Hard Threshold Gradient Pursuit Reconstruction Algorithm for Speech Compressed Sensing

Based on the approximate sparsity of speech signal in the DCT domain, compressed sensing (CS) theory is applied to reconstruct speech signal in this paper. Gradient pursuit (GP) algorithm with low complexity and iterative hard threshold algorithm with simple realization are widely used to reconstruct signals for CS. And the hard threshold gradient pursuit (HTGP) algorithm for speech reconstruction is proposed to solve the problem that the support of GP algorithm is only added one element and the solution may not be the optimal solution in the course of each iterative. The HTGP algorithm selects for atomic in order to update the support through the IHT algorithm, and the support set contains K elements within per iteration. The HTGP algorithm searches for optimal solution through the negative gradient direction instead of the huge computation of least square solution in per iteration. The experimental simulations demonstrate that the HTGP algorithm has faster convergence and higher signal to noise ratio at the same sampling rate.