Synthetic aperture radar (SAR) provides valuable information about the Earth’s surface in all-weather and day-and-night conditions. Due to the inherent presence of speckle phenomenon, a filtering step is often required to improve the performance of downstream tasks. In this article, we focus on dealing with the spatial correlations of speckle, which impacts negatively many of the existing speckle filters. Taking advantage of the flexibility of variational methods based on the plug-and-play (PnP) strategy, we propose to use a Gaussian denoiser trained to restore SAR scenes corrupted by colored Gaussian noise with correlation structures typical of a range of radar sensors. Our approach improves the robustness of PnP despeckling techniques. Experiments conducted on simulated and real polarimetric SAR images show that the proposed method removes speckle efficiently in the presence of spatial correlations without introducing artifacts, with a good level of detail preservation. Our method can be readily applied, without network re-training or fine-tuning, to filter SAR images from various sensors, acquisition modes (SAR, PolSAR, InSAR, PolInSAR), and spatial resolution. The code of the trained models is made freely available at (https://gitlab.telecom-paris.fr/ring/mulog-drunet).

For more than a decade, deep learning algorithms have consistently achieved and improved upon the state-of-the-art performance on image classification tasks. However, there is a general lack of understanding and knowledge about the decision boundaries carved by these modern deep neural network architectures. Recently, an algorithm called DeepDIG was introduced to generate boundary instances between two classes based on the decision regions defined by any deep neural network classifier. Although it is very effective in generating boundary instances, the underlying algorithm was designed to work with two classes at a time in a non-commutative fashion which makes it ill-suited for multi-class problems with hundreds of classes. In this work, we extend the DeepDIG algorithm so that it scales linearly with the number of classes. We show that the proposed U-DeepDIG algorithm maintains the efficacy of the original DeepDIG algorithm while being scalable and more efficient when applied to larger classification problems. We demonstrate this by applying our algorithm on MNIST, Fashion-MNIST and CIFAR10 datasets. In addition to qualitative comparisons, we also perform extensive quantitative comparison by analyzing the margin between the class boundaries and the instances generated.

A new blind image deconvolution technique is developed for atmospheric turbulence deblurring to overcome limitations of ‘generic’ blind deconvolution algorithms that do not take into account the complicated physics of the turbulence. The originality of the proposed approach relies on an actual physical model, known as the Fried kernel, that quantifies the impact of the atmospheric turbulence on the optical resolution of images. While the original expression of the Fried kernel can seem cumbersome at first sight, the authors show that it can be reparameterised in a much simpler form. This simple expression allows to efficiently embed this kernel in the proposed blind atmospheric turbulence deconvolution (BATUD) algorithm. BATUD is an iterative algorithm that alternately performs deconvolution and estimates the Fried kernel by jointly relying on a Gaussian mixture model prior to natural image patches and controlling for the square Euclidean norm of the Fried kernel. Numerical experiments show that the proposed blind deconvolution algorithm behaves well in different simulated turbulence scenarios, as well as on real images. Not only BATUD outperforms state‐of‐the‐art approaches used in atmospheric turbulence deconvolution in terms of image quality metrics but is also faster.

Speckle reduction is a necessary step for many applications. Very effective methods have been developed in the recent years for single-image speckle reduction and multi-temporal speckle filtering. However, to reduce the presence of sidelobes around bright targets, SAR images are spectrally weighted and this processing impacts the speckle statistics by introducing spatial correlations. These correlations severely impact speckle reduction methods that require uncorrelated speckle as input. Thus, spatial down-sampling is typically applied to reduce the speckle spatial correlations prior to speckle filtering. To better preserve the spatial resolution, we describe how to correctly resample SAR images and extract bright targets in order to process full-resolution images with speckle-reduction methods.

