An improved stopping condition guarantee recovery of sparse signal via Subspace Pursuit method

Abstract

The Subspace Pursuit (SP) algorithm is one of greedy pursuit methods which is used to reconstruct of K-sparse signal. Unlike existing condition produced by Dai and Milenkovic in 2004 that suggests the residual value of current iteration is reduced from the previous iteration, our approach eliminates useless information by reducing the number of iterations used to detect the correct support set. This operation is done by suggesting a new halting condition that can capture the best support set which can give the best representation of the reconstructed signal. The new halting conditions enhanced the SP algorithm to low computational complexity and reconstruction accuracy of the sparse signal.A mathematically proven for two halt condition: noiseless setting, and noisy setting for signal affected by Gaussian noise. An error bound relation also is driven.In this paper, we try also to relax the restricted isometry constant RIC value to narrows the gap between the known bounds and ultimate performance, which it produced by Dai.Simulation results show that the new halting condition can overpass best results produce by earlier iteration and rise time consume. Our new halting condition can catch this earlier iteration and enhanced SP algorithm results.