text:
Alexandre Boulch

Pauline Trouvé

Elise Koeniguer

Fabrice Janez

Bertrand Le Saux

LEARNING SPECKLE SUPPRESSION IN SAR IMAGES WITHOUT GROUND TRUTH: APPLICATION TO SENTINEL-1 TIME-SERIES

Keywords: SAR, speckle filtering, deep learning

This paper proposes a method of denoising SAR images, using a deep learning method, which takes advantage of the abundance of data to learn on large stacks of images of the same scene. The approach is based on the use of convolutional networks, used as auto-encoders. Learning is led on a large pile of images acquired on the same area, and assumes that the images of this stack differ only by the speckle noise. Several pairs of images are chosen randomly in the stack, and the network tries to predict the slave image from the master image. In this prediction, the network can not predict the noise because of its random nature. Also the application of this network to a new image fulfills the speckle filtering function. Results are given on Sentinel 1 images. They show that this approach is qualitatively competitive with literature.

INTRODUCTION

Since radar imaging systems are coherent, radar images are corrupted by "speckle" noise and thus look visually very noisy. Denoising Synthetic Aperture Radar images is a common pre-processing and has been the object of several works. However most of existing methods rely either on a strong statistical modeling of the SAR signal, or on machine learning requiring a non-noisy ground truth or objective image, which is not always available. Moreover, the specificity of this data still makes this type of work marginal.

Whether in computer vision or radar remote sensing literature, we can generally discriminate the same categories of algorithms. The methods the most used and easy to implement are based on the observation of the local neighborhood of the pixel. This is the case with local mean or median, bilateral filtering [START_REF] Tomasi | Bilateral filtering for gray and color images[END_REF] or the σ filter [START_REF] Lee | Digital Image Enhancement and Noise Filtering by Use of Local Statistics[END_REF] and its SAR counterpart for multiplicative noise [START_REF] Lee | Improved Sigma Filter for Speckle Filtering of SAR Imagery[END_REF]. Another family of approaches searches for similar patches and operates a weighted sum of these patches to reduce the noise. It is the case for NL-means [START_REF] Buades | A non-local algorithm for image denoising[END_REF] variation for SAR data NL-SAR [START_REF] Deledalle | NL-SAR: A Unified Nonlocal Framework for Resolution-Preserving (Pol)(In)SAR Denoising[END_REF]. In BM3D [START_REF] Dabov | Image denoising by sparse 3-D transform-domain collaborative filtering[END_REF], the authors group similar patches and denoise globally at group level. An extension to SAR, SAR-BM3D, is proposed in [START_REF] Parrilli | A Nonlocal SAR Image Denoising Algorithm Based on LLMMSE Wavelet Shrinkage[END_REF] by taking into account the multiplicative aspect of radar noise. Finally, more recent approaches tackle the denoising problem using machine learning tools, particularly deep convolutional neural networks. It is a very active field, among the papers we can quote the convolutional version of BM3D [START_REF] Yang | BM3D-Net: A Convolutional Neural Network for Transform-Domain Collaborative Filtering[END_REF] or the network of [START_REF] Zhang | Learning deep cnn denoiser prior for image restoration[END_REF] which only uses seven dilated convolutions and reaches very high performances. However, this type of methods makes assumptions about the noise model and has never been tested to our knowledge on SAR images. Moreover, it does not benefit from the redundancy of time series.

Today, SAR image series as Sentinel 1 become easily accessible. The amount of temporal acquisitions on a same site is a benefit to consider to improve quality of images. In this paper we investigate the gain of denoising approaches for multitemporal SAR images, in particular for change detection.

Our contribution is two-fold. First, we present a denoising method, based on the deep neural networks [START_REF] Zhang | Learning deep cnn denoiser prior for image restoration[END_REF] trained without ground truth, but only using data redundancy of time series of SAR images. We also introduce a local histogram loss that improves visual performances of our networks, and compare our results with alternative methods. Second, we show that change detection algorithms can benefit from speckle filtering.

