基于近端梯度的快速字典学习方法的研究

基于稀疏表示的图像处理技术近年来成为研究热点，多种字典学习算法如K-SVD，OLM(Online dictionary learning Method)等予以提出；这类算法使用重叠的图像块来构建字典进行稀疏表示，产生了大量稀疏系数，致使计算过缓，且不能确保收敛。针对此问题开展研究，提出了基于近端梯度的快速字典学习算法；该算法结合了多凸优化求解，采用近端梯度算法求解字典学习过程中涉及的优化问题，有效地降低了每次迭代的复杂度，减少了迭代开销，同时能够确保收敛。合成数据上的实验表明，相较于其它经典算法，该算法进行字典学习速度更快，所耗时间较短，获得的字典更好；且在图像稀疏去噪的应用中，该算法的去噪效果表现优异。

Fast dictionary learning method research based on proximal gradient

In recent years, image processing technology based on sparse representation has become a hot research; a variety of algorithms for dictionary learning such as K-SVD, OLM (Online dictionary learning), etc. have been proposed and have made a huge progress; these algorithms use over-lapping image blocks to build dictionary, and sparse representation, this process produces a plethora of sparse coefficients, leading to calculate slowly. Conducting research to address the problem, and proposing the fast dictionary learning method based on proximal gradient, this method combine the multi-convex optimization, using the proximal gradient algorithm to solve the optimization problem involved in dictionary learning process, which reduces the complexity of each iteration effectively, and cut down the iterations overhead , while ensuring global convergence. In numerical experiments on synthetic data show that, compared to other algorithms, the algorithm can get a better dictionary, which is more competitive in terms of speed and quality. However, in the application of image sparse de-noising, the effect of our method is excellent.