Stepwise Suboptimal Iterative Hard Thresholding Algorithm for Compressive Sensing

The sparse signal reconstruction problem has been the subject of extensive research in several different communities. Tractable reconstruction algorithm is a crucial and fundamental theme of compressive sensing, which has drawn significant interest in the last few years. In this paper, firstly a novel approach was proposed to improve the original IHT algorithm, which is called Orthogonal Iterative Thresholding algorithm. Compared with IHT algorithm, several simulation results verify its efficiency in reconstructing of Gaussian and Zero-one signals. After that we propose another new iterative algorithm to reconstruct a sparse signal from a underdetermined linear measurements. This algorithm modifies Backtracking-based Iterative Hard Thresholding (BIHT) by adding one atom instead of the simple backtracking step in BIHT, which can guarantee the reduction in residual error. Compared with other algorithms, such as Orthogonal IHT(OIHT), BIHT, Normalized IHT (NIHT), the experiments on Gaussian sparse signal and Zero-one sparse signal demonstrate that the proposed algorithm can provide better reconstruction performances with less computational complexity in each iteration than convex optimization method.