The paper is organized as follows: section 2 presents the denoising method and the training process and section 3 exposes the results of speckle removing on single image denoising and change detection.

AUTOENCODED DENOISER

Let X be an observed image, and X * be the objective image, for any noise model. We also suppose that:

X = f (X * , Σ) (1)
where f is a noise model function, and Σ is the noise component, supposedly independent from X * . Our goal is to create a transfer function Φ such that Φ(X) ≈ X * . This Φ function is learned using our neural network. Please note that one strength of our approach is that we never use an explicit expression of the noise model.

In the following paragraph, we illustrate the method with additive noise (X = X * + Σ) and multiplicative noise (X = X * * Σ).

Unsupervised denoising. The usual approach to denoise by machine learning is, given an image without noise (the objective), add noise to create the noisy image and try to revert the process by a supervised machine learning method. In this study, we do not have access to X * , so supervised machine learning techniques cannot be directly applied. To circumvent this issue, one could use supervised learning by predicting the a temporal mean over the area, but that would require a large stack, i.e large temporal horizon and changes between an image and the target may not be considered as inexistent (e.g. for vegetation). Instead we exploit the small revisit time of Sentinel-1. Given two acquisitions X 1 and X 2 , for additive and multiplicative noise model:

X 1 = X * 1 +Σ 1 andX 2 = X * 2 +Σ 2 = X * 1 +(X * 2 -X * 1 )+Σ 2 (2)
X 1 = X * 1 * Σ 1 and X 2 = X * 2 * Σ 2 = X * 1 * (X * 2 /X * 1 ) * Σ 2 (3) where (X * 2 -X * 1 ) (resp. (X * 2 /X * 1 )
) is the structural change image, representing the changes between X 1 and X 2 not related to noise.

First, given the small revisit time of a Sentinel-1 time series, we suppose the change are small between two consecutive dates: (X * 2 -X * 1 ) = 0 (resp. X * 2 /X * 1 = 1). Second, considering the two noise vectors Σ 1 and Σ 2 are independent realizations of the noise process, a statistical estimator aiming at predicting X 2 given X 1 cannot do better than predict X * 2 . Following these assumptions, we train our estimator to predict X 2 given X 1 .

Histogram loss. The loss criterion is the objective function of the optimization process for the previously described network. It should reach a minimum value when predicted values and objective values are similar.

2 and 1 losses are widely used for regression task. However these losses deal with pixels independently without taking into account the local arrangement of the pixel values, i.e. if i losses are first order penalization (value penalization), we would like a second order penalization (local order penalization).

Given a pixel x ∈ X and its neighborhood N x , the histogram H k (N x ) (with k bins) is a good representation of the local distribution around x. Our is simply defined by a 2 distance on the histograms vector. The gradients for back propagation is the differentiation of the previous distance.

Due to the very wide value range, the histograms are computed without scales (first bin at min value, last bin at max value). To retrieve the missing location information (value information at x), we define our loss as a weighted sum of 1 (for location) and histogram loss (for local arrangement):

L(Φ(X), X * ) = (1-λ) X-X * 1 +λ H(X)-H(X * ) 2 (4)
Inference and training processes. The input of the network is normalized (mean and standard deviation are memo-rized to restore the original dynamics). In order to scale up to large images, we do not feed the network with the whole image but patches. To prevent border effect, we use sub-images with an overlap of half the patch size. The result Y is then convoluted with a mask M (linear ramp with zero value at border):

Y = (Φ(X) . σ(I) + Ī) * M ( 5
)
where X is the input of the network, I the original input image and, Ī the mean of I and σ(I) its standard deviation, and * denotes the convolution.

To train the network, given a stack of registered Sentinel-1, we generate on the fly patch pairs by randomly picking sub-images in one image and the time-ordered next or previous one with the same polarization. We also randomly flip or transpose the image for data augmentation.

