Reconstruction for Sparse Signal Based on Bidirectional Sparsity Adaptive and Weak Selection of Atoms Matching Pursuit

Abstract

Under the framework of compressed sensing theory, the greedy algorithm achieves good reconstruction performance with known signal sparsity. However, unknown sparsity of sparse signals in practical applications brings obstacles for signal reconstruction. Specifically, the conventional sparsity adaptive adjustment algorithm takes long time to finish the reconstruction, and the accuracy of reconstruction is not good enough. To solve this problem, this paper proposes a new matching pursuit reconstruction algorithm based on bidirectional sparsity adaptive adjustment and weak selection of atoms (BSA-WSAMP). In this algorithm, the optimization strategy for atom weak selection is employed to update the support set, and the idea of "zoom" bidirectional variable step-size is applied to achieve the sparsity adaptive adjustment. Based on this, the number of iterations can be reduced effectively, and the accurate reconstruction of the sparse signal is obtained. Simulation results indicate that the proposed BSA-WSAMP algorithm achieves better adaptive characteristic of the sparsity, higher reconstruction quality, lower reconstruction complexity, and less reconstruction time than some existing reconstruction algorithms.