中文摘要：

传统的压缩感知重建算法利用信号在某个特征空间下的稀疏性构建目标优化函数,但没有充分考虑信号的局部特性和结构化属性,影响了算法的重建性能和算法的适应性.本文考虑图像的非局部自相似性（Nonlocal Self-Similarity,NLSS）,提出一种基于图像相似块低秩的压缩感知图像重建算法,将图像恢复问题转化为聚合的相似块矩阵秩最小问题.算法以最小压缩感知重建误差为约束构建优化模型,并采用加权核范数最小化算法（Weighed Nuclear Norm Minimization,WNNM）求解低秩优化问题,很好地挖掘了图像自身的信息和结构化稀疏特征,保护了图像的结构和纹理细节.多个测试图像、不同采样率下的实验证明了算法的有效性,特别是在低采率下对于纹理较为丰富的图像,提出的算法图像重建质量较明显的优于最新的同类算法.

英文摘要：

Generally,traditional compressed sensing（ CS） image recovery methods build the objective optimization function by using the signal sparsity in some specific feature spaces. They do not fully take the local features and structural properties of signal into account,which leads to constraints of the recovery performance and flexibility. In this paper,considering the non-local self-similarity（ NLSS） in images,we propose an image CS reconstruction method based on the image low-rank property by converting the CS recovery problem into a matrix rank minimization problem of aggregating similar image patches. The proposed algorithm builds optimization model under the constraint of minimal recovery errors and employs the weighed nuclear norm minimization（ WNNM） method to solve the low-rank optimization problem. By taking advantage of them,the proposed method exploits the self-information and structured sparse characteristics of the image very well,and therefore provides a better protection of image structures and textures. Experiments on different test images under various sampling rates have shown the effectiveness of the proposed algorithm. Especially,for richly-textured images,our method outperforms the art-of-the-state algorithms significantly under lowsampling rates.