中文摘要：

压缩感知理论突破了信号带宽对奈奎斯特采样定理的限制,并且实现了在数据采样的同时进行压缩。目前压缩感知系统通常利用图像在某个变换域具有稀疏性的先验知识,从少量观测值中重构原始图像。本文利用图像像素的邻域结构信息及图像子块的相似性,将图像的非局部相似性作为先验知识运用到压缩感知图像重构中。结合图像的非局部相似性及其在变换域的稀疏性先验知识,提出了基于非局部相似性和交替迭代优化算法的图像压缩感知重构算法,该算法利用迭代阈值法和非局部全变差来交替迭代求解变换域的稀疏性优化问题和非局部相似性的优化问题。实验结果表明,本文算法可以有效提高图像重构的视觉效果和峰值信噪比。

英文摘要：

Compressed Sensing is a new teehrfique for simultaneous data sampling and compression. It breaks through the limits to Nyquist sampling theorem which needs very wide signal bandwidth when sampling. Currently, compressed sensing system used the prior that the image has sparsity in some transform domain to reconstruct the original image from fewer meas- urements. In this paper, the nonlocal similarity was used in image compressed sensing and combined with the sparsity as pri- or. Hence, the neighborhood structure information of the image pixels and the similarity of images are fully used. On the basis of the nonlocal similarity prior and the image has sparsity in some transform domain, a new image compressed sensing algo- rithm based on nonloeal similarity and alternating iterative optimization algorithm is proposed. The proposed algorithm solved the image compressed sensing problem by dealing with the following two optimization problems alternatively： sparsity optimiza- tion problem and the nonloeal similarity optimization problem. And the two optimization problems are solved respectively by the iterative thresholding algorithm and nonlocal total variation. Simulation results show that the performance of the proposed algorithm has significant performance improvement in visual quality of the reconstructed image and peak signal-to-noise ratio.