The tail-Hadamard product parametrization algorithm for compressed sensing

A tail-Hadamard product parametrization (tail-HPP) approach is proposed for sparse signal recovery in compressed sensing. The algorithm has both the efficiency of the HPP technique and the much greater capacity of signal recovery enabled by the tail-ℓ1-minimization approach. We prove that the tail-HPP approach is equivalent to the tail-ℓ1-minimization problem. The efficiency of the tail-HPP algorithm is clearly evident compared to direct solution approaches of the tail-ℓ1-minimization problem. These superiority of the tail-HPP algorithm is confirmed by extensive simulation experiments in comparison with state-of-the-art sparse recovery techniques.