测量矩阵是压缩感知理论的三大核心部分之一，它直接影响着压缩感知理论在图像融合领域的应用。针对随机测量矩阵不易硬件实现的问题，本文设计了一种仅由-1、0和1三个值组成的测量矩阵，并利用基于Gram矩阵的优化方法使其尽可能地与稀疏变换矩阵不相关。实验结果表明，该测量矩阵不仅能提高重构图像的PSNR(Peak Signal to Noise Ratio)，而且将其应用于基于压缩感知的图像融合中，在采样率仅为非压缩域50%的情况下仍能取得较好的融合效果。

The measurement matrix is one of the three core part of the compressed sensing theory, it influences the application of CS (Compressed Sensing) theory in the field of image fusion. In order to solve the problem that random measurement matrix is hard to realize for hardware, this paper designs a measurement matrix which is consisted only of minus one, zero and one, and then makes it no-related to sparse matrix as much as possible according to Gram matrix-based optimization method. The experimental results show that the proposed method can obtain higher PSNR gain of reconstructed image, and in the application of CS-based image fusion, our method can get a favorable fuse effect in the case of only 50% sampled.