基于秩极小化的压缩感知图像恢复算法

Compressed Sensing Image Reconstruction Algorithm Based on Rank Minimization

本文将压缩感知图像恢复问题作为低秩矩阵恢复问题来进行研究.为了构建这样的低秩矩阵,我们采样非局部相似度模型,将相似图像块作为列向量构建一个二维相似块矩阵.由于列向量间的强相关性,因此该矩阵具有低秩属性.然后以压缩感知测量作为约束条件对这样的二维相似块矩阵进行低秩矩阵恢复求解.在算法求解的过程中,使用增广拉格朗日方法将受限优化问题转换为非受限优化问题,同时为了减少计算复杂度,使用基于泰勒展开的线性化技术来加速算法求解.实验表明该算法的收敛率、图像恢复性能均优于目前主流压缩感知图像恢复算法.

The problem of compressed sensing image reconstruction is imagined as a low rank matrix recovery problem for research. In order to construct this low rank matrix,the nonlocal similarity model is exploited,and every similar image block is treated as a column vector in the matrix. The matrix has the low rank property because the column vectors are strong correlation. The algorithm model is to solve the low rank matrix recovery problem subject to the compressed sensing measurement constraints. In the solution of our proposed algorithm,the constrained optimization problem is converted to unconstrained optimization problem by the augmented lagrangian method,and then the alternating direction multiplier method is employed to solve it. To reduce the computational burden,the linear technique based on Taylor series expansion is taken to accelerate the proposed algorithm. The experimental results show that the subjective and objective performance of our proposed reconstruction algorithm is superior to the state of art reconstruction algorithms.