EXPERIMENTS

Data and networks. A Sentinel-1 stack composed of 64 images with both VH and VV polarization has been trained in a unsupervised fashion. The footprint is around Saclay at the South of Paris, images were acquired between 2015 and 2017. Results will be presented both on Saclay for the auto encoder and on another stack centered on Valencia. For the experiments we use the network from [START_REF] Zhang | Learning deep cnn denoiser prior for image restoration[END_REF] (referred in the following as DCNN for Dilated Convolutional Neural Network) trained in a residual fashion. It does not operate a dimension reduction and use only seven convolutions, resulting in a lightweight network. Results will also be compared with another deep approach, Unet [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF], and two classical temporal approaches based on patches but without training, BM3D and SAR-BM3D.

Denoising. Figure 1 presents different results obtained on a detail of the training set (a) and the temporal mean over all the training set (b). Except for the BM3D (c) and SAR-BM3D (d), the dynamic is the same on each image, black (resp. white) is set to the 2 nd percentile (resp. 98 th percentile) of the original image. The DCNN network has been trained with different loss functions: 2 , 1 and Histogram loss (λ = 0.9, 3 bins in histograms and a radius of 3 for neighborhood).

Compared to the original image, applying our network improves greatly the visual aspect of the images. The DCNN performs well with 1 (g) and Histogram loss (h). 2 loss (e) leads to more blurry images. The same method applied with a different architecture, Unet [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF], trained with 1 loss performs worse than DCNN (f). The network succeeds in removing the noise while keeping the bright pixels corresponding to reflectors such as human structures. The histogram loss on DCNN removes greatly the bright halo around scatterers, sometimes hallucinating very dark pixel around the bright point. For comparison with existing methods, we have also run BM3D and SAR-BM3D on the same image. The standard deviation parameter of BM3D has been set to 10 and the input is the log image because it has given better results. In both cases, the result is noisier than ours. This can partly be explained by the differences between the Sentinel-1 and the data they were developed for: optical data (BM3D) and higher resolution SAR, e.g. TerraSAR-X (SAR-BM3D).

Figure 2 presents the results on Valencia, a scene not part of the autoencoding set (red and blue channels for VV and green channel for VH). Most of the noise has been removed, e.g. around the harbor. However, dense urban areas tend to be smoothed. In our opinion, this is the result of three phenomena. First, the training set is not representative: it does not contain dense urban area and has no variability in acquisi- tion parameter such as incidence angle. Second, it only contains one scene, the network may have over-fitted. Finally, the training set is in SLC geometry while Valencia scene is GRD geometry. Still the approach proved robust to various changes in the scene.

Multi-temporal data processing Speckle filtering can also be considered to improve the performance of change detection or activity detection in time series. Also, we considered the impact of the DCNN filtering process for two classic scenarios: bi-date change detection and activity detection on the entire stack.

For the first case, we consider the first and the last image of the stack, we compute a RGB color composition, and also the ratio C of equation [START_REF] Dabov | Image denoising by sparse 3-D transform-domain collaborative filtering[END_REF]. For the second case, we compute the temporal coefficient of variation γ, calculated on the whole stack, equation [START_REF] Parrilli | A Nonlocal SAR Image Denoising Algorithm Based on LLMMSE Wavelet Shrinkage[END_REF], where µ and σ are the temporal mean of the backscattered amplitude, and standard deviation.

C = min( X 1 X 2 , X 2 X 1 ) (6) γ = σ µ (7)
The different results are presented in figure 3, both without and with filtering, on an area of Saclay that contains mostly cultivated fields.

Regarding the change detection between two images, the colored composition clearly shows the effects of smoothing on the various cultivated crops. The ratio criterion is much more contrasted after the filtering than before, revealing more easily changes.

The statistics of the coefficient of variation are completely modified by the filtering. It is known that for a classical speckle distribution such as Nakagami law, this coefficient is constant and depends only on the Equivalent Number of Looks. Indeed, without filtering, we find that its statistical distribution is uni-modal all over the image. It is therefore difficult to extract the changes. With filtering, the distribution of this coefficient becomes bimodal: it is then much easier to extract changes by thresholding, mainly the fields. In any case, removing the noise greatly helps the interpretation, particularly for changes on natural areas such as agricultural areas. Finally, figure 3(d) shows the change map after thresholding using simple mean / standard deviation for raw data and Otsu's method [START_REF] Otsu | A threshold selection method from gray-level histograms[END_REF] for the bimodal filtered product.