The availability of multi-temporal stacks of SAR images opens the way to new speckle reduction methods. Beyond mere spatial filtering, the time series can be used to improve the signal-to-noise ratio of structures that persist for several dates. Among multi-temporal filtering strategies to reduce speckle fluctuations, a recent approach has proved to be very effective: ratio-based filtering (RABASAR). This method, developed to reduce the speckle in multi-temporal intensity images, first computes a "mean image" with a high signal-to-noise ratio (a so-called super-image), and then processes the ratio between the multi-temporal stack and the super-image. In this paper, we propose an extension of this approach to polarimetric SAR images. We illustrate its potential on a stack of fully-polarimetric images from RADARSAT-2 satellite.

Speckle reduction has benefited from the recent progress in image processing, in particular patch-based non-local filtering and deep learning techniques. These two families of methods offer complementary characteristics but have not yet been combined. We explore strategies to make the most of each approach.

In the last decades, several approaches for solving the Phase Unwrapping (PhU) problem using multi-channel Interferometric Synthetic Aperture Radar (InSAR) data have been developed. Many of the proposed approaches are based on statistical estimation theory, both classical and Bayesian. In particular, the statistical approaches based on the use of the whole complex multi-channel dataset have turned to be effective. The latter are based on the exploitation of the covariance matrix, which contains the parameters of interest. In this paper, the added value of the Non Local (NL) paradigm within the InSAR multi-channel PhU framework is investigated. The analysis of the impact of NL technique is performed using multi-channel realistic simulated data and X-band data.

Speckle reduction is a major issue for many SAR imaging applications using amplitude, interferometric, polarimetric or tomographic data. This subject has been widely investigated using various approaches. Since a decade, breakthrough methods based on patches have brought unprecedented results to improve the estimation of radar properties. In this paper, we give a review of the different adaptations which have been proposed in the past years for different SAR modalities (mono-channel data like intensity images, multi-channel data like interferometric, tomographic or polarimetric data, or multimodalities combining optic and SAR images), and discuss the new trends on this subject.

In this paper, we propose a fast and efficient multitemporal despeckling method. The key idea of the proposed approach is the use of the ratio image, provided by the ratio between an image and the temporal mean of the stack. This ratio image is easier to denoise than a single image thanks to its improved stationarity. Besides, temporally stable thin structures are well preserved thanks to the multitemporal mean. The proposed approach can be divided into three steps: 1) estimation of a “superimage” by temporal averaging and possibly spatial denoising; 2) denoising of the ratio between the noisy image of interest and the “superimage”; and 3) computation of the denoised image by remultiplying the denoised ratio by the “superimage.” Because of the improved spatial stationarity of the ratio images, denoising these ratio images with a speckle-reduction method is more effective than denoising images from the original multitemporal stack. The amount of data that is jointly processed is also reduced compared to other methods through the use of the “superimage” that sums up the temporal stack. The comparison with several state-of-the-art reference methods shows better results numerically (peak signal-noise-ratio and structure similarity index) as well as visually on simulated and synthetic aperture radar (SAR) time series. The proposed ratio-based denoising framework successfully extends single-image SAR denoising methods to time series by exploiting the persistence of many geometrical structures.

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 the 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, the FEPLL is the first algorithm that can competitively restore a pixel image in under 0.5 s for all the degradations mentioned earlier without specialized code optimizations, such as CPU parallelization or GPU implementation.

Speckle reduction is a long-standing topic in SAR data processing. Continuous progress made in the field of image denoising fuels the development of methods dedicated to speckle in SAR images. Adaptation of a denoising technique to the specific statistical nature of speckle presents variable levels of difficulty. It is well known that the logarithm transform maps the intrinsically multiplicative speckle into an additive and stationary component, thereby paving the way to the application of general-purpose image denoising methods to SAR intensity images. Multi-channel SAR images such as obtained in interferometric (InSAR) or polarimetric (PolSAR) configurations are much more challenging. This paper describes MuLoG, a generic approach for mapping a multi-channel SAR image into real-valued images with an additive speckle component that has a variance approximately constant. With this approach, general-purpose image denoising algorithms can be readily applied to restore InSAR or PolSAR data. In particular, we show how recent denoising methods based on deep convolutional neural networks lead to state-of-the art results when embedded with MuLoG framework.

