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Charles Deledalle - Software

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Inverse problems and low-rank matrices

GSURE low rank
GSURE in low rank matrix denoising (2017)
Matlab open-source software distributed under CeCILL license for data driven srhinkage of singular values.
 
We consider the problem of estimating a low-rank 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 data-driven 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 finite-dimensional matrix denoising for Gamma-distributed and Poisson-distributed measurements.
 
SUGAR software
SUGAR (2014)
Matlab open-source software for the automatic selection of (multiple) parameters in inverse problems.
 
Algorithms to solve variational regularization of ill-posed 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 so-called 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 non-smooth regularizers, such as the popular l1-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 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 soft-thresholding, the SUGAR is proved to be also a consistent estimator. The SUGAR can then be used as a basis to perform a quasi-Newton optimization. The computation of the SUGAR relies on the closed-form (weak) differentiation of the non-smooth function. We provide its expression for a large class of iterative proximal splitting methods and apply our strategy to regularizations involving non-smooth convex structured penalties. Illustrations on various image restoration and matrix completion problems are given.
 

Denoising

FEPLL software
FEPLL (2017)
Matlab open-source software to perform fast image restoration with a GMM prior.
 
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 work, 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.
 
MuLoG software
MuLoG (2016-2017)
Matlab open-source 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 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) 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 (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.
 
RNLF software
RNLF: Regularized NL-means (RNL) and Noise Level Function (NLF) estimation (2015)
Matlab open-source software to perform (blind) denoising. It implements the followings
  • Generation of several types of signal-dependent noises,
  • Homegeneous block detection insensitive to the noise model,
  • Estimation of signal-dependent noise with 2nd order polynomial variance,
  • Non-local, total-variation and regularized non-local filtering for signal-dependent noises.
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. When the nature of the noise is unknown, a two-step algorithm 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 non-parametric test is applied to decide weather each region is homogeneous or not. Based on Kendall's τ coefficient (a rank-based measure of correlation), this detector has a non-detection rate independent on the unknown distribution of the noise, provided that it is at least spatially uncorrelated. Once homogeneous regions are detected, the noise level function is estimated as a second order polynomial minimizing the l1 error on the statistics of these regions. Given the known or estimated nature of noise, the non-local means (NL-means) can be used to perform denoising by exploiting the natural redundancy of patterns inside an image. Denoising can also be performed by total variation (TV) minimization which leads to restore regular images. The proposed regularized NL-means (RNL) algorithm combines these two methods and reduces both of their respective defaults by minimizing an adaptive total variation with a non-local data fidelity term. Besides, this model adapts to different noise statistics leading to a fully blind denoising algorithm. We develop this model for image denoising and video denoising with 3D patches.
 
NL-SAR software
NL-SAR (2013-2014)
Open-source software distributed under CeCILL license to perform adaptive non-local (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 multi-looking (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 locally adapt the estimation. Non-local means successfully adapt smoothing by deriving data-driven weights from the similarity between small image patches. The generalization of non-local approaches offers a flexible framework for resolution-preserving speckle reduction. NL-SAR is a general method that builds extended non-local neighborhoods for denoising amplitude, polarimetric and/or interferometric SAR images. These neighborhoods are defined on the basis of pixel similarity as evaluated by multi-channel comparison of patches. Several non-local 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 multi-look 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.
 
NLSPCA software
Poisson NLSPCA (2012)
Matlab open-source software to perform non-local filtering in an extended PCA domain for Poisson noise.
 
Photon-limited 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 photon-limited images which combines elements of dictionary learning and sparse patch-based representations of images. The method employs both an adaptation of Principal Component Analysis (PCA) for Poisson noise and recently developed sparsity-regularized convex optimization algorithms for photon-limited images. A comprehensive empirical evaluation of the proposed method helps characterize the performance of this approach relative to other state-of-the-art denois ing methods. The results reveal that, despite its conceptual simplicity, Poisson PCA-based denoising appears to be highly competitive in very low light regimes.
 
NL-PCA software
NLPCA (2011)
Matlab open-source software to perform non-local 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 state-of-the-art 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 image-specific 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, PCA-based denoising appears to be competitive with the state-of-the-art denoising algorithms, espe- cially for large images and moderate signal-to-noise ratios.
 
NLMSAP software
NLMSAP (2011)
Matlab open-source software to perform non-local filtering with shape adaptive patches.
 
This implements an extension of the Non-Local Means (NL-Means) 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 NL-Means 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 NL-Means performance and is close to state-of-the-art methods, both in terms of visual quality and numerical results. Moreover, common visual artifacts usually observed by denoising with NL-Means are reduced or suppressed thanks to our approach.
 
Poisson NL-means software
Poisson NL-means (2010)
Matlab/Mex software to perform non-local 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 Non-Local means (NL means) filter [1] to images sensed in low-light 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 signal-dependent 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 pre-filtered 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.
 
NL-InSAR software
Non-local InSAR (NL-InSAR) filter (2011)
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 Non-Local means (NL means) filter [7] to InSAR images. The NL-InSAR filter is based on the PPB filter [6] which is an extension of the NL means to non-gaussian noise and multivariate data. Then, an efficient estimator as been designed, able to cope with the statistical nature and the multi-dimensionnality of InSAR images. Interferometric synthetic aperture radar (InSAR) data provides reflectivity, interferometric phase and coherence images, which are paramount to scene interpretation or low-level 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 non-local approach for the joint estimation of the reflectivity, the interferometric phase and the coherence images from an interferometric pair of co-registered single-look complex (SLC) SAR images. Non-local 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 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 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..
 
PPB software
Probabilistic Patch Based (PPB) filter (2009)
Matlab/Mex software to perform iterative non-local filtering for reducing: additive white Gaussian noise or, multiplicative speckle noise, i.e Nakagami-Rayleigh distributions (NL-SAR).
 
This work has been achieved by Charles Deledalle supervised by Florence Tupin and Loïc Denis. The aim was to adapt the Non-Local means (NL means) filter [2] to SAR images. Then, an efficient filter as been designed, able to cope with non Gaussian noise, multi-dimensionnal images and especially to the various existing SAR images. Results on the extended filter for amplitude SAR images are given on this page. The NL-InSAR filter is also an extension of the non-local means based on the PPB filter for interferometric SAR images, as well as the Poisson NL means filter for images sensed in low-light conditions.
 

Edition

MooseTeX
MooseTeX (2012 - 2014)
Open-source software distributed under CeCILL license for UNIX-like systems (such as Linux and MacOS-X).
 
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 non-intrusive. 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.
 
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Last modified: Fri Oct 27 18:21:01 Europe/Berlin 2017