An optimization method of observation matrix based on QR decomposition

• Main Authors: Zhou Qibin, Wu Jing, Yu Bo
• Format: Article
• Language: zho
• Published: National Computer System Engineering Research Institute of China 2021-04-01
• Series: Dianzi Jishu Yingyong
• Subjects: compressed sensing; observation matrix; qr decomposition; gram matrix; cross-correlation
• Online Access: http://www.chinaaet.com/article/3000130790

In compressed sensing theory, the most critical issue is the construction of the observation matrix. The factors that affect the image reconstruction quality include the independence between the observation matrix column vectors and the cross-correlation between the observation matrix and the sparse basis. Based on this, an optimization algorithm is proposed. The algorithm uses QR decomposition to increase the independence of the observation matrix columns, and at the same time optimizes the Gram matrix contracted using an equiangular tight frame(ETF). By updating the direction of each gradient descent, the convergence rate is accelerated to reduce The cross-correlation between the small observation matrix and the sparse basis. Simulation experiment results show that the method of optimizing the observation matrix in this paper has certain advantages in improving the quality and stability of image reconstruction under the same signal sparsity or observation times.