A thresholded landweber iteration based on sensing dictionary

Abstract

Thresholded Landweber Iteration (TLI) is an attractive algorithm since it has the advantage of simplicity for the problem of sparse reconstruction. However, this algorithm depends heavily on the coherence property of the redundant dictionary, and its convergence rate is slow. In this paper, we develop a modified version of TLI by using a sensing dictionary. The proposed algorithm significantly improves the reconstruction performance and the convergence properties when compared to the classical TLI. We provide a sufficient condition for which the modified TLI algorithm can be guaranteed to exactly identify the correct atoms and also discuss the convergence properties for this algorithm. Finally, simulation results are presented to demonstrate the superior performance of the proposed algorithm.