Sparse Signal Reconstruction Based on Basis Pursuit-Moore-Penrose Inverse Matrix

The sparse signal reconstruction with Compressed Sensing (CS) is actually solving a system of underdetermined linear equations within the signal sparsity, of which one focus is to reduce recovery errors by the type of iteratively weightedLp(001,p=2) algorithms recently. The Basis Pursuit-Moore-Penrose Inverse Matrix (BP-MPIM) algorithm is proposed in this paper. First, nonzero element coordinates of the sparse signal are acquired by the basis pursuit algorithm, which are renamed with the sparse signal support set (corresponding with columns of the measure matrix). Then, the sparse signal recovery is solved from a set of superdetermined linear equations, which is composed of the submatrix of the sampling matrix and compressed sensing measurements. At the same time, it is proved that the reconstruction of sparse signals by this new algorithm is the one and only minimize L2 norm. Both simulative sparse signals and pulse compressed data of wideband radar echoes indicate that the new algorithm has less recovery errors than the previous algorithms, which are just in the support set.