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Sparse Stochastic Processes With Applications To Biomedical Imaging


Michael Unser
Ecole Polytechnique Federale del Lusanne
Course Type
Group 2
Date of the course: September 5-9, 2016 h. 9:00-13:00
Duration of the course: 20 hours
Room 14
Sparse stochastic processes are continuous-domain processes that admit a parsimonious representation in some matched wavelet-like basis. Such models are relevant for image compression, compressed sensing, and, more generally, for the derivation of statistical algorithms for solving ill-posed inverse problems. The course introduces an extended family of sparse processes that are specified by a generic (non-Gaussian) innovation model or, equivalently, as solutions of linear stochastic differential equations driven by white Le?vy noise. It presents the mathematical tools for their characterisation and a reinterpretation of popular sparsity-promoting processing schemes—such as total-variation denoising, LASSO, and wavelet shrinkage—as MAP estimators for specific types of sparse processes. It also suggests alternative Bayesian recovery procedures that minimize the estimation error. The framework is illustrated with the reconstruction of biomedical images (deconvolution microscopy, MRI, X-ray tomography) from noisy and/or incomplete data. The course is targeted to an audience of graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, and statistics.



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