A New Approach to Sparse Image Representation Using MMV and K-SVD

This paper addresses the problem of image representation based on a sparse decomposition over a learned dictionary. We propose an improved matching pursuit algorithm for Multiple Measurement Vectors (MMV) and an adaptive algorithm for dictionary learning based on multi-Singular Value Decomposition (SVD), and combine them for image representation. Compared with the traditional K-SVD and orthogonal matching pursuit MMV (OMPMMV) methods, the proposed method runs faster and achieves a higher overall reconstruction accuracy

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Robust MEG Source Localization of Event Related Potentials: Identifying Relevant Sources by Non-Gaussianity

Independent Component Analysis (ICA) is a frequently used preprocessing step in source localization of MEG and EEG data. By decomposing the measured data into maximally independent components (ICs), estimates of the time course and the topographies of neural sources are obtained. In this paper, we show that when using estimated source topographies for localization, correlations between neural sources introduce an error into the obtained source locations. This error can be avoided by reprojecting ICs onto the observation space, but requires the identification of relevant ICs. For Event Related Potentials (ERPs), we identify relevant ICs by estimating their non-Gaussianity. The efficacy of the approach is tested on auditory evoked potentials (AEPs) recorded by MEG. It is shown that ten trials are sufficient for reconstructing all important characteristics of the AEP, and source localization of the reconstructed ERP yields the same focus of activity as the average of 250 trials

Immunoglobulin heavy chain genes somatic hypermutations and chromosome 11q22-23 deletion in classic mantle cell lymphoma : a study of the Swiss Group for Clinical Cancer Research

Mantle cell lymphoma (MCL) shares immunophenotypic and karyotypic features with chronic lymphocytic leukaemia. The latter comprises two distinct entities with prognosis dependent upon immunoglobulin heavy chain (IgH) gene mutational status and the presence of 11q deletion. We evaluated the relevance of IgH gene mutational status, IgV gene family usage and presence of 11q deletion in a series of 42 histologically reviewed classical MCL cases to determine the prognostic impact. VH3 was the most common VH family, with VH3-21 being the most frequent individual VH gene. Approximately 30% of the cases had a IgH somatic mutation rate higher than 2%, but was only higher than 4% in ter), with two minimal deleted regions, at 11q22.2 and 11q23.2. There was no association between 11q loss and IgH gene somatic mutation rate; the use of VH3-21 gene could be associated with a better prognosis