An introduction to sparse stochastic processes

by Unser, Michael A.

Type Book

Rate 0.0 /5

Details

Files

Reviews

Download

Title Statements

Full title :An introduction to sparse stochastic processes / Michael Unser and Pouya D. Tafti, École Polytechnique Fédérale, Lausanne.

Summary

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.

Edition Statements

Publication Date:2014.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:2014.

The Physical Object

Description:1 online resource (xviii, 367 pages)

Edition Identifiers

ISBN:9781107415805, 1107415802, 9781316054505, 1316054500
oclc:ocn890603777
LC Classification:QA274.23
Dewey Decimal:519.2/3

Roadmap to the book -- Mathematical context and background -- Continuous-domain innovation models -- Operators and their inverses -- Splines and wavelets -- Sparse stochastic processes -- Sparse representations -- Infinite divisibility and transform-domain statistics -- Recovery of sparse signals -- Wavelet-domain methods -- Conclusion -- Appendix A : Singular integrals -- Appendix B : Positive definiteness -- Appendix C : Special functions.