Sparse signal recovery with prior information by iterative reweighted least squares algorithm

Abstract

Abstract In this paper, the iterative reweighted least squares (IRLS) algorithm for sparse signal recovery with partially known support is studied. We establish a theoretical analysis of the IRLS algorithm by incorporating some known part of support information as a prior, and obtain the error estimate and convergence result of this algorithm. Our results show that the error bound depends on the best ( s + k ) {(s+k)} -term approximation and the regularization parameter λ, and convergence result depends only on the regularization parameter λ. Finally, a series of numerical experiments are carried out to demonstrate the effectiveness of the algorithm for sparse signal recovery with partially known support, which shows that an appropriate q ( 0 < q < 1 {0<q<1} ) can lead to a better recovery performance than that of the case q = 1 {q=1} .