中文摘要：

针对基于固定变换基的协同稀疏图像压缩感知（CS）重构算法不能充分利用图像自相似特性的问题,提出了一种改进的联合全变差与自适应低秩正则化的压缩感知重构方法。首先,通过图像块匹配法寻找结构相似块,并组成非局部相似块组;然后,以非局部相似块组加权低秩逼近替代协同稀疏表示中的三维小波变换域滤波;最后,结合梯度稀疏与非局部相似块组低秩先验构成重构模型的正则化项,并采用交替方向乘子法求解实现图像重构。实验结果表明,相比协同稀疏压缩感知重构（RCo S）算法,该方法重构图像的峰值信噪比平均可提升约2 d B,所提算法在准确描述图像非局部自相似结构特征的前提下显著提高了重构质量,更好地保留了图像的纹理细节信息。

英文摘要：

Aiming at the problem that collaborative sparse image Compressive Sensing（ CS） reconstruction based on fixed transform bases can not adequately exploit the self similarity of images, an improved reconstruction algorithm combining the Total Variation（ TV） with adaptive low-rank regularization was proposed in this paper. Firstly, the similar patches were found by using image block matching method and formed into nonlocal similar patch groups. Then, the weighted low-rank approximation for nonlocal similar patch groups was adopted to replace the 3D wavelet transform filtering used in collaborative sparse representation. Finally, the regularization term of combining the gradient sparsity with low-rank prior of nonlocal similarity patch groups was embedded to reconstruction model, which is solved by Alternating Direction Multiplier Method（ ADMM） to obtain the reconstructed image. The experimental results show that, in comparison with the Collaborative Sparse Recovery（ RCo S） algorithm, the proposed method can increase the Peak Signal-to-Noise Ratio（ PSNR） of reconstructed images about 2 d B on average, and significantly improve the quality of reconstructed image with keeping texture details better for nonlocal self-similar structure is precisely described.