Title: Optimization Algorithms for Sparse Representations: Some History and Recent DevelopmentsProfessor Mário A. T. Figueiredo
Department of Electrical and Computer Engineering
Instituto Superior Técnico (IST)
Convex optimization has played a central role in signal/image processing based on sparse representations, namely in addressing inverse problems (such as reconstruction and deconvolution) using sparsity-based regularization. The optimization problems resulting from these sparsity-based formulations are characterized by a very high dimensionality combined with non-smoothness, and have stimulated much research in special purpose algorithms for these applications. This talk will present an historical overview of this area, from the first algorithms proposed in the early 2000's to the most recent advances, which are orders of magnitude faster than those early methods. In the last part of the talk, some recent non-convex optimization techniques (namely for blind image deconvolution) will also be addressed.
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Title: Morphological Diversities in AstrophysicsProfessor Jean-Luc Starck
Head of CosmoStat Laboratory
Institute of Research into the Fundamental Laws of the Universe (IRFU)
We present the concept of Morphological Diversity, which is based on sparsity and allows us to separate blindly one data set into several components, each one being sparse in a given representation. This method has been extended to multichannel data. We show how this idea allows us to analyze differently astrophysical data set such as cosmic microwave background data provided by WMAP and PLANCK satellites.
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Title: Sparse Stochastic Processes with Application to Biomedical ImagingProfessor Michael Unser
Biomedical Imaging Group
Ecole Polytechnique Fédérale de Lausanne
Sparse stochastic processes are defined in terms of a generalized innovation model: they are characterized by a whitening operator that shapes their Fourier spectrum, and a Lévy exponent that controls their intrinsic sparsity. Starting from the characteristic form of these processes, we derive an extended family of Bayesian signal estimators. While our family of MAP estimators includes the traditional methods of Tikhonov and total-variation (TV) regularization as particular cases, it opens the door to a much broader class of potential functions (associated with infinitely divisible priors) that are inherently sparse and typically nonconvex. We apply our framework to the reconstruction of magnetic resonance images and phase-contrast tomograms and to the deconvolution of fluorescence micrographs; we also present simulation examples where the proposed scheme outperforms the more traditional convex optimization techniques (in particular, TV).
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Panel: Sparse Representation for Image Analysis and Recognition: Trends and Applications
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ICIAR - International Conference on Image Analysis and Recognition
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