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Reducing speckle fluctuations in multi-channel SAR images is essential in many applications of SAR imaging such as polarimetric classification or interferometric height estimation. While single-channel despeckling has widely benefited from the application of deep learning techniques, extensions to multi-channel SAR images are much more challenging.This paper introduces MuChaPro, a generic framework that exploits existing single-channel despeckling methods. The key idea is to generate numerous single-channel projections, restore these projections, and recombine them into the final multi-channel estimate. This simple approach is shown to be effective in polarimetric and/or interferometric modalities. A special appeal of MuChaPro is the possibility to apply a self-supervised training strategy to learn sensor-specific networks for single-channel despeckling.

We tackle covariance estimation in low-sample scenarios, employing a structured covariance matrix with shrinkage methods. These involve convexly combining a low-bias/high-variance empirical estimate with a biased regularization estimator, striking a bias-variance trade-off. Literature provides optimal settings of the regularization amount through risk minimization between the true covariance and its shrunk counterpart. Such estimators were derived for zero-mean statistics with i.i.d. diagonal regularization matrices accounting for the average sample variance solely. We extend these results to regularization matrices accounting for the sample variances both for centered and non-centered samples. In the latter case, the empirical estimate of the true mean is incorporated into our shrinkage estimators. Introducing confidence weights into the statistics also enhance estimator robustness against outliers. We compare our estimators to other shrinkage methods both on numerical simulations and on real data to solve a detection problem in astronomy., Comment: Accepted to EUSIPCO 2024

Understanding the state of changed areas requires that precise information be given about the changes. Thus, detecting different kinds of changes is important for land surface monitoring. SAR sensors are ideal to fulfil this task, because of their all-time and all-weather capabilities, with good accuracy of the acquisition geometry and without effects of atmospheric constituents for amplitude data. In this study, we propose a simplified generalized likelihood ratio ($S_{GLR}$) method assuming that corresponding temporal pixels have the same equivalent number of looks (ENL). Thanks to the denoised data provided by a ratio-based multitemporal SAR image denoising method (RABASAR), we successfully applied this similarity test approach to compute the change areas. A new change magnitude index method and an improved spectral clustering-based change classification method are also developed. In addition, we apply the simplified generalized likelihood ratio to detect the maximum change magnitude time, and the change starting and ending times. Then, we propose to use an adaptation of the REACTIV method to visualize the detection results vividly. The effectiveness of the proposed methods is demonstrated through the processing of simulated and SAR images, and the comparison with classical techniques. In particular, numerical experiments proved that the developed method has good performances in detecting farmland area changes, building area changes, harbour area changes and flooding area changes.

High-contrast long-slit spectrographs can be used to characterize exoplanets. High-contrast long-slit spectroscopic data are however corrupted by stellar leakages which largely dominate other signals and make the process of extracting the companion spectrum very challenging. This paper presents a complete method to calibrate the spectrograph and extract the signal of interest. The proposed method is based on a flexible direct model of the high-contrast long-slit spectroscopic data. This model explicitly accounts for the instrumental response and for the contributions of both the star and the companion. The contributions of these two components and the calibration parameters are jointly estimated by solving a regularized inverse problem. This problem having no closed-form solution, we propose an alternating minimization strategy to effectively find the solution. We have tested our method on empirical long-slit spectroscopic data and by injecting synthetic companion signals in these data. The proposed initialization and the alternating strategy effectively avoid the self-subtraction bias, even for companions observed very close to the coronagraphic mask. Careful modeling and calibration of the angular and spectral dispersion laws of the instrument clearly reduce the contamination by the stellar leakages. In practice, the outputs of the method are mostly driven by a single hyper-parameter which tunes the level of regularization of the companion SED., Comment: Paper under review by Astronomy & Astrophysics

Synthetic aperture radar tomographic imaging reconstructs the three-dimensional reflectivity of a scene from a set of coherent acquisitions performed in an interferometric configuration. In forest areas, a large number of elements backscatter the radar signal within each resolution cell. To reconstruct the vertical reflectivity profile, state-of-the-art techniques perform a regularized inversion implemented in the form of iterative minimization algorithms. We show that light-weight neural networks can be trained to perform the tomographic inversion with a single feed-forward pass, leading to fast reconstructions that could better scale to the amount of data provided by the future BIOMASS mission. We train our encoder-decoder network using simulated data and validate our technique on real L-band and P-band data., Comment: Submitted to IEEE Geoscience and Remote Sensing Letters, January 2023

