中文摘要：

在利用稀疏表示技术重构图像的应用中,传统的方法是独立地计算一组重叠的图像块,在表示中只针对每个图像块进行单独稀疏编码。利用卷积稀疏表示,可以将整个图像看做是一个整体,对其进行稀疏编码,由滤波器字典与相应特征响应的卷积总和代替传统的字典矩阵与编码系数的乘积对图像进行分解。论文基于卷积稀疏表示方法,提出一个图像重构算法,利用交替方向乘法器方法（ADMM）对输入图像进行稀疏逼近,得到特征响应系数,达到对图像卷积分解的目的。实验结果说明卷积分解机制稀疏性能较优,更适合于图像重构。

英文摘要：

In the application of sparse representation in image reconstruction,the traditional method is to compute a set of overlapping image blocks independently.Using convolution sparse representation,the whole image is seen as a whole,the of sparse coding and by the filter dictionary and corresponding characteristic response of the convolution sum instead of the product of traditional dictionary matrix and coding coefficients for image decomposition.In this paper,based on the sparse representation model of convolution,an image reconstruction algorithm is proposed,the input image is approximated by the alternating direction multiplier method（ADMM）,and the characteristic response coefficient is obtained.The experimental results show that the sparse performance of the convolution decomposition mechanism is better,and it is more suitable for image reconstruction.