基于广义低秩矩阵分解的分离字典训练及其快速重建算法

针对传统压缩感知重建算法存在重建质量偏低、重建时间偏长等问题，本文提出了一种基于分离字典训练的快速重建算法.首先选取某类图像作为训练集，建立其广义低秩矩阵分解模型；其次采用交替方向乘子法求解该模型，训练出一组分离字典；最后将该分离字典用于图像重建中，通过简单的线性运算实现图像的快速重建.实验结果表明，本文算法相比于传统的重建算法，针对训练集同类图像，具有十分显著的重建性能，对于其他不同类型的图像，依然有不错的重建质量，极大地降低了重建时间.

Separable Dictionary Training and Its Fast Reconstruction Algorithm Based on Generalized Low-Rank Matrix Approximation

Since traditional compressive sensing reconstruction algorithms have lower reconstruction quality and longer running time,a fast reconstruction algorithm based on separable dictionary training is proposed.Firstly,we choose one class of images as training set and construct their models of generalized low-rank matrix approximation.Then,the alternating direction method is used to solve the model,and we can obtain separable dictionaries.Finally,the separable dictionaries are applied to image reconstruction and realize fast reconstruction of image by simple linear operation.The experimental results show that the proposed algorithm has a better reconstruction performance for training set images compared to traditional reconstruction algorithms.In addition,for other types of images,our algorithm has a good reconstruction quality and a lower reconstruction time.