Charles Deledalle  Software
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Inverse problems and lowrank matrices
Matlab opensource software distributed under CeCILL license for data driven srhinkage of singular values. We consider the problem of estimating a lowrank signal matrix from noisy measurements under the assumption that the distribution of the data matrix belongs to an exponential family. In this setting, we derive generalized Stein's unbiased risk estimation (SURE) formulas that hold for any spectral estimators which shrink or threshold the singular values of the data matrix. This leads to new datadriven spectral estimators, whose optimality is discussed using tools from random matrix theory and through numerical experiments. Under the spiked population model and in the asymptotic setting where the dimensions of the data matrix are let going to infinity, some theoretical properties of our approach are compared to recent results on asymptotically optimal shrinking rules for Gaussian noise. It also leads to new procedures for singular values shrinkage in finitedimensional matrix denoising for Gammadistributed and Poissondistributed measurements. 
Matlab opensource software for the automatic selection of (multiple) parameters in inverse problems. Algorithms to solve variational regularization of illposed inverse problems usually involve operators that depend on a collection of continuous parameters. When these operators enjoy some (local) regularity, these parameters can be selected using the socalled Stein Unbiased Risk Estimate (SURE). While this selection is usually performed by 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 l1norm corresponding to softthresholding 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 in (Ramani et al., 2008). 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 softthresholding, the SUGAR is proved to be also a consistent estimator. The SUGAR can then be used as a basis to perform a quasiNewton optimization. The computation of the SUGAR relies on the closedform (weak) differentiation of the nonsmooth function. We provide its expression for a large class of iterative proximal splitting methods and apply our strategy to regularizations involving nonsmooth convex structured penalties. Illustrations on various image restoration and matrix completion problems are given. 
Denoising
Matlab opensource software distributed under CeCILL license to perform (Pol)(In)SAR filtering with embedded Gaussian denoiser. 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 multichannel and speckle reduction techniques must jointly process all channels to recover polarimetric and interferometric information. The distinctive nature of SAR signal (complexvalued, corrupted by multiplicative fluctuations) called 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 algorithm proposes a general scheme, called MuLoG (MUltichannel LOgarithm with Gaussian denoising), to include such Gaussian denoisers within a multichannel 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 methodspecific artifacts that can be dismissed by comparison between results. 
Matlab opensource software to perform (blind) denoising. It implements the followings

Opensource software distributed under CeCILL license to perform adaptive nonlocal (Pol)(In)SAR filtering. Interface in command line, IDL, Matlab, Python and C dynamic library. Plug in for PolSARpro. Speckle noise is an inherent problem in coherent imaging systems like synthetic aperture radar. It creates strong intensity fluctuations and hampers the analysis of images and the estimation of local radiometric, polarimetric or interferometric properties. 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 pointlike and fine structures and textures requires to locally adapt the estimation. Nonlocal means successfully adapt smoothing by deriving datadriven weights from the similarity between small image patches. The generalization of nonlocal approaches offers a flexible framework for resolutionpreserving speckle reduction. NLSAR is a general method 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 can handle single and multilook images, with or without interferometric or polarimetric channels. Efficient speckle reduction with very good resolution preservation has been demonstrated both on numerical experiments using simulated data and airborne radar images. 
Matlab opensource software to perform nonlocal filtering in an extended PCA domain for Poisson noise. Photonlimited imaging arises when the number of photons collected by a sensor array is small relative to the number of detector elements. Photon limitations are an important concern for many applications such as spectral imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson distribution is used to model these observations, and the inherent heteroscedasticity of the data combined with standard noise removal methods yields significant artifacts. A novel denoising algorithm is implemented for photonlimited images which combines elements of dictionary learning and sparse patchbased representations of images. The method employs both an adaptation of Principal Component Analysis (PCA) for Poisson noise and recently developed sparsityregularized convex optimization algorithms for photonlimited images. A comprehensive empirical evaluation of the proposed method helps characterize the performance of this approach relative to other stateoftheart denois ing methods. The results reveal that, despite its conceptual simplicity, Poisson PCAbased denoising appears to be highly competitive in very low light regimes. 
Matlab opensource software to perform nonlocal filtering in the PCA domain. In recent years, overcomplete dictionaries combined with sparse learning techniques became extremely popular in computer vision. While their usefulness is undeniable, the improvement they provide in specific tasks of computer vision is still poorly understood. The aim of the present work is to demonstrate that for the task of image denoising, nearly stateoftheart results can be achieved using orthogonal dictionaries only, provided that they are learned directly from the noisy image. To this end, we introduce three patch based denoising algorithms which perform hard thresholding on the coefficients of the patches in imagespecific orthogonal dictionaries. The algorithms differ by the method ology of learning the dictionary: local PCA, hierarchical PCA and global PCA. We carry out a comprehensive empirical evaluation of the performance of these algorithms in terms of accuracy and running times. The results reveal that, despite its simplicity, PCAbased denoising appears to be competitive with the stateoftheart denoising algorithms, espe cially for large images and moderate signaltonoise ratios. 
