Fast Thresholding Algorithms with Feedbacks and Partially Known Support for Compressed Sensing

Abstract

Some works in modified compressive sensing (CS) show that reconstruction of sparse signals can obtain better results than traditional CS using the partially known support. In this paper, we extend the idea of these works to the null space tuning algorithm with hard thresholding, feedbacks ([Formula: see text]) and derive sufficient conditions for robust sparse signal recovery. The theoretical analysis shows that including prior information of partially known support relaxes the preconditioned restricted isometry property condition comparing with the [Formula: see text]. Numerical experiments demonstrate that the modification improves the performance of the NST+HT+FB, thereby requiring fewer samples to obtain an approximate reconstruction. Meanwhile, a systemic comparison with different methods based on partially known support is shown.