Unconstrained regularized ℓp-norm based algorithm for the reconstruction of sparse signals

A new algorithm for signal reconstruction in a compressive sensing framework is presented. The algorithm is based on minimizing an unconstrained regularized ℓ_p norm with p 〈 1 in the null space of the measurement matrix. The unconstrained optimization involved is performed by using a quasi-Newton algorithm in which a new line search based on Banach´s fixed-point theorem is used. Simulation results are presented, which demonstrate that the proposed algorithm yields improved reconstruction performance and requires a reduced amount of computation relative to several known algorithms.