用于超分辨率重建的同构过完备字典学习方法

构造合适的过完备字典是基于稀疏表示的超分辨率重建中的关键问题之一。在最大似然估计准则下，建立基于混合高斯的同构过完备字典学习模型。模型采用加权的l2范数来刻画分解残差，由分解残差设计权值矩阵，并且将同构的双字典学习问题转化为单字典的学习。采用稀疏编码和字典更新的交替迭代策略完成目标函数的求解，由内点法进行稀疏编码，采用拉格朗日对偶法完成字典更新。最后将学习得到的字典用于超分辨率重建实验，并与其他方法进行比较。实验结果验证了该模型和算法的有效性。

An isomorphic over complete dictionary learning method for super resolution reconstruction

Constructing an appropriate over complete dictionary is one of the key problems of super resolution based on sparse representation. In the maximum likelihood estimation principle, an isomorphic over complete dictionary learning model based on mixture Gaussian is proposed. Firstly, the sparse coding residual of the model is described by the weight l2 norm and the weight matrix is designed by the residual. Secondly,the isomorphic coupled dictionary learning problem is translated into the single dictionary learning problem. The dictionary is learned by the alternate and iterative strategy using sparse coding and dictionary updating. An interior point method is used in sparse coding and Lagrange dual is used in dictionary updating. Finally, the learned dictionary is used in the super resolution experiment,and compared with other methods.The experimental results demonstrate the effectiveness of the proposed method.