基于双树复数小波和波原子稀疏图像表示的压缩传感图像重构

Compressed Sensing Image Reconstruction Based on Sparse Image Representation Using Dual-tree Complex wavelet and Wave atoms

目前用于压缩传感(CS)图像重构的大部分算法都是基于图像在单一基上的稀疏性来实现。但很多图像在两种或多种基上具有稀疏表示,当用一种基进行稀疏图像表示时,往往不能有效捕捉图像的结构特性,导致图像重构质量不高。为此本文提出了一种基于波原子和双树复数小波混合基的图像稀疏表示方法,利用线性Bregman迭代来进行重构的压缩传感算法。该算法在每一次迭代更新后用梯度下降法进行全变差调整,再分别在两种基上执行软阈值处理来减小图像的l_1范数。实验结果表明本文算法有效提高了重构图像的质量。

At present most algorithms applied to compressed sensing image reconstruction are based on the prior of images have sparse representation in single basis.However,many images have sparse representation in more than one basis,when the image is represented by one basis,it can＇t capture the image structure effectively,and results in the bad quality of recovered image.In this paper, we propose a compressed sensing algorithm based on that images have sparse representation on combined basis of wave atoms and the dual tree complex wavelet transform（DTCWT）,making use of the linear Bregman iteration to reconstruct the original image..The algorithm regulate the total variation with the gradient descend method after updating in each iteration,and then performs the soft-thresholding on these two bases respectively to reduce the l_1 norm of the image.The results of experiments show that our algorithm effectively improves the quality of the recovered image.