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

A new algorithm for the reconstruction of sparse signals, which is referred to as the ℓ_p-regularized least squares ( ℓ_p-RLS) algorithm, is proposed. The new algorithm is based on the minimization of a smoothed ℓ_p-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 ℓ_p-RLS algorithm offers better performance than the basic version, although this is achieved at the cost of increased computational effort.