CONCLUSION

An original method to learn a denoising convolutional neural network has been presented. The network is trained in an autoencoder fashion by trying to predict another image of the same temporal stack. The network fails to predict the random noise of the objective image, producing a denoised version of the input image. It is therefore envisaged to extend the training set from one time series to multiple in different places (urban, agricultural, mountains . . . ) and acquisition conditions (incidence, sensors) to improve robustness and generality of the approach. We also plan to test simulated data allowing us to provide quantitative results.

  (a) Original image. (b) Temporal mean. (c) BM3D with 10 as std. (d) SAR-BM3D. (e) Unet, 2 loss. (f) Unet, 1 loss. (g) Dilated CNN, 1 loss. (h) Dilated CNN, Histo. loss.

Fig. 1 .

 1 Fig. 1. Detail of Saclay stack original and processed with DCNN, different loss functions and other alternative approaches.

  (a) Original image. (b) DCNN, Histo. loss.

Fig. 2 .

 2 Fig. 2. Detail of Valencia original (left) and denoised (right).

  (a) Red: I 1 , Cyan: I 2 (b) Ratio Criterion C (c) γ (d) Change map. Each thumbnail contains both a result without filtering on the top and with filtering on the bottom. (a) Image Pair composition. Red: I1, cyan: I2, (b) Ratio Criterion between I1 and I2, (c) Temporal Coefficient of Variation on N images, (d) Threshold on (c).

Fig. 3 .

 3 Fig. 3. Detail of Saclay products.

MEDUSA project at w3.onera.fr/medusa

DeLTA project at delta-onera.github.io

Acknowledgements This work is supported by two research programs at ONERA: MEDUSA 1 , remote sensing images processing in big data context and DeLTA 2 , machine learning for aerospace applications.


domain: spi phys

text:
Clément Maës

Grégory Vincent

Fernando González-Posada Flores

Laurent Cerutti

Riad Haïdar

Thierry Taliercio

Semiconductors nanostructures for spectral filtering

We present theoretical and experimental study of nanostructured guided-mode resonant filter, made of a highly doped InAsSb grating and a GaSb waveguide.

In the context of infrared spectral filtering, nanostructured components offer simple filter architectures such as GMR (Guided mode resonance). This architecture consists of a planar waveguide and a grating that couples the incident wave to the guided mode. These structures are generally composed entirely of dielectric materials where quality factors are high and losses are low [START_REF] Fehrembach | High Q Polarization Independent Guided-Mode Resonance Filter With "Doubly Periodic" Etched Ta2O5 Bidimensional Grating[END_REF]. In Ref. [START_REF] Sakat | Guided mode resonance in subwavelength metallodielectric free-standing grating for bandpass filtering[END_REF], authors proposed the use of a metallic grating in order to increase the spectral bandwidth, but this leads to losses.

The current trend is to integrate these filters directly at the level of the detection pixel [START_REF] Bierret | Field extension inside guided-mode-resonance filters under a focused beam[END_REF] but at the cost of many manufacturing steps and potential incompatibility with the detector materials. We thus propose a GMR filter made of semiconductors in order to guarantee a monolithic integration. We present the numerical and experimental study of component made of InAsSb and GaSb, which are the materials used in particular for superlattice photodetectors epitaxy [START_REF] Rodriguez | MBE growth and characterization of type-II InAs/Gasb superlattices for mid-infrared detection[END_REF] or in lattice parameter matching. The grating of the GMR filter is made of heavily doped InAsSb, while the waveguide is made of undoped GaSb. In order to demonstrate the filter function, we consider that the GMR is deposited on a GaAs substrate (Figure 1). We define a component geometry operating in the far infrared spectral range (8 μm -14 μm, LWIR), where the highly doped InAsSb behaves as a metal (doping level is N = 5.5e19 cm -3 ). The GaSb is transparent in the LWIR and we have taken a GaAs substrate because it has a refractive index of 3.27, lower than that of GaSb (3.7), which is essential to guide the wave. In the legend of Figure 1(a), we give the opto-geometric parameters of the component. With Figure 1(b), we show a normal incidence transmission spectrum calculation, in transverse magnetic polarization. This theoretical result is obtained using a calculation method RCWA (Rigorous coupled-wave analysis) [START_REF] Hugonin | Reticolo software for grating analysis[END_REF]. We observe a resonant transmission at λ = 12.67 μm, with a maximum transmission Tmax = 81.85%. The permittivity of the InAsSb was modeled with a Drude function, where we took into account an effective mass of 0.1273 mo. The high carrier density is at the origin of this high effective mass. We have evaluated it thanks to reflection measurements, performed on an unstructured GaAs -GaSb -n ++ -InAsSb stack [START_REF] Taliercio | Brewster "mode" in highly doped semiconductor layers: an all-optical technique to monitor doping concentration[END_REF].

