Abstract: The precision of the signal reconstruction by compressed sensing is decided by the sparse degree of signal decomposition. According to the insufficient sparse degree of standard orthogonal basis, this paper establishes two-dimensional Gabor dictionaries which can match the edge and texture of an image. Mixed sparse decomposing of the image on the discrete cosine dictionary and established two-dimensional Gabor dictionaries, it can get the smooth component, edge component and texture component of the image. It measures the obtained sparse components by compressed sensing, by solving an optimization problem, original image can be reconstructed. Experimental results demonstrate that the multi-component dictionaries can give more sparse representation for an image, and the quality of image reconstruction is better than standard orthogonal basis sparse decomposition in the same sampling rate.

Key words: compressed sensing, multi-component dictionaries, sparse image representation, image reconstruction

摘要： 信号分解的稀疏程度决定了压缩感知重构信号的精度，针对标准正交基稀疏程度的不足，提出了基于混合字典的压缩感知图像分解和重构方法。构建匹配图像边缘和纹理的二维Gabor字典，将图像在离散余弦字典与建立的二维Gabor字典上进行混合稀疏分解，得到图像的光滑成分、边缘成分和纹理成分。对得到的稀疏成分进行CS观测，通过求解一个优化问题重构图像。实验结果表明，构造的混合字典能够对图像进行更加稀疏的表示，在相同的采样率下，图像的重构质量优于标准正交基分解。

关键词: 压缩感知, 多成分混合字典, 稀疏图像表示, 图像重构