压缩感知中测量矩阵筛选的等值线图和优化的适用性

Applicability of Contour map and Optimization of Measurement Matrix Screening in Compressed Sensing

针对压缩感知中测量矩阵选择的盲目性,本文提出了通过等值线图筛选测量矩阵的方法。首先统计并绘制了最大列数为256和4096的0-1随机矩阵、0-1循环矩阵和高斯矩阵优化前后的等值线图及其差值图;然后,通过查阅等值线图即可按需筛选测量矩阵和优化潜力大的测量矩阵,大大方便简化了测量矩阵的选择定型工作。研究发现,测量矩阵优化适用于最大列数为256和4096的0-1随机矩阵和0-1循环矩阵,以及最大列数为256的高斯矩阵;但不适用于最大列数为4096的高斯矩阵;给出了相应的理论分析。最后,通过重构实例,验证了等值线图的正确性和测量矩阵优化的适用性。

Aiming at the blindness of measurement matrix selection in compressed sensing,this paper proposed a method of screening measurement matrices through contour maps.This paper first counted and drew the contour map and the difference map of the 0-1 random matrix with the maximum number of columns of 256 and 4096,the 0-1 circulant matrix and the Gaussian matrix before and after optimization;and the,by consulting the contour map,the measurement matrix and the measurement matrix with high optimize potential can be filtered as needed,which greatly facilitates the selection and finalization of the measurement matrix.The study found that the measurement matrix optimization is suitable for 0-1 random matrices and 0-1 circulant matrices with the maximum number of columns of 256 and 4096,and Gaussian matrices with the maximum number of columns of 256;but not suitable for Gaussian matrices with the maximum number of columns of 4096.And the corresponding theoretical analysis was given by this paper.Finally,this paper further validated the correctness of the contour map and the applicability of the optimization of the measurement matrix through reconstruction examples.