TY  - BOOK
AU  - Unser,Michael A.
AU  - Tafti,Pouya
TI  - An introduction to sparse stochastic processes
SN  - 9781107415805 (ebook)
AV  - QA274.23 .U57 2014
U1  - 519.2/3 23
PY  - 2014///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Stochastic differential equations
KW  - Random fields
KW  - Gaussian processes
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015)
N2  - Providing a novel approach to sparsity, this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations, and that admit a parsimonious representation in a matched wavelet-like basis. Two key themes are the statistical property of infinite divisibility, which leads to two distinct types of behaviour - Gaussian and sparse - and the structural link between linear stochastic processes and spline functions, which is exploited to simplify the mathematical analysis. The core of the book is devoted to investigating sparse processes, including a complete description of their transform-domain statistics. The final part develops practical signal-processing algorithms that are based on these models, with special emphasis on biomedical image reconstruction. This is an ideal reference for graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistics
UR  - https://doi.org/10.1017/CBO9781107415805
ER  -