中文摘要：

文中提出了一种基于子空间解析字典学习和观测矩阵优化的图像压缩感知算法.该算法根据图像的局部方向特征,将整个图像空间分成多个子空间,并且采用几何共轭梯度算法分别在各个子空间学习解析字典,以实现对不同子空间图像块的最优稀疏表示.在图像重构过程中,首先在所有的子空间对每个图像块分别进行估计,然后根据稀疏表示最小误差准则获得每个图像块的最优估计.为了进一步提高图像重构质量,文中通过对不同子空间的图像块进行线性判别分析获得优化观测矩阵.实验表明文中算法可以实现高质量的压缩感知图像重构.

英文摘要：

A novel compressed sensing algorithm based on learning analysis dictionary and optimizing measurement matrix from subspaces is proposed in this paper. The whole image space is divided into multiple subspaces based on the local directional features in our algorithm to achieve the optimal sparse representation for the image patches of different subspaces. The analysis dictionaries are learned in each subspace respectively by the geometric conjugate gradient method. In the image reconstruction process, each image patch is estimated in every subspace respectively, and the optimal estimation of each image patch is selected based on the least sparse representation error criterion. Aiming to further improve the quality of the reconstructed image, the measurement matrix is optimized by linear discriminant analysis on the image patch subspaces. Experiments show that the proposed algorithm can achieve high quality image reconstruction.