Reducing speckle and limiting the variations of the physical parameters in Synthetic Aperture Radar (SAR) images is often a key-step to fully exploit the potential of such data. Nowadays, deep learning approaches produce state of the art results in single-image SAR restoration. Nevertheless, huge multi-temporal stacks are now often available and could be efficiently exploited to further improve image quality. This paper explores two fast strategies employing a single-image despeckling algorithm, namely SAR2SAR, in a multi-temporal framework. The first one is based on Quegan filter and replaces the local reflectivity pre-estimation by SAR2SAR. The second one uses SAR2SAR to suppress speckle from a ratio image encoding the multi-temporal information under the form of a "super-image", i.e. the temporal arithmetic mean of a time series. Experimental results on Sentinel-1 GRD data show that these two multi-temporal strategies provide improved filtering results while adding a limited computational cost.

Speckle filtering is generally a prerequisite to the analysis of synthetic aperture radar (SAR) images. Tremendous progress has been achieved in the domain of single-image despeckling. Latest techniques rely on deep neural networks to restore the various structures and textures peculiar to SAR images. The availability of time series of SAR images offers the possibility of improving speckle filtering by combining different speckle realizations over the same area. The supervised training of deep neural networks requires ground-truth speckle-free images. Such images can only be obtained indirectly through some form of averaging, by spatial or temporal integration, and are imperfect. Given the potential of very high quality restoration reachable by multi-temporal speckle filtering, the limitations of ground-truth images need to be circumvented. We extend a recent self-supervised training strategy for single-look complex SAR images, called MERLIN, to the case of multi-temporal filtering. This requires modeling the sources of statistical dependencies in the spatial and temporal dimensions as well as between the real and imaginary components of the complex amplitudes. Quantitative analysis on datasets with simulated speckle indicates a clear improvement of speckle reduction when additional SAR images are included. Our method is then applied to stacks of TerraSAR-X images and shown to outperform competing multi-temporal speckle filtering approaches. The code of the trained models is made freely available on the Gitlab of the IMAGES team of the LTCI Lab, T\'el\'ecom Paris Institut Polytechnique de Paris (https://gitlab.telecom-paris.fr/ring/multi-temporal-merlin/).

Speckle fluctuations seriously limit the interpretability of synthetic aperture radar (SAR) images. Speckle reduction has thus been the subject of numerous works spanning at least four decades. Techniques based on deep neural networks have recently achieved a new level of performance in terms of SAR image restoration quality. Beyond the design of suitable network architectures or the selection of adequate loss functions, the construction of training sets is of uttermost importance. So far, most approaches have considered a supervised training strategy: the networks are trained to produce outputs as close as possible to speckle-free reference images. Speckle-free images are generally not available, which requires resorting to natural or optical images or the selection of stable areas in long time series to circumvent the lack of ground truth. Self-supervision, on the other hand, avoids the use of speckle-free images. We introduce a self-supervised strategy based on the separation of the real and imaginary parts of single-look complex SAR images, called MERLIN (coMplex sElf-supeRvised despeckLINg), and show that it offers a straightforward way to train all kinds of deep despeckling networks. Networks trained with MERLIN take into account the spatial correlations due to the SAR transfer function specific to a given sensor and imaging mode. By requiring only a single image, and possibly exploiting large archives, MERLIN opens the door to hassle-free as well as large-scale training of despeckling networks. The code of the trained models is made freely available at https://gitlab.telecom-paris.fr/RING/MERLIN., Comment: To appear on IEEE Transactions on Geoscience and Remote Sensing

