σ -1/2 2 ) 2 F ( 12
)
where log is the matrix logarithm and • F the Froebenius norm. This similarity offers some interesting invariance properties. In the case of intensity images with pre-estimated radiometry R, this criterion boils down to (log( R 2 ) -log( R 1 )) 2 which is the square distance between observations after applying a homomorphic transform on the pre-estimates. It has been shown in the framework of detection theory that criteria based on variance-stabilization (such as the log transform in SAR) enjoy good properties [START_REF] Deledalle | How to compare noisy patches? Patch similarity beyond Gaussian noise[END_REF]. It is interesting to see that such a criterion can be derived using different interpretations (a geometric founding or a statistical reasoning).

Estimation approach -Lee et al [START_REF] Lee | Improved sigma filter for speckle filtering of SAR imagery[END_REF] have shown that the estimation of radar properties may suffer from a systematic bias arising from the procedure that detects similar noisy values (hard-assignment). For SAR intensity images, they suggest using a pre-selection rule of the form

I 2 ∈ [R 1 ζ, R 1 ζ ′ ]
-called sigma range -for which the pre-selected samples I 2 do not introduce bias in the subsequent estimation when the radiometry is identical (R 1 = R 2 ). Values of ζ and ζ ′ are computed by an iterative method, while the unknown R 1 is replaced by a pre-estimate R 1 called a priori mean [START_REF] Lee | Improved sigma filter for speckle filtering of SAR imagery[END_REF], [START_REF] Zhong | SAR Image Despeckling Using Bayesian Nonlocal Means Filter With Sigma Preselection[END_REF]. By rather considering a pre-selection rule of the form δ(I 1 , I 2 ) ≤ γ, numerical integrations over I 1 and I 2 show that the subsequent estimation is unbiased as soon as the rule can be rewritten as

I 2 ∈ [I 1 /ζ, I 1 ζ].
Detection rules such as GLR [START_REF] Zhong | SAR Image Despeckling Using Bayesian Nonlocal Means Filter With Sigma Preselection[END_REF] verify this property. Some of the estimators used in the second step of nonlocal estimation methods use the similarity ∆(x, x ′ ) in order to weight the importance of the patch v(x ′ ) (i.e., soft-assigment). The similarity ∆(x, x ′ ) is mapped into a weight w(x, x ′ ) using a function termed kernel. Many different kernels have been proposed in the literature, from simple thresholding w(x, x ′ ) = 1[∆(x, x ′ ) < h], exponential kernels as in [START_REF] Lee | Digital image smoothing and the sigma filter[END_REF], to more sophisticated ones [START_REF] Torres | Speckle reduction in polarimetric SAR imagery with stochastic distances and nonlocal means[END_REF], [START_REF] Liu | Nonlocal Means Filter for Polarimetric SAR Data Despeckling Based on Discriminative Similarity Measure[END_REF], [START_REF] Deledalle | NL-SAR: a unified Non-Local framework for resolution-preserving (Pol)(In)SAR denoising[END_REF]. The shape of the kernel (e.g., smooth, discontinuous or trapezoidal) changes the contributions of patches that may correspond to false detections and thus controls the bias / variance trade-off. In [START_REF] Torres | Speckle reduction in polarimetric SAR imagery with stochastic distances and nonlocal means[END_REF], [START_REF] Deledalle | NL-SAR: a unified Non-Local framework for resolution-preserving (Pol)(In)SAR denoising[END_REF], suitable kernels have been defined to guarantee the same bias / variance trade-off, irrespective of the modality, the noise statistic or the patch size.

Step 2: Estimation of radar properties -After selection of a stack of patches and/or computation of relative weights during the first step of the nonlocal estimation method, these patches are combined in a second step to form an estimate of the radar properties. This combination can be a simple (weighted) averaging as in the NL-means, or a more evolved estimator.

In SAR imaging, observations v may denote a collection of intensities I, amplitudes √ I or log-transformed values log(I), a vector of noisy coefficients in a transformed domain (DCT, Fourier, wavelets. . . ), a collection of scattering vectors k or of empirical covariance matrices C. The associated collection of parameters of interest u, are generally the radiometry R or covariance matrice Σ. The estimation step computes radar parameters from the collection of observations v and/or preestimations u gathered during the first step. The most common estimators for patch-based denoising of SAR images are:

