Pseudocolor display of a realization of a Mondrian process
Cover design by Annette Unser 
AbstractSparse stochastic processes are continuousdomain processes that admit a parsimonious representation in some matched waveletlike basis. Such models are relevant for image compression, compressed sensing, and, more generally, for the derivation of statistical algorithms for solving illposed inverse problems. This book introduces an extended family of sparse processes that are specified by a generic (nonGaussian) innovation model or, equivalently, as solutions of linear stochastic differential equations driven by white Lévy noise. It presents the mathematical tools for their characterization. The two leading threads of the exposition are
The core of the book is devoted to the investigation of sparse processes, including the complete description of their transformdomain statistics. The final part develops signalprocessing techniques that are based on these models. This leads to a reinterpretation of popular sparsitypromoting processing schemes—such as totalvariation 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, Xray tomography) from noisy and/or incomplete data. The book is mostly selfcontained. It 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. 
Audio: Sparve vs. GaussianAll the three signals have the same spectral contents (aminor chord)
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