An Adaptive Sparsity Estimation KSVD Dictionary Construction Method for Compressed Sensing of Transient Signal

Abstract

Overcomplete dictionaries occupy an essential position in the sparse representation of signals. The dictionary construction method typically represented by $K$ singular value decomposition (KSVD) is widely used because of its concise and efficient features. In this paper, based on the background of transient signal detection, an adaptive sparse estimation KSVD (ASE-KSVD) dictionary training method is proposed to solve the redundant iteration problem caused by fixed sparsity in existing KSVD dictionary construction. The algorithm features an adaptive sparsity estimation strategy in the sparse coding stage, which adjusts the number of iterations required for dictionary training based on the pre-estimation of the sample signal characteristics. The aim is to decrease the number of solutions of the underdetermined system of equations, reduce the overfitting error under the finite sparsity condition, and improve overall training efficiency. We compare four similar algorithms under the speech signal and actual shock wave sensor network data conditions, respectively. The results show that the proposed algorithm has obvious performance advantages and can be applied to real-life scenarios.