• SME/WSME -NL-means and many of its successors combine similar patches into a weighted average (weighted sample mean estimator, WSME), where the weights are derived from the similarities: see equation [START_REF] Buades | A Review of Image Denoising Algorithms, with a New One[END_REF]. By using weights, the estimation relies more heavily on samples that are more similar (thus, more reliable), which reduces bias. Compared to an estimation based solely on a collection of patches detected as highly similar (i.e., by hard-assignment), the variance can also be reduced by considering a larger number of samples. The sample mean estimator corresponds to the conditional expectation E[v|u]. This expectation may not directly be equal to the parameter of interest u, but require a debiasing step. A notable example is the case of (weighted) averaging of logtransformed SAR images. The estimation of covariance matrices from empirical ones can be performed by WSME [START_REF] Chen | Nonlocal filtering for polarimetric SAR data: A pretest approach[END_REF], [START_REF] Hondt | Iterative Bilateral Filtering of Polarimetric SAR Data[END_REF], [START_REF] Torres | Speckle reduction in polarimetric SAR imagery with stochastic distances and nonlocal means[END_REF], [START_REF] Liu | Nonlocal Means Filter for Polarimetric SAR Data Despeckling Based on Discriminative Similarity Measure[END_REF], [START_REF] Deledalle | NL-SAR: a unified Non-Local framework for resolution-preserving (Pol)(In)SAR denoising[END_REF]:

Σ WSME (x) = x ′ w(x, x ′ )C(x ′ ) x ′ w(x, x ′ ) . (13)
with w(x, x ′ ) the weight depending on the similarity ∆(x, x ′ ) between patches extracted at pixel locations x and x ′ .

• MLE/WMLE -The sample mean is not a correct estimator of some parameters, e.g., the amplitude √ I. The sample mean should then be replaced by an estimator adjusted to the specific noise distribution of the observations, such as the maximum likelihood estimator. Similarly to the WSME, sample weights can be introduced in the estimation method. Maximum likelihood can be generalized into the weighted maximum likelihood estimator (WMLE) [START_REF] Deledalle | Iterative weighted maximum likelihood denoising with probabilistic patch-based weights[END_REF]:

u WMLE (x) = arg max u x ′ w(x, x ′ ) log p[v(x ′ )|u] . ( 14
)
WMLE leads to [START_REF] Deledalle | NL-InSAR: Nonlocal interferogram estimation[END_REF] for Wishart-distributed covariance matrices, but improvements are obtained for matrices with particular structures as in interferometric SAR imaging [START_REF] Deledalle | NL-InSAR: Nonlocal interferogram estimation[END_REF].

• MMSE -Kervrann et al. proposed a method called Bayesian NL-means [START_REF] Kervrann | Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal[END_REF] that estimates the parameters u as a linear combination of pre-estimated patches u, with weights defined by the likelihood of each pre-estimated patch with respect to the observation v:

u MMSE (x) ≈ x ′ p[v(x)| u(x ′ )] u(x ′ ) x ′ p[v(x)| u(x ′ )] (15)
This estimator can be interpreted as an approximation of the minimum mean square error estimator, i.e., the posterior mean. Pre-estimates are usually obtained thanks to a twostep or iterative pre-filtering [START_REF] Zhong | SAR Image Despeckling Using Bayesian Nonlocal Means Filter With Sigma Preselection[END_REF]. Since the pre-estimation step provides only a coarse estimation u of the patches u, a smoothing parameter is introduced to reduce the selectivity of the likelihood function and thus avoid weighting too much patches that are very close to the observation [START_REF] Kervrann | Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal[END_REF].

• LMMSE -The linear minimum mean square error estimator has long been used in SAR imaging [START_REF] Lee | Improved sigma filter for speckle filtering of SAR imagery[END_REF]. This estimator restricts the form of the solution to linear transforms of v, which is most efficient when noise and signal are well separated. In SAR-BM3D [START_REF] Parrilli | A Nonlocal SAR Image Denoising Algorithm Based on LLMMSE Wavelet Shrinkage[END_REF], the LMMSE is computed after an undecimated discrete wavelet transform (UDWT) is applied to the stack of similar patches. Expectation and variance of observations and parameters can be obtained from band-wise statistics and later refined using pre-filtered patches after a first restoration has been performed.

The family of homomorphic approaches transform the multiplicative noise into an additive one by taking the logarithm of the observed intensity / amplitude. Several papers have derived nonlocal estimators in this sense, e.g., [START_REF] Makitalo | Denoising of singlelook SAR images based on variance stabilization and nonlocal filters[END_REF] where an "adjust mean" step is used to deal correctly with the bias arising from the Gaussian assumption (i.e., debiasing step described for SME). Note that estimators that process directly SAR data (i.e., without log-transforms) are often preferable since the debiasing step is then unnecessary.

Step 3: Reprojection to image space -The second step of nonlocal methods provides estimates either for a single pixel (pixel-wise estimation), for a single patch (patch-wise estimation), or for the whole stack of patches (stack-wise estimation). The first option corresponds to basic NL means, already described above, so let us focus on the other two strategies.