In this paper, a generic method is proposed to reduce speckle in multi-temporal stacks of SAR images. The method is based on the computation of a “super-image”, with a large number of looks, by temporal averaging. Then, ratio images are formed by dividing each image of the multi-temporal stack by the “super-image”. In the absence of changes of the radiometry, the temporal fluctuations of the intensity at a given spatial location are due to the speckle phenomenon. In areas affected by temporal changes, fluctuations cannot be ascribed to speckle only but also to radiometric changes. The overall effect of the division by the “super-image” is the spatial stationarity improvement: ratio images are much more homogeneous than the original images. Therefore, filtering these ratio images with a speckle-reduction method is more effective, in terms of speckle suppression, than filtering the original multitemporal stack. After denoising of the ratio image, the despeckled multi-temporal stack is obtained by multiplication with the “super-image”. Results are presented and analyzed both on synthetic and real SAR data and show the interest of the proposed approach.

Patch priors have become an important component of image restoration. A powerful approach in this category of restoration algorithms is the popular expected patch log-likelihood (EPLL) algorithm. EPLL uses a Gaussian mixture model (GMM) prior learned on clean image patches as a way to regularize degraded patches. In this paper, we show that a generalized Gaussian mixture model (GGMM) captures the underlying distribution of patches better than a GMM. Even though GGMM is a powerful prior to combine with EPLL, the non-Gaussianity of its components presents major challenges to be applied to a computationally intensive process of image restoration. Specifically, each patch has to undergo a patch classification step and a shrinkage step. These two steps can be efficiently solved with a GMM prior but are computationally impractical when using a GGMM prior. In this paper, we provide approximations and computational recipes for fast evaluation of these two steps, so that EPLL can embed a GGMM prior on an image with more than tens of thousands of patches. Our main contribution is to analyze the accuracy of our approximations based on thorough theoretical analysis. Our evaluations indicate that the GGMM prior is consistently a better fit for modeling image patch distribution and performs better on average in image denoising task.

Reconstruction of elevation maps from a collection of synthetic aperture radar (SAR) images obtained in interferometric configuration is a challenging task. Reconstruction methods must overcome two difficulties: the strong interferometric noise that contaminates the data and the 2π phase ambiguities. Interferometric noise requires some form of smoothing among pixels of identical height. Phase ambiguities can be solved, up to a point, by combining linkage to the neighbors and a global optimization strategy to prevent from being trapped in local minima. This paper introduces a reconstruction method, PARISAR, that achieves both a resolution-preserving denoising and a robust phase unwrapping (PhU) by combining nonlocal denoising methods based on patch similarities and total-variation regularization. The optimization algorithm, based on graph cuts, identifies the global optimum. Combining patch-based speckle reduction methods and regularization-based PhU requires solving several issues: 1) computational complexity, the inclusion of nonlocal neighborhoods strongly increasing the number of terms involved during the regularization, and 2) adaptation to varying neighborhoods, patch comparison leading to large neighborhoods in homogeneous regions and much sparser neighborhoods in some geometrical structures. PARISAR solves both issues. We compare PARISAR with other reconstruction methods both on numerical simulations and satellite images and show a qualitative and quantitative improvement over state-of-the-art reconstruction methods for multibaseline SAR interferometry.

Starting from a stack of co-registered SAR images in interferometric configuration, SAR tomography performs a reconstruction of the reflectivity of scatterers in 3-D. Several scatterers observed within the same resolution cell of each SAR image can be separated by jointly unmixing the SAR complex amplitude observed throughout the stack. To achieve a reliable tomographic reconstruction, it is necessary to estimate locally the SAR covariance matrix by performing some spatial averaging. This necessary averaging step introduces some resolution loss and can bias the tomographic reconstruction by mistakenly including the response of scatterers located within the averaging area but outside the resolution cell of interest. This paper addresses the problem of identifying pixels corresponding to similar tomographic content, i.e., pixels that can be safely averaged prior to tomographic reconstruction. We derive a similarity criterion adapted to SAR tomography and compare its performance with existing criteria on a stack of Spotlight TerraSAR-X images.

