Iteratively re-weighted least squares for sparse signal reconstruction from noisy measurements

Finding sparse solutions of under-determined systems of linear equations is a problem of significance importance in signal processing and statistics. In this paper we study an iterative reweighted least squares (IRLS) approach to find sparse solutions of underdetermined system of equations based on smooth approximation of the L₀ norm and the method is extended to find sparse solutions from noisy measurements. Analysis of the proposed methods show that weaker conditions on the sensing matrices are required. Simulation results demonstrate that the proposed method requires fewer samples than existing methods, while maintaining a reconstruction error of the same order and demanding less computational complexity.