Iterative Hard Thresholding Algorithm Based on Backtracking

Abstract

The backtracking-based iterative hard thresholding (BIHT) algorithm is proposed to solve the problem that the number of iterations is too large and the iteration time is too long when the iterative hard thresholding (IHT) algorithm is applied to the compressive sensing.The BIHT algorithm optimizes the sub-optimal choice of supports for each iteration and reduces the times of some supports iterated repeatedly by adding the idea of backtracking.The simulation demonstrates that backtracking-based algorithm ensures the reconstruction quality and decreases the time by two orders of magnitude when compared with IHT and Normalized iterative hard thresholding (NHT) algorithms for low noise level.Simulation on the 0-1 sparse signal demonstrates that the reconstruction probability of BIHT algorithm is higher than that of the IHT algorithm if the measurement times and sparsity of the signal are the same.