基于小波树和互补分解的CS-MRI重建算法  

A CS-MRI Algorithm Based on Complementary Dual Decomposition and Wavelet Tree

作　　者：裴颖 朱金秀 杨语晨 吴文霞 PEI Ying;ZHU Jin-xiu;YANG Yu-chen;WU Wen-xia(School of Internet of Things Engineering,Hohai University,Changzhou 213022,China;Research Institute of Ocean and Offshore Engineering,Hohai University,Nantong 226300,China)

机构地区：[1]河海大学物联网工程学院,江苏常州213022 [2]南通河海大学海洋与近海工程研究院,江苏南通226300

出　　处：《计算机技术与发展》2018年第12期152-156,共5页Computer Technology and Development

基　　金：国家自然科学基金(61273170);2016年南通市市级科技计划(2016800303)

摘　　要：针对压缩感知(CS)核磁共振成像(MRI)重建算法中全变分(TV)正则项会导致图像细节丢失的问题,引入互补分解模型,结合小波树结构稀疏(简称小波树),提出一种基于小波树和互补分解的CS-MRI重建算法。利用互补分解将图像分成平滑分量和残差分量两个部分,并将平滑分量用于TV正则项,残差分量用于1范数,可避免TV正则项在滤除噪声的同时滤除过多的细节信息;利用小波树结构稀疏可进一步补充小波稀疏等先验信息,减少测量值或提高信噪比。针对目标函数中存在平滑和残差两个未知分量,将目标函数分解为相应的两个子问题交替最小化进行求解。实验结果表明,与基于小波树的WaTMRI和基于TV的TVCMRI、FCSA等重建算法相比,其能在滤除噪声的同时有效改善MRI图像的细节信息。Aiming at the problem that total variation( TV) regularities in compressed sensing( CS) nuclear magnetic resonance imaging( MRI) reconstruction algorithm can lead to the loss of image details,we propose a CS-MRI reconstruction algorithm based on wavelet tree and complementary decomposition by introducing the complementary decomposition model and combining the sparse wavelet tree structure( referred to as wavelet tree). By using complementary decomposition, the image is divided into smooth component and residual component, and the smooth component is used for TV regular term, and the residual component for 1 norm,which can avoid the TV regular term from filtering out too much details while removing noise. By using the sparse wavelet tree structure, the prior information such as the sparse wavelet can be further supplemented to reduce the measured value or improve the signal-to-noise ratio. The objective function is decomposed into the corresponding subproblems and minimized alternately to solve the unknown components of smooth and residual in it. Experiment demonstrates that compared with WaTMRI based on wavelet tree and TVCMRI and FCSA based on TV, the proposed algorithm can effectively improve the details of MRI images while filtering out noise.

关 键 词：核磁共振成像 压缩感知 互补分解 小波树结构稀疏(小波树) 目标函数 重建算法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]