New Improved Algorithms for Compressive Sensing Based on $\ell_{p}$ Norm

Abstract

A new algorithm for the reconstruction of sparse signals, which is referred to as the lp-regularized least squares ( lp-RLS) algorithm, is proposed. The new algorithm is based on the minimization of a smoothed lp-norm regularized square error with p <; 1 . It uses a conjugate-gradient (CG) optimization method in a sequential minimization strategy that involves a two-parameter continuation technique. An improved version of the new algorithm is also proposed, which entails a bisection technique that optimizes an inherent regularization parameter. Extensive simulation results show that the new algorithm offers improved signal reconstruction performance and requires reduced computational effort relative to several state-of-the-art competing algorithms. The improved version of the lp-RLS algorithm offers better performance than the basic version, although this is achieved at the cost of increased computational effort.