Improved Sufficient Conditions Based on RIC of Order 2s for IHT and HTP Algorithms

Abstract

Reconstructing an s-sparse signal x from an un- derdetermined noisy linear model arises in many applications. The iterative hard thresholding (IHT) and hard thresholding pursuit (HTP) algorithms are two popular sparse signal recovery algorithms. Since their recovery performances can be theoreti- cally characterized by their sufficient conditions of stable sparse signal recovery, it is essential to establish less restrictive sufficient conditions. This work develops δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2s</sub> -based sufficient conditions for stable recovery with IHT and HTP. The two new sufficient conditions are significantly less restrictive than the state-of-the- art ones for IHT and HTP.