Angular and spectral differential imaging is an observational technique of choice to investigate the immediate vicinity of stars. The relative angular motion and spectral scaling between on-axis and off-axis sources are exploited by post-processing techniques to separate two components: the residual star light and the light coming from surrounding objects such as circumstellar disks or point-like objects. This paper introduces a new algorithm to jointly unmix these two components and deconvolve disk images. The proposed algorithm is based on a statistical modeling of the residual star light, accounting for its spatial and spectral correlations. While critical, these correlations are not modeled and compensated for by existing reconstruction algorithms. We leverage dedicated shrinkage techniques to estimate the large number of parameters of our model of correlations in a data-driven fashion. We show that the resulting separable model of the spatial and spectral covariances captures very accurately the star light, thus allowing its efficient suppression. We apply our method on several datasets from the VLT/SPHERE instrument and compare the performances against standard algorithms of the field (cADI, PCA). We show that accounting for the multiple correlations of the data significantly enhances the reconstruction quality, leading to better preservation of both the disk morphology and photometry. Thanks to its unique joint spectral modeling of the data, the proposed algorithm can reconstruct disks having a circular symmetry (e.g., rings, spirals) at intensities one million times fainter than the star, without resorting to additional reference datasets free from the off-axis objects., Comment: Submitted to MNRAS

Remote sensing provides valuable information about objects or areas from a distance in either active (e.g., RADAR and LiDAR) or passive (e.g., multispectral and hyperspectral) modes. The quality of data acquired by remotely sensed imaging sensors (both active and passive) is often degraded by a variety of noise types and artifacts. Image restoration, which is a vibrant field of research in the remote sensing community, is the task of recovering the true unknown image from the degraded observed image. Each imaging sensor induces unique noise types and artifacts into the observed image. This fact has led to the expansion of restoration techniques in different paths according to each sensor type. This review paper brings together the advances of image restoration techniques with particular focuses on synthetic aperture radar and hyperspectral images as the most active sub-fields of image restoration in the remote sensing community. We, therefore, provide a comprehensive, discipline-specific starting point for researchers at different levels (i.e., students, researchers, and senior researchers) willing to investigate the vibrant topic of data restoration by supplying sufficient detail and references. Additionally, this review paper accompanies a toolbox to provide a platform to encourage interested students and researchers in the field to further explore the restoration techniques and fast-forward the community. The toolboxes are provided in https://github.com/ImageRestorationToolbox., Comment: Published in IEEE Geoscience and Remote Sensing Magazine

Aims. The purpose of this paper is to describe a new post-processing algorithm dedicated to the reconstruction of the spatial distribution of light received from off-axis sources, in particular from circumstellar disks. Methods. Built on the recent PACO algorithm dedicated to the detection of point-like sources, the proposed method is based on the local learning of patch covariances capturing the spatial fluctuations of the stellar leakages. From this statistical modeling, we develop a regularized image reconstruction algorithm (REXPACO) following an inverse problem approach based on a forward image formation model of the off-axis sources in the ADI sequences. Results. Injections of fake circumstellar disks in ADI sequences from the VLT/SPHERE-IRDIS instrument show that both the morphology and the photometry of the disks are better preserved by REXPACO compared to standard postprocessing methods like cADI. In particular, the modeling of the spatial covariances proves usefull in reducing typical ADI artifacts and in better disentangling the signal of these sources from the residual stellar contamination. The application to stars hosting circumstellar disks with various morphologies confirms the ability of REXPACO to produce images of the light distribution with reduced artifacts. Finally, we show how REXPACO can be combined with PACO to disentangle the signal of circumstellar disks from the signal of candidate point-like sources. Conclusions. REXPACO is a novel post-processing algorithm producing numerically deblurred images of the circumstellar environment. It exploits the spatial covariances of the stellar leakages and of the noise to efficiently eliminate this nuisance term.

SAR (Synthetic Aperture Radar) tomography reconstructs 3-D volumes from stacks of SAR images. High-resolution satellites such as TerraSAR-X provide images that can be combined to produce 3-D models. In urban areas, sparsity priors are generally enforced during the tomographic inversion process in order to retrieve the location of scatterers seen within a given radar resolution cell. However, such priors often miss parts of the urban surfaces. Those missing parts are typically regions of flat areas such as ground or rooftops. This paper introduces a surface segmentation algorithm based on the computation of the optimal cut in a flow network. This segmentation process can be included within the 3-D reconstruction framework in order to improve the recovery of urban surfaces. Illustrations on a TerraSAR-X tomographic dataset demonstrate the potential of the approach to produce a 3-D model of urban surfaces such as ground, fa\c{c}ades and rooftops.

This paper presents a despeckling method for Sentinel-1 GRD images based on the recently proposed framework "SAR2SAR": a self-supervised training strategy. Training the deep neural network on collections of Sentinel 1 GRD images leads to a despeckling algorithm that is robust to space-variant spatial correlations of speckle. Despeckled images improve the detection of structures like narrow rivers. We apply a detector based on exogenous information and a linear features detector and show that rivers are better segmented when the processing chain is applied to images pre-processed by our despeckling neural network.