The difference in patch-wise filtering is that all pixels in the patch, not just the central one, are estimated at once. Since each pixel is estimated several times, a suitable aggregation phase is necessary to combine all such estimates. In particular, we need to define a reprojection function, g(•), to get an estimate in the pixel domain: u(x) = g( u 1 (x), . . . , u K (x)) . What is more important, these estimates refer to different patches, with different reliability levels, an information that can be exploited to improve results. The reprojection can be performed through a weighted average of the K estimators:

u(x) = K k=1 α k u k (x) . (16)
The simplest form of aggregation is to consider uniform weights α k , as done in the blockwise NL-means [START_REF] Buades | A Review of Image Denoising Algorithms, with a New One[END_REF]. Another strategy is to set the weight associated with each estimate as inversely proportional to its variance [START_REF] Dabov | Image denoising by sparse 3-D transform-domain collaborative filtering[END_REF].

To illustrate why patch-wise estimation improves performance, let us consider the special case of a pixel near the boundary between two homogeneous regions. Since the patch centered on it is strongly heterogeneous, most other patches of the search area, coming from homogeneous regions on either side of the boundary, are markedly dissimilar from it, and contribute very little to the average. The estimate, thus, involves only a small effective number of predictors, those along the edge, which results in a high variance. As a result, a visible "halo" of residual noise is observed near edges, a phenomenon well-known in NL-means, also referred to as the rare patch effect. The target pixel, however, belongs to a large number of patches, not just the patch centered on it, many of them drawn from the homogeneous region the pixel belongs to. In patch-wise re-projection all these patches are included in the average reducing the estimate variance, especially if suitable weights are used to take into account the reliability of each contribution.

Let us now consider the third strategy, with stack-wise filtering. A first difference w.r.t. patch-wise filtering is that now all patches collected in the stack are collaboratively filtered before reprojecting them to their original position. The major improvement is that the stack is filtered in three dimensions, that is, not only along the stack but also in the spatial domain. In BM3D [START_REF] Dabov | Image denoising by sparse 3-D transform-domain collaborative filtering[END_REF] and, with necessary adjustments to the SAR domain, in SAR-BM3D [START_REF] Parrilli | A Nonlocal SAR Image Denoising Algorithm Based on LLMMSE Wavelet Shrinkage[END_REF], the whole stack, formed by just a limited number of similar patches, is wavelet transformed, Wiener filtered, and back transformed. By so doing, strong spatial structures are emphasized through filtering while random noise is efficiently suppressed. As a matter of fact, these techniques exhibit significant improvements especially in highly structured areas (edges, point reflectors, textures). The efficiency of collaborative filtering comes from the full exploitation of the redundancy of information in a stack of similar patches.

The box titled "Overview of nonlocal estimation methods in SAR imaging" gives a synthetic view of some of the main methods developed for nonlocal estimation in SAR imaging. Needless to say, performance depends on the setting of several parameters, like patch size and search area size, which should be related to image resolution, smoothing strength, and balance between original and pre-estimated data. In most of the nonlocal approaches these parameters are set by hand. Few works have considered semi-supervised setting or automatic setting with spatial adaptation [START_REF] Deledalle | NL-SAR: a unified Non-Local framework for resolution-preserving (Pol)(In)SAR denoising[END_REF]. Some sample experimental results that confirm the potential of nonlocal methods are presented in figure 2 for an amplitude image with SAR-BM3D [START_REF] Parrilli | A Nonlocal SAR Image Denoising Algorithm Based on LLMMSE Wavelet Shrinkage[END_REF] and in figure 3 for a polarimetric data with NL-SAR [START_REF] Deledalle | NL-SAR: a unified Non-Local framework for resolution-preserving (Pol)(In)SAR denoising[END_REF]. Visual inspection shows the performance of the approach in reducing strong fluctuations while preserving important features like targets and lines. Note that no systematic artefacts should be observed with these approaches unless the parameters are not set properly (e.g., no consideration of over-sampled data). A rigorous performance evaluation of nonlocal despeckling techniques is beyond the scope of this paper. Some frameworks for SAR despeckling evaluation and comparison are proposed in [START_REF] Martino | Benchmarking framework for SAR despeckling[END_REF] and [START_REF] Argenti | A tutorial on Speckle Reduction in Synthetic Aperture Radar Images[END_REF].

IV. OPEN ISSUES AND FUTURE TRENDS

Patch-based approaches provide the best performance todate for speckle reduction in SAR intensity images [START_REF] Martino | Benchmarking framework for SAR despeckling[END_REF] and polarimetric or interferometric SAR images [START_REF] Deledalle | NL-SAR: a unified Non-Local framework for resolution-preserving (Pol)(In)SAR denoising[END_REF]. Beyond speckle suppression, they improve parameter estimation, drastically enhancing radar measures. Therefore, they can be expected to have a strong impact, in the near future, on major applications of radar imaging, improving the biomass estimation with polarimetric -interferometric data; increasing the spatial resolution in urban monitoring with radar tomography; enabling more reliable phase unwrapping methods for interferometric SAR.

As a by-product of patch-based speckle reduction methods, several similarity criteria especially suited for SAR imaging have been established. These criteria are central to many applications: for classification and indexing using patch clustering; for change detection; for movement monitoring by patch tracking.

