Abstract: Compressed Sensing (CS) is a new framework for simultaneous sensing and compression, and how to reconstruct sparse signal form limited measurements is the key problem in CS. In this paper, a novel method called Iterative Smoothed l 0  -norm (ISL0) is proposed for sparse signal reconstruction. This method estimates a support set  I  from a current reconstruction and obtains a new reconstruction by solving the minimization problem based on the support set  I, and it iterates these two steps for a small number of times. Simulation results show that the proposed method needs fewer measurements than existing methods, while needing the low computational cost.

Key words: Compressed sensing, Sparse signal reconstruction, Basis pursuit, Smoothed , l 0 norm