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分裂增广拉格朗日收缩法在基于压缩感知的磁共振成像中的应用研究
发表时间：2014-10-31 浏览量：2289 下载量：989
| 全部作者： | 郑清彬，董恩清，杨佩，刘伟 |
| 作者单位： | 山东大学（威海）机电与信息工程学院 |
| 摘 要： | 为满足减少磁共振成像(magnetic resonance imaging，MRI)扫描时间、加快成像速度，尽可能用较少的测量数据获取高质量重建图像的实际需求，提出应用分裂增广拉格朗日收缩法(split augmented Lagrangian shrinkage algorithm，SALSA)实现多正则项［包括全变差(total variation，TV)范数和L1范数相结合的2个正则项和同时考虑TV范数、L1范数和小波树结构的3个正则项］的压缩感知(compressed sensing，CS)MRI方法。针对基于TV范数和L1范数相结合的MRI重构问题，提出利用复合分裂去噪(composite split denoising，CSD)思想将原始复杂问题分裂为相应的TV正则项和L1正则项的2个简单易解的子问题，将该子问题的解线性组合得到重构图像。由于所分裂得到的子问题可以看作单一正则项的CSMRI模型，且对于解决这一模型问题，SALSA算法的收敛速度比现有的高效算法FIST(fast iterative shrinkage thresholding)和TwIST(two step iterative shrinkage thresholding)都要快，提出采用SALSA算法进行求解子问题。另外，对于同时考虑TV范数、L1范数和小波树结构3个正则项的MRI问题，采用同样的方法可以将原始问题分裂为3个简单的子问题，然后通过现有的迭代方法进行处理。实验结果表明，提出的应用SALSA算法实现多正则项CSMRI的方法能够有效重构原始图像，与现有算法TVCMRI(compressed MRI reconstruction based on total variation)，RecPF(reconstruction from Partial Fourier data)，CSA(composite splitting algorithms)，FCSA(fast composite splitting algorithms)和WaTMRI(wavelet tree sparsity MRI)相比，大大改善了重构图像质量，具有较好的视觉效果。 |
| 关 键 词： | 图像处理；磁共振成像；压缩感知；分裂增广拉格朗日；TV范数；L1范数 |
| Title： | Application research on split augmented Lagrangian shrinkage algorithm in magnetic resonance imaging based on compressed sensing |
| Author： | ZHENG Qingbin, DONG Enqing, YANG Pei, LIU Wei |
| Organization： | School of Mechanical, Electrical & Information Engineering, Shandong University |
| Abstract： | In order to meet the demand of reducing scan time of magnetic resonance imaging (MRI), accelerating MRI and reconstructing a high quality image from less acquisition data is as much as possible. MRI method based on compressed sensing (CS) with multiple regularizations (two regularizations including total variation norm and L1 norm or three regularizations consist of total variation, L1 norm and wavelet tree structure) is proposed in this paper, which is implemented by applying split augmented Lagrangian shrinkage algorithm (SALSA). To solve magnetic resonance image reconstruction problems with linear combinations of total variation and L1 norm, we utilize composite split denoising (CSD) to split the original complex problem into total variation (TV) norm and L1 norm regularization subproblems which are simple and easy to be solved respectively in this paper. The reconstructed image is obtained from the weighted average of solutions from two subproblems in an iterative framework. Because each of the splitted subproblems can be regarded as MRI model based on CS with single regularization, and for solving the kind of model, split augmented Lagrangian shrinkage algorithm has advantage over existing fast algorithm such as fast iterative shrinkage thresholding (FIST) and two step iterative shrinkage thresholding (TwIST) in convergence speed. Therefore, we propose to adopt SALSA to solve the subproblems. Moreover, in order to solve magnetic resonance image reconstruction problems with linear combinations of total variation, L1 norm and wavelet tree structure, we can split the original problem into three subproblems in the same manner, which can be processed by existing iteration scheme. A great deal of experimental results shows that the proposed CSMRI methods can effectively reconstruct the original image. Compared with existing algorithms such as compressed MRI reconstruction based on total variation (TVCMRI), reconstruction from partial Fourier data (RecPF), composite splitting algorithms (CSA), fast composite splitting algorithms (FCSA) and wavelet tree sparsity MRI (WaTMRI), the proposed methods have greatly improved the quality of the reconstructed image and have better visual effects. |
| Key words： | image processing; magnetic resonance imaging; compressed sensing; split augmented Lagrangian; total variation norm; L1 norm |
| 发表期数： | 2014年10月第20期 |
| 引用格式： | 郑清彬，董恩清，杨佩，等. 分裂增广拉格朗日收缩法在基于压缩感知的磁共振成像中的应用研究[J]. 中国科技论文在线精品论文，2014，7（20）：2082-2091. |
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