Patch-based methods are at their beginning and many open issues have yet to be solved. The speckle model consider so far (simple complex Gaussian) is known to inaccurately describe very high resolution images or textured areas. Introduction of more accurate models (e.g., Weibull, Fisher or generalized gamma distributions for amplitude, and corresponding matrixvariate polarimetric distributions) raises questions about the increased complexity of estimators and the possible loss of robustness with the increase of degrees of freedom. Another limit is the geometric deformations appearing on SAR images with elevated objects. Such deformations should be considered to perform joint restoration of images taken from multiple incidence angles.

Fig. 1 .

 1 Fig. 1. Typical fragments of SAR images (51 × 51 pixels), from the left: a homogeneous region, a line, a texture and a structure. For each target patch (green) several similar 8 × 8 patches (red) are easily found in the same fragment.

Fig. 2 .

 2 Fig. 2. Single-look TerraSAR-X image of Barcelona (image courtesy c Infoterra GmbH) and the radiometry estimated by the nonlocal method [11]. Images are 511 × 1043 pixels with a spatial resolution of 2.5 m.

Fig. 3 .

 3 Fig. 3. On the left, two PolSAR images of the area of Kaufbeuren (Germany) sensed by F-SAR, single-look, X-band (top), S-band (bottom) (image courtesy c DLR). On the center and right images, estimated polarimetric signatures using the nonlocal patch-based method [14]. Images are 400 × 512 pixels with a spatial resolution of 0.5 m.

  This modality (PolSAR) is widely used to study vegetation growing or urban areas. interferometric: The combination of two backscattered signals k 1 and k 2 measured by two close configurations of the acquisition systems can yield elevation information or ground displacement maps. In interferometric configurations, a composite signal k can be defined by the concatenation of the two received signals k = [k t 1 , k t 2 ] t . These can be single (InSAR) or multi-polarization (PolInSAR) signals.

Although speckle is itself a signal of possible interest, in the context of despeckling it is an undesired component, and hence customarily referred as "noise" with a slight abuse of terminology[START_REF] Argenti | A tutorial on Speckle Reduction in Synthetic Aperture Radar Images[END_REF]

This work has been supported in part by the following grants: ANR DEFI 09-EMER-008-01, ANR-11-IDEX-0007, ANR-11-LABX-0063, and MIUR-PRIN 2012: "Telerilevamento a risoluzione spaziale e spettrale molto elevata: un nuovo sistema integrato di analisi dei dati".

OVERVIEW OF NONLOCAL ESTIMATION METHODS IN SAR IMAGING

Nonlocal estimation methods perform the three steps depicted in the box "Nonlocal estimation in action". A great variety of methods dedicated to SAR images have been proposed over the last few years. These methods follow different paths to implement each of the three steps:

1) similar patches identification (choice of the similarity criterion); 2) estimation of radar properties (choice of the estimator); 3) reprojection of estimates onto the image space (choice of the domain). Below an overview of some of the main methods devoted to SAR imaging.


Myriam Bormans
email: myriam.bormans@univ-rennes1.fr

Marion Lengronne

Luc Brient

Charlotte Duval

Bormans Myriam

Lengronne Marion

Brient Luc

Duval Charlotte

Cylindrospermopsin accumulation and release by the benthic cyanobacterium Oscillatoria sp PCC 6506 under different light conditions and growth phases

Keywords: Benthic cyanobacteria, cylindrospermopsin content, intracellular, extracellular, light intensity, growth phase

    Cylindrospermopsin accumulation and release by the benthic cyanobacterium Oscillatoria sp. PCC 6506 under different light conditions and growth phases.

INTRODUCTION

Cyanobacteria are known to produce a variety of toxins, which have adverse effects on animals and humans [START_REF] Codd | Cyanobacterial toxins: risk management for health protection[END_REF]. These toxins include microcystins, cylindrospermopsins, saxitoxins, nodularins, anatoxins and more recently beta-methylamino-L-alinine or BMAA. Although microcystin is the only toxin routinely monitored for health risks, there are an increasing number of studies reporting on the presence of all types of toxins in waterbodies. In particular, cylindrospermopsin (CYN) is rapidly being recognised as one of the globally problematic freshwater toxin due to its ever expanding distribution from tropical to temperate zones [START_REF] Rücker | Concentrations of particulate and dissolved cylindrospermopsin (CYN) in 21 Aphanizomenon dominated lakes of North East Germany[END_REF][START_REF] Brient | First occurrence of cylindrospermopsin in freshwater in France[END_REF][START_REF] Sinha | Increased incidence of Cylindrospermopsis raciborskii in temperate zones -Is climate change responsible?[END_REF]) and its ability to bioaccumulate in freshwater organisms [START_REF] Kinnear | Cylindrospermopsin : A decade of progress on bioaccumulation research[END_REF].