Matlab opensource software to perform nonlocal filtering with shape adaptive patches. This implements an extension of the NonLocal Means (NLMeans) denoising algorithm. The idea is to replace the usual square patches used to compare pixel neighborhoods with various shapes that can take advantage of the local geometry of the image. We provide a fast algorithm to compute the NLMeans with arbitrary shapes thanks to the Fast Fourier Transform. We then consider local combinations of the estimators associated with various shapes by using Stein’s Unbiased Risk Estimate (SURE). Experimental results show that this algorithm improve the standard NLMeans performance and is close to stateoftheart methods, both in terms of visual quality and numerical results. Moreover, common visual artifacts usually observed by denoising with NLMeans are reduced or suppressed thanks to our approach. 
Matlab/Mex software to perform nonlocal filtering for Poisson noise with automatic selection of the denoising parameters. This work has been achieved by Charles Deledalle supervised by Florence Tupin and Loïc Denis. The aim was to adapt the NonLocal means (NL means) filter [1] to images sensed in lowlight conditions. The Poisson NL means filter is based on the PPB filter [2] which ables to extend the NL means to deal with the Poisson distribution followed by the noise in such images. An efficient estimator has been designed, able to cope with the statistics and especially with the signaldependent nature of such images. The Poisson NL means filter is an an extension of the non local (NL) [1] means for images damaged by Poisson noise. The proposed method is guided by the noisy image and a prefiltered image and is adapted to the statistics of Poisson noise as recommended in [2]. The influence of both images can be tuned using two filtering parameters. These two parameters are automatically set to minimize an estimation of the mean square error (MSE). This selection uses an estimator of the MSE for NL means with Poisson noise and a Newton's method to find the optimal parameters in few iterations. 
Matlab/Mex software of the PPB version for SAR interferometry. This work has been achieved by Charles Deledalle supervised by Florence Tupin and Loïc Denis. The aim was to adapt the NonLocal means (NL means) filter [7] to InSAR images. The NLInSAR filter is based on the PPB filter [6] which is an extension of the NL means to nongaussian noise and multivariate data. Then, an efficient estimator as been designed, able to cope with the statistical nature and the multidimensionnality of InSAR images. Interferometric synthetic aperture radar (InSAR) data provides reflectivity, interferometric phase and coherence images, which are paramount to scene interpretation or lowlevel processing tasks such as segmentation and 3D reconstruction. These images are estimated in practice from hermitian product on local windows. These windows lead to biases and resolution losses due to local heterogeneity caused by edges and textures. We propose a nonlocal approach for the joint estimation of the reflectivity, the interferometric phase and the coherence images from an interferometric pair of coregistered singlelook complex (SLC) SAR images. Nonlocal techniques are known to efficiently reduce noise while preserving structures by performing a 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. A statistically grounded patchsimilarity criterion suitable to SLC images is derived. A weighted maximum likelihood estimation of the SAR interferogram is then computed with weights derived in a datadriven way. Weights are defined from 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.. 
Matlab/Mex software to perform iterative nonlocal filtering for reducing: additive white Gaussian noise or, multiplicative speckle noise, i.e NakagamiRayleigh distributions (NLSAR). This work has been achieved by Charles Deledalle supervised by Florence Tupin and Loïc Denis. The aim was to adapt the NonLocal means (NL means) filter [2] to SAR images. Then, an efficient filter as been designed, able to cope with non Gaussian noise, multidimensionnal images and especially to the various existing SAR images. Results on the extended filter for amplitude SAR images are given on this page. The NLInSAR filter is also an extension of the nonlocal means based on the PPB filter for interferometric SAR images, as well as the Poisson NL means filter for images sensed in lowlight conditions. 
Edition
Opensource software distributed under CeCILL license for UNIXlike systems (such as Linux and MacOSX). MooseTeX helps you generate high quality LaTeX documents of any kind such as articles, letters, reports, theses, presentations or posters. Based on the technology of Makefile(s), the purpose of MooseTeX is ``to determine automatically which pieces of a (large) LaTeX project need to be recompiled, and issue the commands to recompile them''. For doing so, MooseTeX also includes a suite of tools to recompile each of such pieces. Note that MooseTeX is nonintrusive. It does not change the way you use LaTeX and is, as a consequence, compatible with your older projects. You can also use MooseTeX within collaborative LaTeX projects without imposing the use of MooseTeX to other collaborators. 
In France (currently out of this office): Charles Deledalle charlesalban(dot)deledalle(at)math.ubordeaux(dot)fr Bureau 209 Institut de Mathématiques de Bordeaux Université Bordeaux 351, cours de la Libération  F33405 TALENCE cedex FRANCE +33 (0)5 40 00 21 14 
In USA (currently at this office): Charles Deledalle cdeledalle(at)ucsd(dot)edu Jacobs Hall, Room 4808 Jacobs School of Engineering University of California, San Diego 9500 Gilman Drive La Jolla, CA 92093 USA 