Deep learning approaches show unprecedented results for speckle reduction in SAR amplitude images. The wide availability of multi-temporal stacks of SAR images can improve even further the quality of denoising. In this paper, we propose a flexible yet efficient way to integrate temporal information into a deep neural network for speckle suppression. Archives provide access to long time-series of SAR images, from which multi-temporal averages can be computed with virtually no remaining speckle fluctuations. The proposed method combines this multi-temporal average and the image at a given date in the form of a ratio image and uses a state-of-the-art neural network to remove the speckle in this ratio image. This simple strategy is shown to offer a noticeable improvement compared to filtering the original image without knowledge of the multi-temporal average.

The speckle phenomenon remains a major hurdle for the analysis of SAR images. The development of speckle reduction methods closely follows methodological progress in the field of image restoration. The advent of deep neural networks has offered new ways to tackle this longstanding problem. Deep learning for speckle reduction is a very active research topic and already shows restoration performances that exceed that of the previous generations of methods based on the concepts of patches, sparsity, wavelet transform or total variation minimization. The objective of this paper is to give an overview of the most recent works and point the main research directions and current challenges of deep learning for SAR image restoration.

An adaptive optics system with a single deformable mirror is being implemented on the THEMIS 90cm solar telescope. This system is designed to operate in the visible and is required to be as robust as possible in order to deliver the best possible correction in any atmospheric conditions, even if wavefronts are sensed on some low-contrast solar granulation. In extreme conditions, the images given by the subapertures of the Shack-Hartmann wavefront sensor get randomly blurred in space, in the set of subapertures, and the distribution of blurred images is rapidly changing in time, some of them possibly fading away. The algorithms we have developed for such harsh conditions rely on inverse problem approach. As an example, with the gradients of the wavefronts, the wavefront sensor also estimates their errors, including their covariance. This information allows the control loop to promptly optimize itself to the fast varying conditions, both in space (wavefront reconstruction) and in time. A major constraint is to fit the calculations in a low-cost multi-core CPU. An overview of the algorithms in charge of implementing this strategy is presented, focusing on wavefront sensing.

Speckle reduction is a longstanding topic in synthetic aperture radar (SAR) images. Many different schemes have been proposed for the restoration of intensity SAR images. Among the different possible approaches, methods based on convolutional neural networks (CNNs) have recently shown to reach state-of-the-art performance for SAR image restoration. CNN training requires good training data: many pairs of speckle-free / speckle-corrupted images. This is an issue in SAR applications, given the inherent scarcity of speckle-free images. To handle this problem, this paper analyzes different strategies one can adopt, depending on the speckle removal task one wishes to perform and the availability of multitemporal stacks of SAR data. The first strategy applies a CNN model, trained to remove additive white Gaussian noise from natural images, to a recently proposed SAR speckle removal framework: MuLoG (MUlti-channel LOgarithm with Gaussian denoising). No training on SAR images is performed, the network is readily applied to speckle reduction tasks. The second strategy considers a novel approach to construct a reliable dataset of speckle-free SAR images necessary to train a CNN model. Finally, a hybrid approach is also analyzed: the CNN used to remove additive white Gaussian noise is trained on speckle-free SAR images. The proposed methods are compared to other state-of-the-art speckle removal filters, to evaluate the quality of denoising and to discuss the pros and cons of the different strategies. Along with the paper, we make available the weights of the trained network to allow its usage by other researchers., Comment: Article accepted for publication on Remote Sensing, MDPI. Notebook with Colab compatibility is available at https://gitlab.telecom-paris.fr/RING/SAR-CNN

Speckle reduction is a key step in many remote sensing applications. By strongly affecting synthetic aperture radar (SAR) images, it makes them difficult to analyse. Due to the difficulty to model the spatial correlation of speckle, a deep learning algorithm with self-supervision is proposed in this paper: SAR2SAR. Multi-temporal time series are leveraged and the neural network learns to restore SAR images by only looking at noisy acquisitions. To this purpose, the recently proposed noise2noise framework has been employed. The strategy to adapt it to SAR despeckling is presented, based on a compensation of temporal changes and a loss function adapted to the statistics of speckle. A study with synthetic speckle noise is presented to compare the performances of the proposed method with other state-of-the-art filters. Then, results on real images are discussed, to show the potential of the proposed algorithm. The code is made available to allow testing and reproducible research in this field., Comment: The manuscript is the accepted version of IEEE STARS. Code is made available at https://gitlab.telecom-paris.fr/RING/SAR2SAR

