Sparse Signal Recovery with Dynamic Update of Overcomplete Dictionary

Sparse signal priors help in a variety of modern signal processing tasks. In a typical sparse recovery problem, a sparse signal needs to be recovered from an underdetermined system of equations. For example, sparse representation of signal in an overcomplete dictionary or reconstruction of a sparse signal from a small number of linear measurements. In recent years, several results have been presented which guarantee reliable reconstruction under certain conditions. In this paper we investigate the problem of recovering sparse signals when elements are added to (or removed from) the overcomplete dictionary. We propose a dynamic update algorithm for basis pursuit denoising (BPDN), when new columns are added to (or removed from) the dictionary. We use this update procedure to iteratively update the working set of basis elements, chosen from a large library of basis elements, to compute the sparse solution. We also discuss the extension of the same ideas for the analysisbased BPDN.