In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus on image processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization, we develop an approach refitting the results of standard methods toward the input data. Total variation regularizations and nonlocal means are special cases of interest. We identify important covariant information that should be preserved by the refitting method and emphasize the importance of preserving the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we provide an approach that has a “twicing” flavor and allows refitting the restored signal by adding back a local affine transformation of the residual term. We illustrate the benefits of our method on numerical simulations for image restoration tasks.

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.

In this paper, we aim at super-resolving a low-resolution texture under the assumption that a high-resolution patch of the texture is available. To do so, we propose a variational method that combines two approaches that are texture synthesis and image reconstruction. The resulting objective function holds a nonconvex energy that involves a quadratic distance to the low-resolution image, a histogram-based distance to the high-resolution patch, and a nonlocal regularization that links the missing pixels with the patch pixels. As for the histogram-based measure, we use a sum of Wasserstein distances between the histograms of some linear transformations of the textures. The resulting optimization problem is efficiently solved with a primal-dual proximal method. Experiments show that our method leads to a significant improvement, both visually and numerically, with respect to the state-of-the-art algorithms for solving similar problems.

We consider the problem of recovering a high-resolution image from a pair consisting of a complete low-resolution image and a high-resolution but incomplete one. We refer to this task as the image zoom completion problem. After discussing possible contexts in which this setting may arise, we introduce a nonlocal regularization strategy, giving full details concerning the numerical optimization of the corresponding energy and discussing its benefits and shortcomings. We also derive two total variation-based algorithms and evaluate the performance of the proposed methods on a set of natural and textured images. We compare the results and get with those obtained with two recent state-of-the-art single-image super-resolution algorithms.

In this paper we propose a new approach for height retrieval using multi-channel SAR interferometry. It combines patch-based estimation and total variation regularization to provide a regularized height estimate. The non-local likelihood term adaptation relies on NL-SAR method, and the global optimization is realized through graph-cut minimization. The method is evaluated both with synthetic and real experiments.

Due to their coherent nature, SAR (Synthetic Aperture Radar) images are very different from optical satellite images and more difficult to interpret, especially because of speckle noise. Given the increasing amount of available SAR data, efficient image processing techniques are needed to ease the analysis. Classifying this type of images, i.e., selecting an adequate label for each pixel, is a challenging task. This paper describes a supervised classification method based on local features derived from a Gaussian mixture model (GMM) of the distribution of patches. First classification results are encouraging and suggest an interesting potential of the GMM model for SAR imaging.

We propose a two-step algorithm that automatically estimates the noise level function of stationary noise from a single image, i.e., the noise variance as a function of the image intensity. First, the image is divided into small square regions and a nonparametric test is applied to decide whether each region is homogeneous or not. Based on Kendall's $\tau$ coefficient (a rank-based measure of correlation), this detector has a nondetection rate independent of the unknown distribution of the noise, provided that it is at least spatially uncorrelated. Moreover, we prove, on a toy example, that its overall detection error vanishes with respect to the region size as soon as the signal to noise ratio level is nonzero. Once homogeneous regions are detected, the noise level function is estimated as a second order polynomial minimizing the $\ell^1$ error on the statistics of these regions. Numerical experiments show the efficiency of the proposed approach in estimating the noise level function, with a relative error under 10% obtained on a large data set. We illustrate the interest of the approach for an image denoising application.

