分块OSTM测量矩阵构造及自适应压缩感知算法

针对目前随机测量矩阵物理实现困难、成本较高等不足,在研究确定性测量矩阵构造的基础上,基于分块循环结构,提出了分块正交对称Toeplitz矩阵(OSTM)的构造方法.分块OSTM具有伪随机循环结构,易于硬件实现,其独立变元个数大大减少,可降低存储和运算时间.针对目前图像分块压缩感知中单一采样的缺陷,将图像块进行分类,根据图像局部结构自适应分配采样率,结合分块OSTM设计,提出了基于分块OSTM的自适应压缩采样算法.仿真实验结果表明,基于分块OSTM的压缩测量获得的重构图像PSNR显著提高,图像主观质量得到了有效改善.

Construction of Block OSTM and the Adaptive Compressed Sensing Algorithm

In order to resolve the problems of physical implementation difficulties and high cost of the existing ran-dom measurement matrices, the construction method of block orthogonal symmetric Toeplitz matrices （OSTM） wasput forward in this paper based on the research of the deterministic measurement matrices. The block OSTM couldmore easily achieve physical implementation due to its pseudo random cyclic structure. The storage and computingtime could be shortened as the matrix＇s independent variable number was greatly reduced. To overcome the shortcoming of single sampling in image block compressed sensing （BCS）, the image blocks were firstly classified accordingto the local structure of image, and then allocated to different sampling rates adaptively. Finally, this paper proposed anadaptive BCS algorithm based on the block OSTM. Simulation results show that the proposed method can acquirehigher PSNR and eliminate the block effect significantly.