压缩感知中测量矩阵与重建算法的协同构造

Collaborative Construction of Measurement Matrix and Reconstruction Algorithm in Compressive Sensing

本文提出基于感知字典的迭代硬阈值(SDIHT)算法,以此协同构造压缩感知中测量矩阵与重建算法.将成对测量矩阵与感知字典分别用于压缩投影和构造重建算法,重建迭代至残差为零,从而精确恢复原始稀疏信号.本文证明了SDIHT算法精确恢复原始稀疏信号的充分条件.SDIHT算法的优点是重建精度高和计算复杂度低.仿真实验表明,当信号稀疏度或测量次数相同时,相比IHT、OMP和BIHT算法,SDIHT算法重建0-1稀疏信号和二维图像效果更好、算法效率更高.

This paper proposes a novel Sensing Dictionary-based Iterative Hard Thresholding（SDIHT） algorithm,which can collaboratively construct the measurement matrix and the reconstruction algorithm in compressive sensing.Pairs of measurement matrix and sensing dictionary are used for compressive projection and designing reconstruction algorithm respectively.The original sparse signal can be recovered exactly until the residual is reduced to zero as iteration proceeds.A sufficient condition for SDIHT algorithm is given and proved.The benefit of SDIHT is its high reconstruction accuracy and low computational complexity.Computer simulation indicates that when the signal sparsity or the measurement number is fixed,SDHIT algorithm can reconstruct 0-1 sparse signal and two dimensional images with better performance and higher efficiency than IHT,OMP and BIHT algorithm can.