压缩感知二进制测量矩阵的构造

摘要

To solve the problem of the reconstruction performance of the existing binary measurement matrix and the negative correlation from hardware implementation,this paper proposed a new type of compressed sensing pseudo-random block diagonal (PRBD) matrix.It constructed the PRBD measurement matrix by a structured method with the orthogonal balanced Gold sequences,the block diagonal matrix and the downsampling matrix,which not only had the advantages of easy-hardware implementation and low computing complexity of deterministic measurement matrices,but also made the greedy pursuit algorithm reconstruct image smoothly.Theoretical analysis and experimental results show that the PRBD measurement matrix has a good reconstruction pedormance and introduces an increment of 0.5 dB or more in the indicator of PSNR when comparing to the conventional binary measurement matrix.Meanwhile,the PRBD measurement matrix will also bring a shorter time for image reconstruction by using image block reconstruction method without impacting the performance of reconstruction.%针对现有二进制测量矩阵重构性能和硬件实现的负相关性,提出了一种新型压缩感知二进制测量矩阵——伪随机块对角矩阵(PRBD).PRBD矩阵使用平衡正交Gold序列、块对角矩阵和降采样矩阵,通过结构化的方法构造,不仅保留了确定性矩阵易于硬件实现和计算复杂度低的优点,而且有利于贪婪追踪算法进行图像重构.实验结果表明,PRBD测量矩阵具有良好的重构性能,在峰值信噪比(PSNR)的指标上比常用的二进制测量矩阵提高0.5 dB以上.特别地,PRBD测量矩阵可采用图像分块重构的方法,在保证重构性能良好的情况下,图像重构需要的时间较短.