A modified reconstruction algorithm for compressed sensing with least square residual

L1-norm based solver has been successfully used for sparse signal reconstruction in compressed sensing. In the paper, we propose a modified method to boost the decoding performance with least-square residual for L1 algorithms. A further performance improvement is obtained by applying iteratively reweighted L1 minimization for sparsity pattern detection. Numerical experiments show that both the proposed methods lead to a better sparsity-measurement tradeoff than their benchmark algorithms.