基于截断核范数低秩分解的自适应字典学习算法

针对过完备字典直接对图像进行稀疏表示不能很好地剔除高频噪声的影响，压缩感知后图像重构质量不高的问题，提出了基于截断核范数低秩分解的自适应字典学习算法。该算法首先利用截断核范数正则化低秩分解模型对图像矩阵低秩分解得到低秩部分和稀疏部分，其中低秩部分保留了图像的主要信息，稀疏部分主要包含高频噪声及部分物体轮廓信息；然后对图像低秩部分进行分块，依据图像块纹理复杂度对图像块进行分类；最后使用K奇异值分解（K-single value decomposition, K-SVD）字典学习算法，针对不同类别训练出多个不同大小的过完备字典。仿真结果表明，本文所提算法能够对图像进行较好的稀疏表示，并在很好地保持图像块特征一致性的同时显著提升图像重构质量。

Adaptive Dictionary Learning Algorithm Based on Truncated Nuclear Norm and Low Rank Decomposition

Aiming at the problem that the direct sparse representation of the over-complete dictionary on the image cannot effectively remove the effect of high-frequency noise, and the image reconstruction quality after compressed sensing is not high, an adaptive dictionary learning algorithm based on truncated nuclear norm and low rank decomposition is proposed. The algorithm firstly uses the truncated nuclear norm regularization low-rank decomposition model to decompose the low-rank part and sparse part of the image matrix. The low-rank part retains the main information of the image, and the sparse part mainly contains high-frequency noise and some object contour information. Then, the low-rank part of the image is divided into blocks, and the image blocks are classified according to the texture complexity of the image block. Finally, a K-single value decomposition(K-SVD) dictionary learning algorithm is used to train multiple over-complete dictionaries of different sizes for different categories. Simulation results show that the proposed algorithm can perform better sparse representation of the image, while significantly maintaining the consistency of image block features and significantly improving the quality of image reconstruction.