Recovery of sparse signals from noisy measurements using an ℓp regularized least-squares algorithm

A new algorithm for the reconstruction of sparse signals from noise corrupted compressed measurements is presented. The algorithm is based on minimizing an ℓ
_p,ϵ
-norm regularized ℓ
₂
error. The minimization is carried out by iteratively taking descent steps along the basis vectors of the null space of the measurement matrix and its complement space. The step size is computed using a line search based on Banach's fixed-point theorem. 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.