General similar sensing matrix pursuit: An efficient and rigorous reconstruction algorithm to cope with deterministic sensing matrix with high coherence

In this paper, a novel algorithm, called the general similar sensing matrix pursuit (GSSMP), is proposed to deal with the deterministic sensing matrix with high coherence. First, the columns of the sensing matrix are divided into a number of similar column groups based on the similarity distance. Each similar column group presents a set of coherent columns or a single incoherent column, which provides a unified frame work to construct the similar sensing matrix. The similar sensing matrix is with low coherence provided that the minimum similar distance between any two condensed columns is large. It is proved that under appropriate conditions the GSSMP algorithm can identify the correct subspace quite well, and reconstruct the original K-sparse signal perfectly. Moreover, we have enhanced the proposed GSSMP algorithm to cope with the unknown sparsity level problem, by testing each individual contributing similar column group one by one to find the true vectors spanning the correct subspace. The simulation results show that the modified GSSMP algorithm with the contributing similar column group test process can estimate the sparse vector representing the radar scene with an unknown number of targets