Two-pass ℓp-regularized least-squares algorithm for compressive sensing

A two-pass algorithm for signal reconstruction in compressive sensing (CS) is proposed. It is based on using a new regularization in the objective function which elevates functional value at a previously obtained optimal or near-optimal point. Elevation in the objective function causes the optimization to converge to a new solution which would be optimal or near-optimal. Either previously obtained solution or the newly obtained solution is selected as the final solution based on which one yields lower value of the objective function. This algorithm is suitable for nonconvex optimization-based sparse signal reconstruction in CS. Simulation results are presented which indicate that the proposed algorithm is effective for not only improving the percentage of perfect reconstructions from noiseless measurements by upto 3.4% but also offering similar performance improvement for the reconstruction from noisy measurements.