Sparse Optimization Theory and Methods

Seeking sparse solutions of underdetermined linear systems is crucial in engineering and science, and mathematical optimization plays a fundamental role in developing these results. Sparse Optimization Theory and Methods presents the state-of-the-art theory and algorithms for signal recovery under the sparsity assumption, including the up-to-date uniqueness conditions for the sparsest solution and the results for sparse signal recovery under the matrix property called range space property (RSP). Two efficient sparsity-seeking algorithms are presented, and a novel stability analysis for popular optimization methods is provided.

Format: Paperback / softback
Length: 284 pages
Publication date: 31 March 2021
Publisher: Taylor & Francis Ltd

Seeking sparse solutions of underdetermined linear systems is a crucial requirement in numerous fields of engineering and science, including signal and image processing. The efficient sparse representation plays a pivotal role in various big or high-dimensional data processing, yielding fruitful theoretical and practical outcomes in these domains. The mathematical optimization assumes a fundamental role in the development of these results and serves as the mainstream numerical algorithms for the sparsity-seeking problems arising from big-data processing, compressed sensing, statistical learning, computer vision, and other related areas. This has garnered significant interest from researchers at the intersection of engineering, mathematics, and computer science.

Sparse Optimization Theory and Methods provides an comprehensive overview of the state-of-the-art theory and algorithms for signal recovery under the sparsity assumption. The book describes the up-to-date uniqueness conditions for the sparsest solution of underdetermined linear systems. Moreover, it introduces the results for sparse signal recovery under the matrix property called range space property (RSP), which is a deep and mild condition for the sparse signal to be recovered by convex optimization methods. This framework is extended to 1-bit compressed sensing, leading to a novel sign recovery theory in this area. Two efficient sparsity-seeking algorithms, namely reweighted l1-minimization in primal space and the algorithm based on complementary slackness property, are presented. The theoretical efficiency of these algorithms is rigorously analyzed within the book.

Under the RSP assumption, the author also presents a novel and unified stability analysis for several popular optimization methods for sparse signal recovery, including l1-mininization, Dantzig selector, and LASSO. This book incorporates a wealth of practical examples and case studies to illustrate the theoretical concepts and algorithms discussed. It serves as a valuable resource for researchers, practitioners, and students interested in signal processing, optimization, and their applications in various fields.

Weight: 544g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367781101