图像的多成分混合字典压缩感知表示及重构

Image representation and reconstruction for compressed sensing by multi-component combined dictionary

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。

The precision of the signal reconstruction by compressed sensing is decided by the sparse degree of signal decomposi- tion. According to the insufficient sparse degree of standard orthogonal basis, this paper establishes two-dimensional Gabor dic- tionaries which can match the edge and texture of an image. Mixed sparse decomposing of the image on the discrete cosine dic- tionary and established two-dimensional Gabor dictionaries, it can get the smooth component, edge component and texture com- ponent 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 decom- position in the same sampling rate.