基于低秩和稀疏性先验知识的压缩感知图像重构

压缩感知（CS）图像重建算法是CS图像获取问题的一个研究重点。针对当前重建效果最好的基于低秩先验的NLR重建算法，忽略了图像的局部结构信息，不能有效地重建图像的边缘，为了在测量值数量不变情况下进一步提高图像的重建质量，在低秩先验的基础上，引入稀疏约束（梯度域的稀疏性-总变差）作为图像额外的先验知识，建立了基于总变差和低秩约束的CS图像重建模型。增广拉格朗日-交替方向乘子算法用于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，所提算法能够获得更高的图像重构质量。

Compressed sensing image reconstruction based on low-rank and sparse prior

Compressive sensing (CS) image reconstruction algorithm is a key point in the CS image acquisition problem. The NLR algorithm which exploits low-rank prior and shows the state-of-the-art performance ignores image local structural information and cannot effectively reconstruct the edges. In order to improve the reconstruction precision with the same number of measurements, the sparisty regularization as the additional prior information of image are introduced, and a total variation and low-rank property based CS image reconstruction model has been proposed. The augmented Lagrange method-alternating direction method has been used to solve the resulting non-convex optimization problem. Compared with the traditional sparisty regularized algorithms and NLR method, the proposed algorithm can achieve better image reconstruction results.