基于局部和非局部正则化的图像压缩感知

Image Compressed Sensing Based on Local and Nonlocal Regularizations

基于低秩正则化的非局部低秩约束(Nonlocal low-rank regularization,NLR)算法利用相似块的结构稀疏性,获得了目前最好的重构结果。但是它仅仅利用了图像的非局部信息,忽略了图像像素间的局部信息,不能有效地重建图像的边缘,同时Logdet函数不能很好地替代矩阵秩,因为它跟真实解之间存在着不可忽视的差距。因此,本文提出了一种基于局部和非局部正则化的压缩感知图像重建方法,同时考虑图像的非局部低秩性和图像像素的局部稀疏梯度性。选择利用Schatten-p范数来替代矩阵秩,同时选择交替方向乘子算法求解产生的非凸优化问题。实验结果表明,与传统的稀疏性先验重建算法和NLR算法相比,本文算法能够获得更高的图像重构质量。

Nonlocal low‐rank regularization based approach （NLR） shows the state‐of‐the‐art performance in compressive sensing （CS） recovery which exploits both structured sparsity of similar patches .Howev‐er ,it cannot efficiently preserve the edges because it only exploits the nonlocal regularization and ignores the relationship between pixels .Meanwhile ,Logdet function that is used in NLR cannot well approxi‐mate the rank ,because it is a fixed function and the optimization results obtained by this function essen‐tially deviate from the real solution .A local and nonlocal regularization based CS approach is proposed to‐ward exploiting the local sparse‐gradient property of image and low‐rank property of similar patches . Schatten‐p norm is used as a better non‐convex surrogate for the rank function .In addition ,the alterna‐ting direction method of multipliers method （ADMM ） is utilized to solve the resulting nonconvex optimi‐zation problem .Experimental results demonstrate that the proposed method outperforms existing state‐of‐the‐art CS algorithms for image recovery .