Image restoration methods aim to recover the underlying clean image from corrupted observations. The Expected Patch Log-likelihood (EPLL) algorithm is a powerful image restoration method that uses a Gaussian mixture model (GMM) prior on the patches of natural images. Although it is very effective for restoring images, its high runtime complexity makes EPLL ill-suited for most practical applications. In this paper, we propose three approximations to the original EPLL algorithm. The resulting algorithm, which we call the fast-EPLL (FEPLL), attains a dramatic speed-up of two orders of magnitude over EPLL while incurring a negligible drop in the restored image quality (less than 0.5 dB). We demonstrate the efficacy and versatility of our algorithm on a number of inverse problems such as denoising, deblurring, super-resolution, inpainting and devignetting. To the best of our knowledge, FEPLL is the first algorithm that can competitively restore a 512x512 pixel image in under 0.5s for all the degradations mentioned above without specialized code optimizations such as CPU parallelization or GPU implementation.

Speckle reduction is a longstanding topic in synthetic aperture radar (SAR) imaging. Since most current and planned SAR imaging satellites operate in polarimetric, interferometric or tomographic modes, SAR images are multi-channel and speckle reduction techniques must jointly process all channels to recover polarimetric and interferometric information. The distinctive nature of SAR signal (complex-valued, corrupted by multiplicative fluctuations) calls for the development of specialized methods for speckle reduction. Image denoising is a very active topic in image processing with a wide variety of approaches and many denoising algorithms available, almost always designed for additive Gaussian noise suppression. This paper proposes a general scheme, called MuLoG (MUlti-channel LOgarithm with Gaussian denoising), to include such Gaussian denoisers within a multi-channel SAR speckle reduction technique. A new family of speckle reduction algorithms can thus be obtained, benefiting from the ongoing progress in Gaussian denoising, and offering several speckle reduction results often displaying method-specific artifacts that can be dismissed by comparison between results.

Matching patches from a noisy image to atoms in a dictionary of patches is a key ingredient to many techniques in image processing and computer vision. By representing with a single atom all patches that are identical up to a radiometric transformation, dictionary size can be kept small, thereby retaining good computational efficiency. Identification of the atom in best match with a given noisy patch then requires a contrast-invariant criterion. In the light of detection theory, we propose a new criterion that ensures contrast invariance and robustness to noise. We discuss its theoretical grounding and assess its performance under Gaussian, gamma and Poisson noises.

Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with multi-chromatic interferometric data have consisted in recovering a gray image of the object or independent monochromatic images in some spectral bandwidths. The main challenge is now to recover the full 3-D (spatio-spectral) brightness distribution of the astronomical target given all the available data. We describe a new approach to implement multi-wavelength image reconstruction in the case where the observed scene is a collection of point-like sources. We show the gain in image quality (both spatially and spectrally) achieved by globally taking into account all the data instead of dealing with independent spectral slices. This is achieved thanks to a regularization which favors spatial sparsity and spectral grouping of the sources. Since the objective function is not differentiable, we had to develop a specialized optimization algorithm which also accounts for non-negativity of the brightness distribution., Comment: This version has been accepted for publication in J. Opt. Soc. Am. A

The orthogonal matching pursuit (OMP) is an algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the solution of ill-posed inverse problems in general and in particular for two deconvolution examples from mass spectrometry and digital holography respectively. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by the so-called incoherence. This idea cannot be transfered to ill-posed inverse problems since here the atoms are typically far from orthogonal: The ill-posedness of the operator causes that the correlation of two distinct atoms probably gets huge, i.e. that two atoms can look much alike. Therefore one needs conditions which take the structure of the problem into account and work without the concept of coherence. In this paper we develop results for exact recovery of the support of noisy signals. In the two examples in mass spectrometry and digital holography we show that our results lead to practically relevant estimates such that one may check a priori if the experimental setup guarantees exact deconvolution with OMP. Especially in the example from digital holography our analysis may be regarded as a first step to calculate the resolution power of droplet holography.