Improved Stochastic Gradient Matching Pursuit Algorithm Based on the Soft-Thresholds Selection

Abstract

The preliminary atom set exits redundant atoms in the stochastic gradient matching pursuit algorithm, which affects the accuracy of the signal reconstruction and increases the computational complexity. To overcome the problem, an improved method is proposed. Firstly, a limited soft-threshold selection strategy is used to select the new atoms from the preliminary atom set, to reduce the redundancy of the preliminary atom set. Secondly, before finding the least squares solution of the residual, it is determined whether the number of columns of the measurement matrix is smaller than the number of rows. If the condition is satisfied, the least squares solution is calculated; otherwise, the loop is exited. Finally, if the length of the candidate atomic index set is less than the sparsity level, the current candidate atom index set is the support atom set. If the condition is not satisfied, the support atom index set is determined by the least squares solution. Simulation results indicate that the proposed method is better than other methods in terms of the reconstruction probability and shorter running time than the stochastic gradient matching pursuit algorithm.