中文摘要：

从过完备字典中得到图像的最稀疏表示是一个NP难问题，即使是次优的匹配追踪也相当复杂．针对Gabor多成份字典，提出基于多种群离散差分进化的图像稀疏分解算法．该算法采用3个子种群在不同成份子字典中搜索最佳匹配原子，父代通过多种变异算子生成多个子代，保持群体多样性，同时引入相关系数避免残差更新时多原子匹配重叠的问题．实验表明相比于快速匹配追踪算法，在稀疏逼近性能相当的情况下，文中算法的稀疏分解速度更快；与其他基于进化算法的稀疏分解方法相比，文中算法的稀疏逼近性能更优．最后的结果分析验证文中算法参数设置的合理性．

英文摘要：

To obtain the sparsest representation of an image using a redundant dictionary is NP-hard, and the existing sub-optimal algorithms for solving this problem such as matching pursuit （MP） are highly complex. An image sparse decomposition algorithm based on multi-population discrete differential evolution for multi-component Gabor dictionaries is proposed. Three sub-populations are adopted to search the best matching atoms in different sub-dictionaries, and the correlation coefficient is used to solve overlap-matching in updating process of residual image. To maintain the population diversity,several mutation operators are employed to generate the offspring population in the proposed algorithm. Experimental results show that the sparse approximation performances of the proposed algorithm are comparable with fast matching pursuit （FMP） algorithm. Meanwhile, the computation speed is improved. The proposed algorithm obtains competitive performance compared with other sparse representation methods based on evolution algorithm. Finally, the rationality of the parameters setting in the proposed algorithm is verified by result analysis.