CYN is a tricyclic alkaloid cytotoxin produced by several cyanobacterial species : Cylindrospermopsis raciborskii, Aphanizomenon ovalisporum, Aphanizomenon flos aquae, Anabaena bergii, Anabaena lapponica, Umezakia natans, Raphidiopsis curvata and other unidentified species. Recently, several oscillatoriales have been identified as producing CYN as Lyngbya wollei [START_REF] Seifert | First evidence for the production of cylindrospermopsin and deoxy-cylyndrospermopsin by the freshwater benthic cyanobacterium, Lyngbia wollei (Fallow ex Gomont) Spezialeand Dick[END_REF]) and Oscillatoria sp. [START_REF] Mazmouz | Biosynthesis of cylindrospermopsin and 7-epicylindrospermopsin in Oscillatoria PCC 6506 ; Identification of the gene cluster and toxin analysis[END_REF]. CYN is highly water soluble and is primary present in extracellular form [START_REF] Chiswell | Stability of cylindrospermopsin, the toxin from the cyanobacterium, Cylindrospermopsis raciborskii : Effect of pH, temperature and sunlight on decomposition[END_REF][START_REF] Rücker | Concentrations of particulate and dissolved cylindrospermopsin (CYN) in 21 Aphanizomenon dominated lakes of North East Germany[END_REF]. CYN degrades relatively slowly by photodegradation [START_REF] Wörmer | Natural photodegradation of the cyanobacterial toxins microcystin and cylindrospermopsin[END_REF] and biodegradation [START_REF] Wörmer | Cylindrospermopsin is not degraded by cooccurring natural bacterial communities during a 40-day study[END_REF] explaining relatively high extracellular concentrations in the water.

In the field, [START_REF] Wiedner | Seasonal dynamics of cylindrospermopsin and cyanobacteria in two German lakes[END_REF] found that CYN was essentially produced as extracellular form during the decline of a bloom. Some laboratory experiments on Cylindrospermopsis raciborskii [START_REF] Saker | Effects of temperature on growth and cylindrospermopsin content of seven isolates of C. raciborskii (Nostocales, Cyanophyceae) from water bodies in northern Australia[END_REF][START_REF] Hawkins | Phenotypical variation in a toxic strain of the phytoplankter, Cylindrospermopsis raciborskii (Nostocales, Cyanophyceae) during batch culture[END_REF][START_REF] Dyble | Effects of light intensity on cylindrospermopsin production in the cyanobacterial HAB species Cylindrospermopsis raciborskii[END_REF]) confirm this tendency by demonstrating an increased accumulation of extracellular CYN during the stationary growth phase.

Abiotic factors that influence the accumulation and release of CYN have been studied both in the field and in laboratory experiments. The effect of temperature has been studied showing globally that an increase in temperature results in a decrease of CYN accumulation [START_REF] Saker | Effects of temperature on growth and cylindrospermopsin content of seven isolates of C. raciborskii (Nostocales, Cyanophyceae) from water bodies in northern Australia[END_REF][START_REF] Preuβel | Response of cylindrospermopsin production and release in Aphanizomenon flos-aquae (cyanobacteria) to varying light and temperature conditions[END_REF][START_REF] Cires | Cylindrospermopsin production and release by the potentially invasive cyanobacterium Aphanizomenon ovalisporum under temperature and light gradients[END_REF]. Nutrient concentrations also play a role in CYN accumulation. In studies with Aphanizomenon ovalisporum, an increase of CYN accumulation with limiting phosphorus conditions was shown [START_REF] Bar-Yosef | Enslavement in the water body by toxic Aphanizomenon ovalisporum, inducing alkaline phosphatase in phytoplanktons[END_REF]) while higher CYN accumulation in cells grown in a culture medium with lower phosphorus concentration was also observed by [START_REF] Cires | Cylindrospermopsin production and release by the potentially invasive cyanobacterium Aphanizomenon ovalisporum under temperature and light gradients[END_REF]. Higher intracellular CYN concentration was also observed in controlled laboratory experiments with several strains of Cylindrospermopsis raciborskii in lower nitrogen medium [START_REF] Saker | Varied diazotrophies, morphologies, and toxicities of genetically similar isolates of Cylindrospermopsis raciborskii (Nostocales, Cyanophyceae) from Northern Australia[END_REF]. Light intensity has also been examined as a factor influencing CYN accumulation. [START_REF] Dyble | Effects of light intensity on cylindrospermopsin production in the cyanobacterial HAB species Cylindrospermopsis raciborskii[END_REF] indicated an increase of total CYN concentration with an increase in light intensity between 18 and 75 μE m -2 s -1 for the species Cylindrospermopsis raciborskii at 25°C. Similarly [START_REF] Cires | Cylindrospermopsin production and release by the potentially invasive cyanobacterium Aphanizomenon ovalisporum under temperature and light gradients[END_REF] observed a significant increase of intracellular CYN between 15 and 60 μE m -2 s -1 on the species Aphanizomenon ovalisporum at 28°C. However, according to [START_REF] Preuβel | Response of cylindrospermopsin production and release in Aphanizomenon flos-aquae (cyanobacteria) to varying light and temperature conditions[END_REF], the impact of light intensity is temperature dependent, it increased at 20°C and decreased at 25°C for Aphanizomenon flos aquae for light ranging between 10 and 60 μE m -2 s -1 .

