An Introduction to Sparse Stochastic Processes

'Over the last twenty years, sparse representation of images and signals became a very important topic in many applications, ranging from data compression, to biological vision, to medical imaging. The book An Introduction to Sparse Stochastic Processes by Unser and Tafti is the first work to systematically build a coherent framework for non-Gaussian processes with sparse representations by wavelets. Traditional concepts such as Karhunen-Loeve analysis of Gaussian processes are nicely complemented by the wavelet analysis of Levy Processes which is constructed here. The framework presented here has a classical feel while accommodating the innovative impulses driving research in sparsity. The book is extremely systematic and at the same time clear and accessible, and can be recommended both to engineers interested in foundations and to mathematicians interested in applications.' David Donoho, Stanford University 'This is a fascinating book that connects the classical theory of generalised functions (distributions) to the modern sparsity-based view on signal processing, as well as stochastic processes. Some of the early motivations given by I. Gelfand on the importance of generalised functions came from physics and, indeed, signal processing and sampling. However, this is probably the first book that successfully links the more abstract theory with modern signal processing. A great strength of the monograph is that it considers both the continuous and the discrete model. It will be of interest to mathematicians and engineers having appreciations of mathematical and stochastic views of signal processing.' Anders Hansen, University of Cambridge