Abstract: The sparse representation of images play a vital role in the process of image reconstruction.According to the Meyer’s image model，an image is separated into piecewise smooth（cartoon） and texture parts.Constructing two concatenate dictionaries by Symlet series of wavelet bases，Contourlet base and wave atoms，cosine bases to represent the cartoon and texture content sparsely，then，solving the optimization problem with block coordinate relaxation，the image reconstruction based on concatenate dictionary and two-layer sparse representation is proposed.The experimental results show that the new algorithm greatly improves the reconstruction quality compared to the algorithm based on single optimal wavelet base and matching pursuit based on concatenate dictionary.

Key words: sparse representation, concatenate dictionary, image reconstruction, block coordinate relaxation

摘要： 图像重构问题中一个关键的问题是如何选取变换基实现对图像的稀疏分解。根据Meyer图像模型将图像分割为卡通部分（cartoon，or piecewise smooth）和纹理部分（texture），并用Symlet系列小波基、Contourlet基和离散余弦变换基、波原子分别构造级联字典表示图像的卡通部分和纹理部分。然后利用块坐标松弛法求解优化问题提出结合级联字典和双层稀疏分解的图像重构算法。实验结果表明，与基于单一最佳小波基的重构算法和基于级联字典的匹配追踪算法比较，该算法获得更高的图像重构质量。

关键词: 稀疏分解, 级联字典, 图像重构, 块坐标松弛法