语音重构的DCT域加速Landweber迭代硬阈值算法

重构信号的最基本理论依据是该信号在某个变换域是稀疏的或近似稀疏的。基于语音信号在DCT域的近似稀疏性，可以采用压缩感知(Compressed Sensing, CS)理论对其进行重构。压缩感知理论中的迭代硬阈值(Iterative hard thresholding, IHT)算法以其较好的性能被广泛用来重构信号，但其收敛速度比较慢，如何提高收敛速度，一直是迭代硬阈值算法研究的重点之一。针对压缩感知理论中的IHT算法收敛速度相当慢的问题，提出了语音重构的DCT域加速Landweber迭代硬阈值(Accelerated Landweber iterative hard thresholding, ALIHT)算法。该算法对原始语音信号做DCT变换，然后在DCT域将每一步Landweber迭代分解为矩阵计算和求解两步，通过修改其中的矩阵计算部分实现Landweber迭代加速，最后通过迭代硬阈值对信号做阈值处理。实验结果表明，加速Landweber迭代硬阈值算法加快了收敛速度、减少了计算量。 

Accelerated Landweber Iterative Hard Thresholding Algorithm in the DCT Domain for Speech Reconstruction

The basic theory of reconstruction signals is that the signals are sparse or approximate sparse in a transform domain. Based on the approximate sparsity of speech signal in the DCT domain,compressed sensing theory is applied to reconstruct speech signal.The iterative hard thresholding(IHT) algorithm with good performances is widely used to reconstruct signals, however,its convergence speed is too slow.How to improve the convergence speed of the iterative hard thresholding algorithm has been a hot topic.The accelerated Landweber iterative hard thresholding(ALIHT) algorithm in the DCT domain for speech reconstruction is proposed to solve the problem that the convergence speed is too slow when the iterative hard thresholding algorithm is applied to the compressed sensing.The accelerated Landweber iterative hard thresholding algorithm firstly transforms the original speech signal to its DCT domain,and then speeds up the convergence speed by discomposing the each one step of the Landweber iteration in the iterative hard thresholding algorithm into two steps as the matrix computation and solution in the DCT domain,and modifying the matrix computation step.The experimental simulations show that the accelerated Landweber iterative hard thresholding algorithm increases convergence speed and reduces the calculation measures.