可压缩传感重构算法与近似QR分解

讨论了可压缩传感CS重构算法，并提出了一种新的改进算法效率、提高图像质量的方法，即：测量矩阵的近似QR分解。精确的重构算法（极小化L0范数）是一个NP完全问题，而这种算法的一个近似估计（极小化L1范数）能够对信号或图像高效率地重构。本文研究了L1算法的重构效果，通过改变测量矩阵的奇异值能够提高算法的重构效率。对测量矩阵的近似QR分解进行了研究，并给出了对测量矩阵的一些改进和相关的实验。

Reconstruction of compressive sensing and semi-QR factorization

In this paper, the signal reconstruction algorithms of Compressive Sensing (CS) were discussed and a new method to enhance the efficiency was found, and the quality of recovered images was improved: proximate QR factorization of measurement matrix. The exact reconstruction of minimum l0 norm is NP-complete problem. Minimum l1 norm reconstruction can approximate compressible vectors with high probability. In the study, the quality of solutions of l1 optimization can be enhanced further by changing the singular values of the measurement matrix with QR factorization. We illustrated the effectiveness of QR factorization of the measurement matrix and gave a comparison of the Gaussian random matrix and its QR factorization.