基于加权Schatten p范数最小化的磁共振图像重构方法研究

doi:10.3969/j.issn.0372-2112.2019.04.003

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摘要本文提出了一种基于加权Schatten p范数最小化（Weighted Schatten p-Norm Minimization，WSNM）的磁共振图像重构算法，该方法利用磁共振图像的非局部自相似性，并结合Schatten p范数和不同秩元素重要性的加权因子，实现磁共振图像重构过程的低秩约束.此外，采用交替方向乘子算法（Alternating Direction Method of Multipliers，ADMM）来求解基于WSNM磁共振图像重构的非凸最小化问题.实验结果表明，相比于最近的磁共振重构算法，基于WSNM的磁共振图像重构方法具有更好的重建效果，可获得更高的峰值信噪比（Peak Signal to Noise Ratio，PSNR）和更好的结构相似性（Structural Similarity，SSIM）.

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	蒋明峰
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	汪亚明

关键词 ：磁共振图像重构, 非局部自相似性, 加权Schatten p范数最小化

Abstract：In this paper,the weighted Schatten p-norm minimization (WSNM) method is proposed to implement magnetic resonance imaging (MRI) reconstruction.The nonlocal self-similarity of magnetic resonance images,Schatten p-norm and the weighting factors of the importance of different rank elements are integrated together as the low rank constraint to regularize the MRI reconstruction.In addition,the Alternating Direction Method of Multipliers (ADMM) algorithm is used to solve the non-convex minimization problem of MRI reconstruction based WSNM.Compared with other state-of-the-art methods in numerical experiments,the proposed method achieves a higher reconstruction quality with higher peak signal to noise ratio (PSNR) and better structural similarity (SSIM) index.

Key words： magnetic resonance imaging (MRI) reconstruction nonlocal self-similarity weighted Schatten p-norm minimization

收稿日期: 2018-05-02

ZTFLH:

TP302

基金资助:国家自然科学基金（No.61672466，No.61672476）；浙江省自然科学基金（No.LSZ19F010001，No.LZ15F020004）；浙江省科技厅公益项目（No.2015C31075）；浙江理工大学521人才培养计划

作者简介: 蒋明峰 男,1977年生于江西丰城,现为浙江理工大学信息学院教授、硕士生导师,主要研究方向为计算机医学图像处理、生物医学信号处理.E-mail:m.jiang@zstu.edu.cn;陆亮男,1990年生于江苏南通,现为浙江理工大学信息学院硕士研究生,主要研究方向为医学图像处理.E-mail:lianglu118@126.com

引用本文:

蒋明峰, 陆亮, 吴龙, 徐文龙, 汪亚明. 基于加权Schatten p范数最小化的磁共振图像重构方法研究[J]. 电子学报, 2019, 47(4): 784-790. JIANG Ming-feng, LU Liang, WU Long, XU Wen-long, WANG Ya-ming. The Research of MRI Reconstruction Method by Using Weighted Schatten P-Norm Minimization. Acta Electronica Sinica, 2019, 47(4): 784-790.

链接本文:

http://www.ejournal.org.cn/CN/10.3969/j.issn.0372-2112.2019.04.003 或 http://www.ejournal.org.cn/CN/Y2019/V47/I4/784

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