语音压缩感知硬阈值梯度追踪重构算法

Hard Threshold Gradient Pursuit Reconstruction Algorithm for Speech Compressed Sensing

本文基于语音信号在DCT域的近似稀疏性,采用压缩感知(Compressed Sensing,CS)理论对其进行压缩采样和重构。CS中的梯度追踪(Gradient Pursuit,GP)算法因计算量小,迭代硬阈值(Iterative Hard Threshold,IHT)算法因实现简单,被广泛用来重构信号。针对压缩感知理论中的GP算法的支撑集在每次迭代时仅增加一个元素,以及该算法每步迭代时仅经过一次沿负梯度方向搜索求得的解可能不是最优解的问题,本文提出了语音重构的硬阈值梯度追踪(Hard Threshold Gradient Pursuit,HTGP)算法。该算法利用IHT算法的思想选择原子更新支撑集,每步迭代时支撑集中含有K个元素,而且HTGP算法每步迭代时经过k次沿负梯度方向搜索得到最优解来代替使用计算量巨大的最小二乘来求解。实验结果表明,压缩比相同的情况下,HTGP算法具有更快速的收敛性和更高的信噪比。

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.