We developed a fabrication process in IES facilities to realize a sample. It consists of a GaAs substrate where are grown by solid source molecular beam epitaxy a thick layer of totally relaxed GaSb (the waveguide) and a thick layer of n ++ -InAs0.91Sb0.09 lattice matched to GaSb. On n ++ -InAsSb layer, the grating geometry is defined with contact photolithography and it is then etched with reactive ion etching (RIE) process.

Fig. 1 (

 1 Fig. 1 (a) Guided-mode resonance filter composed of a GaAs (n=3,27) substrate, a waveguide in GaSb (n=3,7) and a grating in InAsSb doped at 5.5e19 cm -3 . d = 3.9 μm; w = 1.2 μm; tg = 1.1 μm and tg = 2.2 μm. (b) Transmission spectra calculated in TM polarization and normal incidence. (c) Scanning electron microscope image of a sample (d=4 μm, w=1.9 μm, tg =1.26 μm and tw =2.8 μm).

Figure 1 (

 1 c) shows a top view scanning electron microscope image of the component, where we can evaluate the anisotropy of the etching and measure the lateral geometries of the grating: d = 4 μm and w = 1.9 μm. Transmission measurements of the sample is in progress in our laboratory.


text:
Matthieu Piniard
email: matthieu.piniard@onera.fr

Pascal Picart

Béatrice Sorrente

Gilles Hug

Decorrelation-induced speckle phase noise in twowavelength digital holographic profilometry

Keywords:

This paper proposes a realistic wavelength decorrelation induced speckle noise simulator. The investigation of the dependence of the coherence factor versus the surface shape, the surface roughness and the wavelength change is carried out.

Introduction

Digital holographic two-wavelength profilometry is a very efficient technique for the measurement of surface shapes [START_REF] Schiller | Multiwavelength digital holography: height measurements on linearly moving and rotating objects[END_REF][START_REF] Seebacher | The determination of material parameters of microcomponents using digital holography[END_REF][START_REF] Kolenovic | Miniaturized digital holography sensor for distal threedimensional endoscopy[END_REF][START_REF] Kühn | Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition[END_REF][START_REF] Falldorf | Reduction of speckle noise in multiwavelength contouring[END_REF][START_REF] Agour | Speckle noise reduction in single-shot holographic two-wavelength contouring[END_REF]. Due to the surface roughness, the phase extracted from each numerically reconstructed image is speckled. It follows that the phase difference permitting to measure the surface shape is corrupted by speckle decorrelation noise. This decorrelation phase noise is closely related both to the angle of illumination and/or the angle of observation and to the small change in the speckle pattern when changing the wavelength. This paper considers the influence of the wavelength shift. In recent work, the coherence factor of the speckle field was used for quantitative appraisal of the impact of decorrelation noise [START_REF] Poittevin | Quality assessment of combined quantization-shot-noise-induced decorrelation noise in high-speed digital holographic metrology[END_REF]. It was found that a coherence factor higher than 0.85 is required to perform high quality measurements. Although speckle decorrelation was deeply studied by few authors [START_REF] Goodman | Speckle Phenomena in Optics: Theory and Applications[END_REF][START_REF] Montresor | Quantitative appraisal for noise reduction in digital holographic phase imaging[END_REF], especially from the point of view of intensity [START_REF] George | Space and wavelength dependence of speckle intensity[END_REF], the dependence of the phase versus the surface roughness and wavelength has not been investigated. In this paper, we present a realistic wavelength decorrelation induced speckle noise simulator considering the surface shape and roughness. The investigation of the dependence of the coherence factor versus the roughness and the wavelength change is carried out and permits to determine sets of wavelength couples, for a given shape and roughness, which yield a convenient coherence factor.