Speckle noise is an inherent problem in coherent imaging systems such as synthetic aperture radar. It creates strong intensity fluctuations and hampers the analysis of images and the estimation of local radiometric, polarimetric, or interferometric properties. Synthetic aperture radar (SAR) processing chains thus often include a multilooking (i.e., averaging) filter for speckle reduction, at the expense of a strong resolution loss. Preservation of point-like and fine structures and textures requires to adapt locally the estimation. Nonlocal (NL)-means successfully adapt smoothing by deriving data-driven weights from the similarity between small image patches. The generalization of nonlocal approaches offers a flexible framework for resolution-preserving speckle reduction. We describe a general method, i.e., NL-SAR, that builds extended nonlocal neighborhoods for denoising amplitude, polarimetric, and/or interferometric SAR images. These neighborhoods are defined on the basis of pixel similarity as evaluated by multichannel comparison of patches. Several nonlocal estimations are performed, and the best one is locally selected to form a single restored image with good preservation of radar structures and discontinuities. The proposed method is fully automatic and handles single and multilook images, with or without interferometric or polarimetric channels. Efficient speckle reduction with very good resolution preservation is demonstrated both on numerical experiments using simulated data, airborne, and spaceborne radar images. The source code of a parallel implementation of NL-SAR is released with this paper.

The classical super-resolution (SR) setting starts with a set of low-resolution (LR) images related by subpixel shifts and tries to reconstruct a single high-resolution (HR) image. In some cases, partial observations about the HR image are also available. Trying to complete the missing HR data without any reference to LR ones is an inpainting (or completion) problem. In this paper, we consider the problem of recovering a single HR image from a pair consisting of a complete LR and incomplete HR image pair. This setting arises in particular when one wants to fuse image data captured at two different resolutions. We propose an efficient algorithm that allows to take advantage of both image data by first learning nonlocal interactions from an interpolated version of the LR image using patches. Those interactions are then used by a convex energy function whose minimization yields a super-resolved complete image.

In this paper, an extension of the framework proposed by Deledalle et al. [1] for Non Local Means (NLM) method is proposed. This extension is a general adaptive method to denoise images containing multiple noises. It takes into account a segmentation stage that indicates the noise type of a given pixel in order to select the similarity measure and suitable parameters to perform the denoising task, considering a certain patch on the image. For instance, it has been experimentally observed that fetal 3D ultrasound images are corrupted by different types of noise, depending on the tissue. Finally, the proposed method is applied to denoise these images, showing very good results.

We derive a denoising method based on an adaptive regularization of the non-local means. The NL-means reduce noise by using the redundancy in natural images. They compute a weighted average of pixels whose surroundings are close. This method performs well but it suffers from residual noise on singular structures. We use the weights computed in the NL-means as a measure of performance of the denoising process. These weights balance the data-fidelity term in an adapted ROF model, in order to locally perform adaptive TV regularization. Besides, this model can be adapted to different noise statistics and a fast resolution can be computed in the general case of the exponential family. We adapt this model to video denoising by using spatio-temporal patches. Compared to spatial patches, they offer better temporal stability, while the adaptive TV regularization corrects the residual noise observed around moving structures.

Patches have proven to be very effective features to model natural images and to design image restoration methods. Given the huge diversity of patches found in images, modeling the distribution of patches is a difficult task. Rather than attempting to accurately model all patches of the image, we advocate that it is sufficient that all pixels of the image belong to at least one well-explained patch. An image is thus described as a tiling of patches that have large prior probability. In contrast to most patch-based approaches, we do not process the image in patch space, and consider instead that patches should match well everywhere where they overlap. In-order to apply this modeling to the restoration of SAR images, we define a suitable data-fitting term to account for the statistical distribution of speckle. Restoration results are competitive with state-of-the art SAR despeckling methods.

This paper presents a change detection and classification method of Synthetic Aperture Radar (SAR) multi-temporal images. The change criterion based on a generalized likelihood ratio test is an extension of the likelihood ratio test, in which both the noisy data and the multi-temporal denoised data are used. The changes are detected by a thresholding and then classified into step, impulse and cycle changes according to their temporal behaviors. The results show the effective performance of the proposed method.

Adding invariance properties to a dictionary-based model is a convenient way to reach a high representation capacity while maintaining a compact structure. Compact dictionaries of patches are desirable because they ease semantic interpretation of their elements (atoms) and offer robust decompositions even under strong speckle fluctuations. This paper describes how patches of a dictionary can be matched to a speckled image by accounting for unknown shifts and affine radio-metric changes. This procedure is used to build dictionaries of patches specific to SAR images. The dictionaries can then be used for denoising or classification purposes.

