在基于稀疏表示的超分辨率重建过程中，当对图像进行稀疏编码时由于其分解残差并不是简单的符合高斯分布或拉普拉斯分布，针对这一问题提出混合高斯稀疏编码模型。模型基于最大似然估计准则，首先定义目标函数为加权 l2范数逼近问题，根据分解残差定义其权值，采用迭代重加权稀疏编码算法进行求解。然后基于此模型建立超分辨率重建模型和算法，利用此方法学习训练出同构的高 /低分辨率过完备字典并求得图像的稀疏表示，最后对重建过程进行改进以提高算法对噪声的鲁棒性。实验结果验证了本文方法的有效性。

In the processing of Super-resolution (SR) based on sparse representation, when a testing image is sparsely coded, the coding residual doesn’t simply follow Gaussian or Laplacian distribution. In the maximum likelihood estimation principle, a mixture Gaussian sparse coding model is proposed to solve this problem. Firstly, a weighted l2 norm function is defined to approximate the optimization problem, different weight is defined for different coding residual, and the function is solved by iteratively reweighed sparse coding algorithm. Then the SR model and algorithm are established based on the proposed model, the isomorphic high/low resolution over-complete dictionaries are trained and the sparse representation coefficients of the testing image is learned by the proposed method. At last, the reconstruct method is mended to improve the robustness to noise. The experimental results demonstrate the effectiveness of the proposed method.