Sparse Optimization Theory and Methods

ISBN-13: 9781138080942 / Angielski / Twarda / 2018 / 284 str.

Yun-Bin Zhao

Opis

This book presents the state-of-the-art in theory and algorithms for signal recovery under the sparsity assumption. The unique conditions for the sparsest solution of underdetermined linear systems are described, and the results for sparse signal recovery under the range space property (RSP) are introduced. This framework is generalized to 1-bit compressed sensing, leading to a novel sign recovery theory in this area. Two efficient sparsity-seeking algorithms are presented, and theoretical efficiency of these algorithms are rigorously analysed. Under the RSP assumption, the author also provides a unified stability analysis for several popular optimization methods for sparse signal recovery.

Spis treści

Preface. Uniqueness of the Sparsest Solution of Linear Systems. Uniqueness of Solutions to `1-Minimization Problems. Equivalence of `0- and `1-Minimization. Bit Compressed Sensing. Stability of Linear Sparse Optimization Methods. Stability of Nonlinear Sparse Optimization Methods. Reweighted `1-Algorithms. Sparsity via Dual Density. References.

O autorze

YUN-BIN ZHAO is a Senior Lecturer in Theoretical and Computational Optimization at the School of Mathematics, University of Birmingham. He holds a PhD of Operations Research and Control Theory from the Chinese Academy of Sciences. He has been a Research Fellow at the Chinese University of Hong Kong, Fields Institute, and University of Toronto, and was also an Associate Professor of Operations Research at the Chinese Academy of Sciences. He is an Associate Editor or Area Editor for several journals in the areas of Applied Mathematics, Management Science, Operations Research, and Statistics. He has published 50 journal articles in operations research and applied and computational mathematics.