Realistic two-wavelength holographic simulator

In order to evaluate the influence of decorrelation noise in the process of 2-wavelength digital holography, a realistic numerical simulation was developed. The goal of the simulation is to produce phase map at two different wavelengths with corruption by speckle decorrelation noise having the adequate probability density function. In experiments, the amount of speckle phase decorrelation is naturally controlled by the numerical aperture of the setup and by the surface shape and roughness. The arrangement to produce speckle phase decorrelation at two wavelengths is depicted in Fig. 1. The surface has a given surface shape. Its roughness has Gaussian statistics and correlation length. The surface is sequentially illuminated at normal incidence by a plane wave at, first, λ 1 , last λ 2 . The value of R u is adjusted to control the speckle grain size in the image plane and to simulate realistic images. The surface shape with roughness, h(x,y)=h 0 (x,y)+ρ(x,y), generates an optical phase ψ=4πh/λ. The surface is simulated with the membrane MATLAB function with realistic amplitude of any micro-object (~100 µm). In order to get the phase change due to twowavelength illumination, and including speckle phase decorrelation, the procedure is as follows: first calculate the speckle image at λ 1 , second at λ 2 , last calculate their phase difference and evaluate the speckle noise. From the realistic simulator, the speckle phase decorrelation noise follows the theoretical statistics as given in [START_REF] Montresor | Quantitative appraisal for noise reduction in digital holographic phase imaging[END_REF]. Figure 2 shows data from the simulator: Fig. 2

Results

Several surface roughness and wavelengths were chosen as inputs of the simulator. The speckle size in the image plane was chosen to 4 pixels per speckle grain. This amount corresponds to the experimental conditions in digital off-axis holography. The surface roughness was varied from 0.98 µm to 6.35 µm and the wavelength shift from 0.1 nm to 10 nm (initial wavelength at λ 1 =0.6328 µm). Figure 3 shows the coherence factor versus the wavelength shift and the surface roughness. The variation range of the coherence factor is included between 0.14 and 0.99. Figure 2 and Fig. 3 demonstrate that the proposed simulator is adapted for studying noise induced for measurement of surfaces with roughness several times higher than the wavelength. It is quite adapted to quantitatively predict the amount of noise in experiments. According to Fig. 3, the more the roughness increases the more the wavelength shift decreases to remain in the high-quality measurements zone.

Conclusion

This paper presents a realistic wavelength decorrelation induced speckle noise simulator considering the surface shape and the surface roughness. Future work includes comparison with theoretical analysis and experimental data.

Fig. 1

 1 Fig. 1 Basic scheme of the realistic simulator of decorrelation-induced speckle phase noise in two-wavelength digital holographic profilometry.

  (a) shows the simulated surface and roughness, Fig. 2(b) exhibits a zoom on the surface roughness having Gaussian statistics, and Fig. 2(c) shows the probability densities obtained from theory and simulation. So, the noise simulation is quite realistic and corresponds to what is observed in real experiments.

Fig. 2

 2 Fig. 2 Examples of outputs from the simulator, (a) surface with roughness, (b) zoom on roughness, (c) probability densities of the speckle noise (blue: simulation, red: theoretical)

Fig. 3

 3 Fig. 3 Coherence factor vs the roughness and the wavelength shift, (a) 3D view, (b) 2D view with colormap (c) Binary image with coherence factor ≥ 0.85 (white) and coherence factor < 0.85 (black)