Algorithms for solving variational regularization of ill-posed inverse problems usually involve operators that depend on a collection of continuous parameters. When the operators enjoy some (local) regularity, these parameters can be selected using the so-called Stein Unbiased Risk Estimator (SURE). While this selection is usually performed by an exhaustive search, we address in this work the problem of using the SURE to efficiently optimize for a collection of continuous parameters of the model. When considering nonsmooth regularizers, such as the popular $\ell_1$-norm corresponding to soft-thresholding mapping, the SURE is a discontinuous function of the parameters preventing the use of gradient descent optimization techniques. Instead, we focus on an approximation of the SURE based on finite differences as proposed by Ramani and Unser for the Monte-Carlo SURE approach. Under mild assumptions on the estimation mapping, we show that this approximation is a weakly differentiable function of the parameters and its weak gradient, coined the Stein Unbiased GrAdient estimator of the Risk (SUGAR), provides an asymptotically (with respect to the data dimension) unbiased estimate of the gradient of the risk. Moreover, in the particular case of soft-thresholding, it is proved to also be a consistent estimator. This gradient estimate can then be used as a basis for performing a quasi-Newton optimization. The computation of the SUGAR relies on the closed-form (weak) differentiation of the nonsmooth function. We provide its expression for a large class of iterative methods including proximal splitting methods and apply our strategy to regularizations involving nonsmooth convex structured penalties. Illustrations of various image restoration and matrix completion problems are given.

This paper presents a denoising approach for multitemporal synthetic aperture radar (SAR) images based on the concept of nonlocal means (NLM). It exploits the information redundancy existing in multitemporal images by a two-step strategy. The first step realizes a nonlocal weighted estimation driven by the redundancy in time, whereas the second step makes use of the nonlocal estimation in space. Using patch similarity miss-registration estimation, we also adapted this approach to the case of unregistered SAR images. The experiments illustrate the efficiency of the proposed method to denoise multitemporal images while preserving new information.

Image denoising is a central problem in image processing and it is often a necessary step prior to higher level analysis such as segmentation, reconstruction, or super-resolution. The nonlocal means (NL-means) perform denoising by exploiting the natural redundancy of patterns inside an image; they perform a weighted average of pixels whose neighborhoods (patches) are close to each other. This reduces significantly the noise while preserving most of the image content. While it performs well on flat areas and textures, it suffers from two opposite drawbacks: it might over-smooth low-contrasted areas or leave a residual noise around edges and singular structures. Denoising can also be performed by total variation minimization-the Rudin, Osher and Fatemi model-which leads to restore regular images, but it is prone to over-smooth textures, staircasing effects, and contrast losses. We introduce in this paper a variational approach that corrects the over-smoothing and reduces the residual noise of the NL-means by adaptively regularizing nonlocal methods with the total variation. The proposed regularized NL-means algorithm combines these methods and reduces both of their respective defaults by minimizing an adaptive total variation with a nonlocal data fidelity term. Besides, this model adapts to different noise statistics and a fast solution can be obtained in the general case of the exponential family. We develop this model for image denoising and we adapt it to video denoising with 3D patches.

This paper presents a change detection method between two Synthetic Aperture Radar (SAR) images with similar incidence angles and using a likelihood ratio test (LRT). To address the composite hypothesis problem of the LRT, we propose to replace the noise-free values by their estimated results. Thus, a multi-temporal non local means denoising method proposed in [1] is used in this paper to estimate the noise-free values using both spatial and temporal information. The change detection results show the effective performance of the proposed method compared with the state of the art ones, such as log-ratio operator and generalized likelihood ratio test.