To our knowledge, all of the studies reported in the literature on the role of abiotic factors in CYN accumulation have involved planktonic species. As CYN concentration has recently been measured on benthic species, we examined how abiotic factors affect CYN accumulation and release by a benthic species. In particular, this study examines the role of light intensity and growth phase on both intracellular and extracellular CYN concentrations by the benthic Oscillatoria sp. PCC 6506 recently identified as producing CYN [START_REF] Mazmouz | Biosynthesis of cylindrospermopsin and 7-epicylindrospermopsin in Oscillatoria PCC 6506 ; Identification of the gene cluster and toxin analysis[END_REF] under unlimited nutrient conditions. We hypothesize that CYN content will vary as a function of stressed conditions, therefore we expect differences between growth phases and between light levels.

MATERIALS AND METHODS Strain and cultures conditions

The strain PCC 6506 is a filamentous species with slightly flexed trichomes. The CYN producing strain Oscillatoria sp. PCC 6506 was provided by the Pasteur Culture Collection of Cyanobacteria (Pasteur Institute in Paris) as an axenic culture which was grown in a BG11 medium at 20°C in a 14h/10h light dark cycle. Three light intensities were tested (2, 10 and 20 μE m -2 s -1 ) after a preliminary experiment identified that the culture was not growing at higher light intensity. Prior to the experiment each culture was pre-adapted for three weeks to its appropriate light intensity. All experiments were performed in triplicate batch cultures. An initial biomass of 10 5 cells mL -1 was used in each culture. Toxin concentrations were measured at the same time (day 2, day 23 and day 51) for all three light levels.

Biomass and growth kinetics

Oscillatoria sp cell density was estimated by converting the OD at 750 nm into cell density (cells mL -1 ) based on a linear relationship between these two parameters. The specific growth rates, μ (day -1 ), were calculated during the exponential growth phase according to the following equation:

μ=

(ln C t+t -ln C t )/(t)
where C t and C t+t represent the cell density (cells mL -1 ) at times t and t + t, respectively.

Cell counts were obtained with a Nageotte cell on an optical microscope counting a minimum of 2000 cells. Optical density was measured twice a week to follow the evolution of the biomass, identify growth phases and calculate growth rates. The toxin concentration was tested prior to the experiment to determine appropriate volumes to sample. Samples of 1 mL were collected in each replicate during the different phases (latent, exponential and stationary) and analysed for intracellular and extracellular CYN concentrations.

Toxin analyses

Separation of intracellular and extracellular CYN was achieved by low vacuum filtration on a GF/F filter. The filtrate was stored at -18°C for extracellular analysis. For the intracellular form, the biomass recovered on the filter was dried for 3h at 35°C and resuspended in 5 mL of ultrapure water before being stored with the filter at -18°C. After thawing, extractions were performed according to [START_REF] Welker | HPLC-PDA detection of cylindrospermopsinopportunities and limits[END_REF] and adapted for the specification of strain PCC 6506 as of [START_REF] Mazmouz | Biosynthesis of cylindrospermopsin and 7-epicylindrospermopsin in Oscillatoria PCC 6506 ; Identification of the gene cluster and toxin analysis[END_REF]. Samples (biomass and filter) were subjected to ultrasounds using a Sonics Vibracell probe for 60s at 130 W then placed on an orbital shaker at 300 rpm for 1h at room temperature. They were again subjected to 60s of ultrasounds and filtered on 0.45 μm nylon filter.

Concentrations were measured using a Cylindrospermopsin ELISA kit from Abraxis and analysed with a spectrophotometer ELX800UV from BioTEK instruments. The detection limit was estimated at 0.04 μg L -1 and the range between 0.04 and 2.5 μg L -1 . Therefore, the samples had to be diluted with ultrapure water before analysis. Concentrations of both intracellular and extracellular forms are reported per cell.

Statistical analysis

Results are expressed as mean +/-standard deviations. One-way ANOVA for non equal variance followed by a post-hoc Tukey test was performed for all statistical tests during each of the growth phases with significance threshold set at 0.05.

