Applications of sparse representation and compressive sensing

Abstract

Applications of sparse representation and compressive sensing are discussed. A sparse signal is a signal that can be represented as a linear combination of relatively few base elements in a basis or an over complete dictionary. The new theory of sparse representation and compressive sensing not only establishes a more rigorous mathematical framework for studying high-dimensional data, but also provides computationally feasible ways to uncover the structures of the data, giving rise to a large repertoire of efficient algorithms. The papers aim to provide good survey or review of past achievements in the field, or feature some new exciting developments by the authors, or discuss promising new directions and extensions. The new theory of sparse representation and compressive sensing not only establishes a more rigorous mathematical framework for studying high-dimensional data, but also provides computationally feasible ways to uncover the structures of the data, giving rise to a large repertoire of efficient algorithms.