Photon limitations arise in spectral imaging, nuclear medicine, astronomy and night vision. The Poisson distribution used to model this noise has variance equal to its mean so blind application of standard noise removals methods yields significant artifacts. Recently, overcomplete dictionaries combined with sparse learning techniques have become extremely popular in image reconstruction. The aim of the present work is to demonstrate that for the task of image denoising, nearly state-of-the-art results can be achieved using small dictionaries only, provided that they are learned directly from the noisy image. To this end, we introduce patch-based denoising algorithms which perform an adaptation of PCA (Principal Component Analysis) for Poisson noise. We carry out a comprehensive empirical evaluation of the performance of our algorithms in terms of accuracy when the photon count is really low. The results reveal that, despite its simplicity, PCA-flavored denoising appears to be competitive with other state-of-the-art denoising algorithms.

In this paper, we propose a rigorous derivation of the expression of the projected Generalized Stein Unbiased Risk Estimator (GSURE) for the estimation of the (projected) risk associated to regularized ill-posed linear inverse problems using sparsity-promoting ℓ1penalty. The projected GSURE is an unbiased estimator of the recovery risk on the vector projected on the orthogonal of the degradation operator kernel. Our framework can handle many well-known regularizations including sparse synthesis- (e.g. wavelet) and analysis-type priors (e.g. total variation). A distinctive novelty of this work is that, unlike previously proposed ℓ1risk estimators, we have a closed-form expression that can be implemented efficiently once the solution of the inverse problem is computed. To support our claims, numerical examples on ill-posed inverse problems with analysis and synthesis regularizations are reported where our GSURE estimates are used to tune the regularization parameter.

This paper presents a processing chain to combine a CosmoSkyMed (CSK) image and a TerraSAR-X (TSX) image. After registration and calibration steps, processing at different levels is studied: pixel level for the detection of stable features and joint filtering, primitive level for stability analysis and object level (like roads) for joint interpretation.

This paper presents a denoising approach for multi-temporal Synthetic aperture radar (SAR) images based on Non-Local Means (NLM) method. To exploit redundancy existing in multi-temporal images, we develop a new strategy of NLM for multi-temporal data. Instead of directly overspreading the NLM operator from one image to temporal images, a two steps weighted average is proposed in this paper. The first step is a maximum likelihood estimate with binary weights on temporal pixels and the second step is iterative NL means on spatial pixels. Experiments in this paper illustrate that the proposed method can effectively exploit image redundancy and denoise multi-temporal images.

International audience

Many tasks in computer vision require to match image parts. While higher-level methods consider image features such as edges or robust descriptors, low-level approaches compare groups of pixels (patches) and provide dense matching. Patch similarity is a key ingredient to many techniques for image registration, stereo-vision, change detection or denoising. A fundamental difficulty when comparing two patches from “real” data is to decide whether the differences should be ascribed to noise or intrinsic dissimilarity. Gaussian noise assumption leads to the classical definition of patch similarity based on the squared intensity differences. When the noise departs from the Gaussian distribution, several similarity criteria have been proposed in the literature. We review seven of those criteria taken from the fields of image processing, detection theory and machine learning. We discuss their theoretical grounding and provide a numerical comparison of their performance under Gamma and Poisson noises.

This paper analyzes the effects of speckle filtering on polarimetric SAR decomposition and classification. We compared the results of the refined Lee, ID AN and Non-Local Polarimetric filters, and discussed their influence on the Cloude-Pottier decomposition and the Wishart H/α classification. ALOS/PALSAR and RadarSat-2 polarimetric SAR data are used for illustration.

