Applications of Sparse Representation and Compressive Sensing [Scanning the Issue]

Sparse representation and compressive sensing establishes a more rigorous mathematical framework for studying high-dimensional data and ways to uncover the structures of the data, giving rise to a large repertoire of efficient algorithms. A sparse signal is a signal that can be represented as a linear combination of relatively few base elements in a basis or an overcomplete dictionary. A sufficiently sparse linear representation can be correctly and efficiently computed by greedy methods and convex optimization (i.e., the l¹-l⁰ equivalence), even though this problem is extremely difficult-NP-hard in the general case.