TLS-FOCUSS for sparse recovery with perturbed dictionary

In this paper, we propose a new algorithm, TLS-FOCUSS, for sparse recovery for large underdetermined linear systems, based on total least square (TLS) method and FOCUSS(FOCal Underdetermined System Solver). The problem of sparse recovery when perturbations appear in both the measurements and the dictionary (sensing matrix) is considered. FOCUSS algorithm is extended with main idea of TLS to reduce the impact of the perturbation of dictionary on the performance of sparse recovery. The simulation results illustrate the advantage of TLS-FOCUSS on accuracy and stability compared with ordinary FOCUSS algorithm.