RESULTS

A high correlation (R 2 = 0.92 ; n = 45 not shown) was found between optical density at 750 nm and cell numbers estimated by counting on an optical microscope. This relation, which was similar for the three light intensities, was used to infer the evolution of biomass. Growth rates and length of growth phases varied with light intensities. Growth rates were significantly different (p<0.05, Tukey test) between each light intensity with the highest value of 0.136 ± 0.003 day -1 at 10 μE m -2 s -1 , an intermediate value of 0.118 ± 0.005 day -1 at 2 μE m -2 s -1 and the lowest value of 0.100 ± 0.003 day -1 at 20 μE m -2 s -1 . Very low variance was observed between the triplicates for each modality. While the latent phase length (4 days) was similar for all light intensities, the exponential growth phase was longer at 10 μE m -2 s -1 (40 days) and was equal to 30 days at the other two light intensities.

At the beginning of the experiment, during the latent phase, there was no significant difference in the CYN content (either forms) between the replicates cultured at different light intensities (p>0.05, Tukey test). We observed an intracellular CYN concentration varying between 1.9 and 2.6 fg cell -1 and an extracellular CYN concentration varying between 9.3 and 12.4 fg cell -1 with over 80% as extracellular CYN (Fig. 1). During the exponential growth phase the highest proportion of the toxin was again in extracellular form at all light levels varying between 56 % at 2 μE m -2 s -1 to 84 % at 10 μE m -2 s -1 . CYN concentrations were significantly lower (p<0,05, Tukey test) at 2 μE m -2 s -1 for both forms with values of 1.40 ± 0.04 fg cell -1 as intracellular and 1.77 ± 0.06 fg cell -1 as extracellular form compared to the other light levels (Fig. 1). During the exponential growth phase, we therefore observed a significantly lower (p<0.05, Tukey test) total CYN content at 2 μE m -2 s -1 compared to the other two light levels.

During the stationary phase, again most of the toxin was in extracellular form with proportions varying with light levels between 89 % at 10 μE m -2 s -1 and 96 % at 2 μE m -2 s -1 .

Both intracellular and extracellular CYN concentrations varied with light intensity and were significantly higher (p<0.05, Tukey test) at 20 μE m -2 s -1 than at the other light levels. Total CYN content was maximal at 20 μE m -2 s -1 during the stationary phase with concentrations per cell of 19.6 ± 2.4 fg cell -1 (Fig. 1). For a typical biomass observed in the field of 10 5 cells mL -1 , these values would be equivalent to 2 μg L -1 , a value twice the recommended drinking water guideline of 1 μg L -1 [START_REF] Humpage | Oral toxicity of the cyanobacterial toxin cylindrospermopsin in male Swiss albino mice: Determination of no observed adverse effect level for deriving a drinking water guideline value[END_REF].

Although the maximum total CYN content during the exponential growth phase coincided with the maximum growth rate (at 10 μE m -2 s -1 ), the lowest CYN contents at 2 μE m -2 s -1 were not associated with the lowest growth rates. Therefore we did not observe a consistent relationship between growth rate and either intracellular or total CYN content (Fig. 2).

DISCUSSION

In this study, we showed a dominance of extracellular CYN content regardless of the growth phase and the light level for the benthic species Oscillatoria sp. Dominance of extracellular CYN (62%) for the same strain Oscillatoria sp. PCC 6506 was also observed by [START_REF] Mazmouz | Biosynthesis of cylindrospermopsin and 7-epicylindrospermopsin in Oscillatoria PCC 6506 ; Identification of the gene cluster and toxin analysis[END_REF] after 11 days of growth at 20°C and in a nutrient rich medium and a constant light level of 15 μE m -2 s -1 , which was likely to correspond to the exponential phase. The results presented here on the CYN content for a benthic species being mostly extracellular are in accordance with results for planktonic species, although very few studies have reported on CYN release and presented extracellular concentrations values. Dominance of extracellular CYN was observed in the field in lakes dominated by the Aphanizomenon genus [START_REF] Wiedner | Seasonal dynamics of cylindrospermopsin and cyanobacteria in two German lakes[END_REF]. In laboratory experiments, extracellular proportions varied with abiotic factors and species. [START_REF] Cires | Cylindrospermopsin production and release by the potentially invasive cyanobacterium Aphanizomenon ovalisporum under temperature and light gradients[END_REF] reported over 60% of extracellular CYN at extreme temperature for Aphanizomenon ovalisporum and [START_REF] Preuβel | Response of cylindrospermopsin production and release in Aphanizomenon flos-aquae (cyanobacteria) to varying light and temperature conditions[END_REF] reported extracellular CYN concentration up to 58% under stress conditions, suggesting that the release of CYN was stress induced. Increases in extracellular concentrations under stress conditions have also been reported for microcystin (MC) producers associated with high light [START_REF] Wiedner | Effects of light on the microcystin content of Microcystis strain PCC 7806[END_REF] or grazing pressure [START_REF] Zhang | The effect of Poterioochromonas abundance on production of intra and extracellular microcystin-LR concentration[END_REF]. Nevertheless, for MC producers, the majority of the toxin is in intracellular form except during cell lysis.

