An Introduction to Sparse Stochastic Processes 1st Edition by Michael Unser, Pouya Tafti ISBN 978-1107058545 1107058546

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Product details: 

ISBN 10:  1107058546

ISBN 13: 978-1107058545

Author: Michael Unser, Pouya D. Tafti

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.

Table of contents: 

1. Introduction

2. Roadmap to the Book

3. Mathematical Context and Background

4. Continuous-Domain Innovation Models

5. Operators and Their Inverses

6. Splines and Wavelets

7. Sparse Stochastic Processes

8. Sparse Representations

9. Infinite Divisibility and Transform-Domain Statistics

10. Recovery of Sparse Signals

11. Wavelet-Domain Methods

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Tags: Michael Unser, Pouya Tafti, An Introduction, Sparse Stochastic