一种利用相关性优化压缩感知测量矩阵的方法

Optimization method of measurement matrix used of mutual coherence matrix in the compressed sensing

传统的采样方法要求采样频率不小于奈奎斯特频率的2倍,然而采集到的数据存在很大程度的冗余。压缩感知方法则利用少量的非适应线性测量就能够实现对原始信号压缩采样,进而也能精确的恢复出原始信号,因此压缩感知中测量矩阵的研究具有重要的理论意义。提出了一种基于梯度迭代实现对测量矩阵的优化方法。实验表明利用梯度迭代方法优化的测量矩阵恢复得到图像的PSNR,高于Valid提出方法恢复图像的PSNR,以及未优化的测量矩阵恢复图像的PSNR。另外梯度迭代方法改善了G矩阵中非对角元素的分布情况,更集中分布在0附近,达到了测量矩阵与稀疏矩阵的互相关系数减小的目的。

Traditional sampling method request that the sampling rate should not be less than twice the Nyquist sampling rate,which result in lots of redundancy data. Making use of less nonlinear measurements, the compressed sensing method can realize the original signal compressed sampled at the same time,then recovered the original signal precisely. So the research of measurement matrix of compressed sensing has important theoretical significance. A novel method of gradient-based iteration has been proposed in the paper to optimize measurement matrix. And the experimental results show that PSNR of recovered image, which is achieved by the method of gradient-based iteration,is higher than non- optimized as the well as Valid＇s method＇s. In addition, the gradient-based iteration proposed in the paper makes more off-diagonal entries of G distribute around zero,achieving the purpose of getting the mutual coherence more smaller.