Although the CYN concentration was found to be mostly in extracellular form, we observed a growth phase effect. Our results suggest relatively higher intracellular CYN content during the exponential growth phase and higher extracellular CYN content during the stationary phase. Very few studies have examined the CYN accumulation and release during the stationary phase [START_REF] Hawkins | Phenotypical variation in a toxic strain of the phytoplankter, Cylindrospermopsis raciborskii (Nostocales, Cyanophyceae) during batch culture[END_REF][START_REF] Dyble | Effects of light intensity on cylindrospermopsin production in the cyanobacterial HAB species Cylindrospermopsis raciborskii[END_REF]). However, they all report an increase of extracellular form during the stationary phase in accord with an increase observed in the field at the end of the bloom in a seasonal dynamics [START_REF] Wiedner | Seasonal dynamics of cylindrospermopsin and cyanobacteria in two German lakes[END_REF]. This characteristic seems therefore to be common to all CYN producers studied so far.

We observed also a light effect on CYN accumulation and release. A statistically significant lower concentration of extracellular CYN was observed at the intermediate light level during the stationary phase. Due to the higher biomass reached this result can be in part due to a dilution effect, which occurs when the growth rate is higher than the toxin production rate. Observed higher extracellular CYN concentration at lower and higher light levels are consistent with a more limiting environment associated with stressed conditions. Indeed, stress related release of extracellular CYN has been suggested under N limitation [START_REF] Preuβel | Response of cylindrospermopsin production and release in Aphanizomenon flos-aquae (cyanobacteria) to varying light and temperature conditions[END_REF]). We also observed a light intensity effect with lower CYN content of both intracellular and extracellular form during the exponential phase at low light leading to a lower total CYN content. This result is similar to that of planktonic species, which tend to show higher accumulation of intracellular CYN concentration at higher light levels.

We did not observe a monotonic relationship between growth rate and either intracellular or total CYN concentration. This result is similar to published studies on other CYN producers, which do not show a consistent relationship between CYN concentration and µ. Indeed high CYN concentrations have been measured at high light intensities in Cylindrospermopsis raciborskii when growth rates were not at their maximum [START_REF] Dyble | Effects of light intensity on cylindrospermopsin production in the cyanobacterial HAB species Cylindrospermopsis raciborskii[END_REF]. Similarly, [START_REF] Saker | Varied diazotrophies, morphologies, and toxicities of genetically similar isolates of Cylindrospermopsis raciborskii (Nostocales, Cyanophyceae) from Northern Australia[END_REF] found high intracellular CYN concentrations in low nitrogen Cylindrospermopsis raciborskii cultures while growth rates were suboptimal. There were no correlations between growth rates associated with variations of both temperature and light and either intracellular or total CYN contents in studies on Aphanizomenon flos aquae [START_REF] Preuβel | Response of cylindrospermopsin production and release in Aphanizomenon flos-aquae (cyanobacteria) to varying light and temperature conditions[END_REF][START_REF] Cires | Cylindrospermopsin production and release by the potentially invasive cyanobacterium Aphanizomenon ovalisporum under temperature and light gradients[END_REF]. This lack of relationship between growth rate and CYN content contrasts with MC producers which often show a strong linear relationship between intracellular MC and µ [START_REF] Orr | Relationship between microcystin production and cell division rates in nitrogenlimited Microcystis aeruginosa cultures[END_REF][START_REF] Briand | Evidence of the cost of the production of Microcystins by Microcystis aeruginosa under differing light and nitrate environmental conditions[END_REF] suggesting different functional roles for these toxins.

In summary, we found that a benthic species produced predominantly extracellular CYN with an increase during the stationary phase in accord with planktonic CYN producers possibly indicating a stress response. No correlation was found between growth rate and CYN content again in a similar way to planktonic CYN producers' response. Hence the results presented in this study, although preliminary, suggest many similarities with planktonic CYN producers. Further studies should include testing intra species variability amongst Oscillatoria as well as other benthic species before generalization can be attempted. As the CYN toxin is predominantly present in an extracellular form in the environment, its presence is particularly problematic in water bodies used for drinking water purposes or recreational activities. In view of major ecological implications from benthic CYN producers, which include grazing by benthic organisms bioaccumulating in the food chain, it is somewhat surprising that benthic cyanobacteria have received so little attention.

Fig. 1 :

 1 Fig. 1 : Intracellular and extracellular CYN concentrations (fg cell -1 ) as a function of light during the latent, exponential and stationary growth phase

Fig. 2 :

 2 Fig. 2 : Total and intracellular CYN concentrations (fg cell -1 ) versus growth rates (d -1 ) during the exponential phase at different light intensities.

Acknowledgements

This work was financed by the National Agency for Security of Environment and Health (ANSES) through the TOXCYN project. The experiment was run in the phytotronic chambers of the experimental facilities ECOLEX of ECOBIO.