Interferometric synthetic aperture radar (SAR) data provide reflectivity, interferometric phase, and coherence images, which are paramount to scene interpretation or low-level processing tasks such as segmentation and 3-D reconstruction. These images are estimated in practice from a Hermitian product on local windows. These windows lead to biases and resolution losses due to the local heterogeneity caused by edges and textures. This paper proposes a nonlocal approach for the joint estimation of the reflectivity, the interferometric phase, and the coherence images from an interferometric pair of coregistered single-look complex (SLC) SAR images. Nonlocal techniques are known to efficiently reduce noise while preserving structures by performing the weighted averaging of similar pixels. Two pixels are considered similar if the surrounding image patches are “resembling.” Patch similarity is usually defined as the Euclidean distance between the vectors of graylevels. In this paper, a statistically grounded patch-similarity criterion suitable to SLC images is derived. A weighted maximum likelihood estimation of the SAR interferogram is then computed with weights derived in a data-driven way. Weights are defined from the intensity and interferometric phase and are iteratively refined based both on the similarity between noisy patches and on the similarity of patches from the previous estimate. The efficiency of this new interferogram construction technique is illustrated both qualitatively and quantitatively on synthetic and true data.

An extension of the non local (NL) means is proposed for images damaged by Poisson noise. The proposed method is guided by the noisy image and a pre-filtered image and is adapted to the statistics of Poisson noise. The influence of both images can be tuned using two filtering parameters. We propose an automatic setting to select these parameters based on the minimization of the estimated risk (mean square error). This selection uses an estimator of the MSE for NL means with Poisson noise and Newton's method to find the optimal parameters in few iterations.

Synthetic aperture radar (SAR) images provide scattering information which can be used under any weather conditions for glacier monitoring. Our purpose is to estimate a displacement field characterizing at each position the local speeds and orientations of the glacier displacement. Recent proposed methods build a vector field by tracking patches between two SAR images co-registered on static areas and sensed at different times. The tracking is performed either by evaluating the correlations or the similarities from one acquisition to the other. We propose to estimate locally the displacement vectors by using either the maximum correlation or a maximum likelihood estimator. This local estimation is then refined to provide a sub-pixelic result. The efficiency of both methods are compared.

Recently, non-local approaches have proved very powerful for image denoising. Unlike local filters, the non-local (NL) means introduced in decrease the noise while preserving well the resolution. In the proposed paper, we suggest the use of a non-local approach to estimate single-look SAR reflectivity images or to construct SAR interferograms. SAR interferogram construction refers to the joint estimation of the reflectivity, phase difference and coherence image from a pair of two co-registered single-look complex SAR images. The weighted-maximum likelihood is introduced as a generalization of the weighted average performed in the NL means. We propose to set the weights according to the probability of similarity which provides an extension of the Euclidean distance used in the NL means. Experiments and results are presented to show the efficiency of the proposed approach.

During the past few years, the non-local (NL)means have proved their efficiency for image denoising. This approach assumes there exist enough redundant patterns in images to be used for noise reduction. We suggest that the same assumption can be done for polarimetric synthetic aperture radar (PolSAR) images. In its original version, the NLmeans deal with additive white Gaussian noise, but several extensions have been proposed for non-Gaussian noise. This paper applies the methodology proposed in ato PolSAR data. The proposed filter seems to deal well with the statistical properties of speckle noise and themulti-dimensional nature of such data. Results are given on synthetic and L-Band E-SAR data to validate the proposed method.

Image denoising is an important problem in image processing since noise may interfere with visual or automatic interpretation. This paper presents a new approach for image denoising in the case of a known uncorrelated noise model. The proposed filter is an extension of the nonlocal means (NL means) algorithm introduced by Buades , which performs a weighted average of the values of similar pixels. Pixel similarity is defined in NL means as the Euclidean distance between patches (rectangular windows centered on each two pixels). In this paper, a more general and statistically grounded similarity criterion is proposed which depends on the noise distribution model. The denoising process is expressed as a weighted maximum likelihood estimation problem where the weights are derived in a data-driven way. These weights can be iteratively refined based on both the similarity between noisy patches and the similarity of patches extracted from the previous estimate. We show that this iterative process noticeably improves the denoising performance, especially in the case of low signal-to-noise ratio images such as synthetic aperture radar (SAR) images. Numerical experiments illustrate that the technique can be successfully applied to the classical case of additive Gaussian noise but also to cases such as multiplicative speckle noise. The proposed denoising technique seems to improve on the state of the art performance in that latter case.