部分哈达玛矩阵分段弱正交匹配追踪算法

Segment Weak Orthogonal Matching Pursuit Algorithm Based on Partial Hadamard Matrix

为解决分段弱正交匹配追踪算法在测量过程中难以获得高精度重构信号的问题,首先对以高斯矩阵为测量矩阵的传统SWOMP算法进行了分析,指出问题的关键在于高斯矩阵列相干性过大会影响残差信号的匹配过程,从而导致部分信号丢失,使重构精度下降;然后,根据分析提出了一种基于部分哈达玛矩阵的分段弱正交匹配追踪(PH-SWOMP)算法,其中部分哈达玛矩阵根据偶数行抽取原则进行构造,可以显著降低测量矩阵的互相关性;最后,通过与传统SWOMP算法的图像重构对比仿真实验对PH-SWOMP算法性能进行了验证,其中传统SWOMP算法分别选取高斯矩阵、托普利兹矩阵等4种矩阵作为测量矩阵.仿真结果表明,在相同条件下,相比于传统SWOMP算法,PH-SWOMP算法信噪比最大提高了53.95%,相应的重构时间缩短了15.41%,具有更小的恢复残差以及更高的信号重构成功率.

In order to solve the problem that the segment weak orthogonal matching pursuit algorithm was difficult to obtain high-precision reconstructed signals during the measurement process,firstly,the traditional SWOMP algorithm with Gaussian matrix as the measurement matrix was analyzed,and the key to the problem lay in the column coherence of the Gaussian matrix,which excessive assembly affects the matching process of the residual signal,resulting in partial signal loss and reduced reconstruction accuracy.Then,based on the analysis,a piecewise weak orthogonal matching tracking algorithm(PH-SWOMP)based on partial Hadamard matrix was proposed.Part of the Hadamard matrix was constructed according to the principle of even row extraction,which can significantly reduce the cross-correlation of the measurement matrix.Finally,the performance of the PH-SWOMP algorithm was verified through the image simulation experiment with the traditional SWOMP algorithm.Among them,the traditional SWOMP algorithm selected the Gaussian matrix,the Toeplitz matrix and other two matrices as the measurement matrix.The simulation results show that under the same conditions,compared with the traditional SWOMP algorithm,the PH-SWOMP algorithm has a maximum signal-to-noise ratio increase of 53.95%,the corresponding reconstruction time is reduced by 15.41%,and has a smaller recovery residual and higher signal reconstruction power.