计算机应用 ›› 2020, Vol. 40 ›› Issue (8): 2358-2364.DOI: 10.11772/j.issn.1001-9081.2019122187

• 虚拟现实与多媒体计算 • 上一篇    下一篇

基于非凸全变差正则的核磁共振图像重构算法

沈马锐, 李金城, 张亚, 邹健   

  1. 长江大学 信息与数学学院, 湖北 荆州 434023
  • 收稿日期:2019-12-30 修回日期:2020-02-28 出版日期:2020-08-10 发布日期:2020-05-13
  • 通讯作者: 邹健(1983-),男,湖北荆州人,副教授,博士,主要研究方向:信号处理、图像处理、数值优化。zoujian@yangtzeu.edu.cn
  • 作者简介:沈马锐(1996-),男,湖北荆州人,硕士研究生,主要研究方向:信号处理、图像处理、最优化理论与算法;李金城(1997-),女,四川达州人,硕士研究生,主要研究方向:最优化理论与算法;张亚(1994-),女,湖北黄石人,硕士研究生,主要研究方向:最优化理论与算法。
  • 基金资助:
    国家自然科学基金资助项目(61503047)。

Magnetic resonance image reconstruction algorithm via non-convex total variation regularization

SHEN Marui, LI Jincheng, ZHANG Ya, ZOU Jian   

  1. College of Information and Mathematics, Yangtze University, Jingzhou Hubei 434023, China
  • Received:2019-12-30 Revised:2020-02-28 Online:2020-08-10 Published:2020-05-13
  • Supported by:
    This work is partially supported by the National Natural Science Foundation of China (61503047).

摘要: 针对于核磁共振(MR)图像重构中由于欠采样导致的重构图像不够完整、边缘模糊以及噪声残留等问题,提出了一种基于L2正则的非凸全变差正则重构模型。首先,以Moreau包络和最小最大凹罚函数为工具构造L2范数的非凸正则;然后,将其应用于全变差正则上来构造各向同性的非凸全变差正则稀疏重构模型。所提的非凸正则可以有效地避免凸正则中对较大非零元欠估计现象,能够更有效地重构目标的边缘轮廓;同时,在一定条件下可以保证目标函数的整体凸性,从而最后可以利用交替方向乘子法(ADMM)对模型进行求解。仿真实验对若干MR图像在不同的采样模板和采样率下进行了重构。实验结果均表明,与几种典型的图像重构方法相比,所提模型性能更优,相对误差明显降低,峰值信噪比(PSNR)有明显改善,较经典的L1非凸正则重构模型提升了大约4 dB,并且重构后的图像视觉效果显著提升,有效地保留了原始图像的边缘细节。

关键词: 核磁共振成像, 全变差正则, Moreau包络, 最小最大凹罚函数, 交替方向乘子法

Abstract: To solve the problems of incomplete reconstruction, blurred boundary and residual noise in Magnetic Resonance (MR) image reconstruction, a non-convex total variation regularization reconstruction model based on L2 regularization was proposed. First, Moreau envelope and minmax-concave penalty function were used to construct the non-convex regularization of L2 norm, then it was applied into the total variation regularization to construct the sparse reconstruction model based on the isotropic non-convex total variation regularization. The proposed non-convex regularization was able to effectively avoid the underestimation of larger non-zero elements in convex regularization, so as to reconstruct the edge contour of the target more effectively. At the same time, it was able to guarantee the global convexity of objective function under certain conditions. Therefore, Alternating Direction Method of Multipliers (ADMM) was able to be used to solve the model. Simulation experiments were carried out to reconstruct several MR images under different sampling templates and sampling rates. Experimental results show that compared with several typical image reconstruction methods, the proposed model has better performance and lower relative error, its Peak Signal-to-Noise Ratio (PSNR) is significantly improved, which is 4 dB higher than that of traditional reconstruction method based on the non-convex regularization of L1 norm; in addition, the visual effects of the reconstructed images are promoted significantly, effectively maintaining the edge details of the original images.

Key words: Magnetic Resonance Imaging (MRI), total variation regularization, Moreau envelope, minmax-concave penalty function, Alternating Direction Method of Multipliers (ADMM)

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