核磁共振图像重构的即插即用算法

doi:10.3778/j.issn.1002-8331.2105-0128

摘要/Abstract

摘要： 为解决核磁共振图像重构中由于欠采样导致的重构图像质量较低的问题，提出了一种基于凸-非凸稀疏正则和即插即用近似点梯度下降的核磁共振图像重构算法。首先给出了凸-非凸稀疏正则的近似点算子。然后基于该近似点算子提出近似点梯度下降算法。最后将上述算法中的近似点算子用某种合适的去噪器（如神经网络去噪器）替换，得到即插即用近似点梯度下降算法，并将其应用到核磁共振图像重构上。数值实验中，分别用不同的待重构图像、采样模板和去噪器进行对比实验，实验结果表明，所提算法在使用神经网络去噪器时，峰值信噪比较已有算法提升了6.26?dB。同时视觉效果也得到了显著的提升，在处理边缘和纹路方面效果都更加明显，从而验证了算法的有效性。

关键词: 核磁共振成像, 凸-非凸稀疏正则, 近似点梯度下降算法, 即插即用算法, 神经网络去噪器

Abstract: A magnetic resonance image reconstruction algorithm based on convex-nonconvex sparse regularization and plug-and-play proximal gradient descent algorithm is proposed to deal with low reconstruction quality due to undersampling. Firstly, the proximal operator of convex-nonconvex sparse regularization is given. Then, a proximal gradient descent algorithm is proposed. Finally, properly trained denoisers, such as neural network denoisers, are used to replace the proximal operator and plug in the above algorithm. The so-called plug-and-play proximal gradient descent algorithm is then applied to magnetic resonance image reconstruction. In numerical experiments, different images, sampling templates and denoisers are used for comparison experiments. The experimental results show that compared with other algorithms, the peak signal-to-noise ratio of the proposed algorithm with a properly trained neural network denoiser improves 6.26 dB. Visual effects have also been significantly improved, the effect of processing edges and textures is more obvious, thus verifying the effectiveness of the algorithm.

Key words: magnetic resonance imaging, convex-nonconvex sparse regularization, proximal gradient descent algorithm, plug-and-play algorithm, neural network denoiser

李金城, 谢朝阳, 李金兰, 张涛, 邹健. 核磁共振图像重构的即插即用算法[J]. 计算机工程与应用, 2022, 58(22): 239-245.

LI Jincheng, XIE Zhaoyang, LI Jinlan, ZHANG Tao, ZOU Jian. Plug-and-Play Algorithm for Magnetic Resonance Image Reconstruction[J]. Computer Engineering and Applications, 2022, 58(22): 239-245.

参考文献

[1] 刘晓晖，张鑫媛，路利军，等.磁共振图像的原始-对偶近似迭代重建算法[J].计算机工程与应用，2018，54（8）：28-35.
LIU X H，ZHANG X Y，LU L J，et al.Proximal iterative reconstruction algorithm for MR images based on primal-dual framework[J].Computer Engineering and Applications，2018，54（8）：28-35.
[2] KNOLL F，HAMMERNIK K，ZHANG C，et al.Deep-learning methods for parallel magnetic resonance imaging reconstruction：a survey of the current approaches，trends，and issues[J].IEEE Signal Processing Magazine，2020，37（1）：128-140.
[3] 沈马锐，李金城，邹健，等.基于非凸全变差正则的核磁共振图像重构算法[J].计算机应用，2020，40（8）：194-200.
SHEN M R，LI J C，ZOU J，et al.Magnetic resonance imaging reconstruction algorithm via non-convex total variation regularization[J].Journal of Computer Applications，2020，40（8）：194-200.
[4] LIU Y Y，DU H，WANG Z，et al.Convex MR brain image reconstruction via non-convex total variation minimization[J].International Journal of Imaging Systems Technology，2018，28（4）：246-253.
[5] LUSTIG M，DONOHO D L，SANTOS J M，et al.Compressed sensing MRI[J].IEEE Signal Processing Magazine，2008，25（2）：72-82.
[6] SELESNICK I.Sparse regularization via convex analysis[J].IEEE Transactions on Signal Processing，2017，65（17）：4481-4494.
[7] WEN F，CHU L，LIU P，et al.A survey on nonconvex regularization based sparse and low-rank recovery in signal processing，statistics，and machine learning[J].IEEE Access，2018，6：69883-69906.
[8] SELESNICK I，LANZA A，MORIGI S，et al.Non-convex total variation regularization for convex denoising of signals[J].Journal of Mathematical Imaging，2020，14：1-17.
[9] LANZA A，MORIGI S，SELESNICK I W，et al.Sparsity-inducing nonconvex nonseparable regularization for convex image processing[J].SIAM Journal on Imaging Sciences，2019，12（2）：1099-1134.
[10] SELESNICK I.Sparsity amplified[C]//2017 IEEE International Conference on Acoustics，Los Angeles，2017：1-5.
[11] 刘浩洋，户将，李勇锋，等.最优化：建模、算法与理论[M].北京：高等教育出版社，2020：343-359.
LIU H Y，HU J，LI Y F，et al.Optimization：modeling，algorithms and theories[M].Beijing：Higher Education Press，2020：343-359.
[12] MOLINARI C，PEYPOUQUET J，ROLDAN F.Alternating forward-backward splitting for linearly constrained optimization problems[J].Optimization Letters，2020，14（5）：1071-1088.
[13] 杨航.基于即插即用先验与神经网络的编码衍射成像算法研究[D].秦皇岛：燕山大学，2019.
YANG H.Research on coded diffraction imaging algorithm based on plug and play prior and neural network[D].Qinhuangdao：Yanshan University，2019.
[14] ZHAO X L，XU W H，JIANG T X.Deep plug-and-play prior for low-rank tensor completion[J].Neurocomputing，2020，400：137-149.
[15] MAKINEN Y，AZZARI L，FOI A.Exact transform-domain noise variance for collaborative filtering of stationary correlated noise[C]//2019 IEEE International Conference on Image Processing，Taipei，China，2019：185-189.
[16] 刘迪，贾金露，赵玉卿，等.基于深度学习的图像去噪方法研究综述[J].计算机工程与应用，2021，57（7）：1-13.
LIU D，JIA J L，ZHAO Y Q，et al.Overview of image denoising methods based on deep learning[J].Computer Engineering and Applications，2021，57（7）：1-13.
[17] RYU E K，LIU J，WANG S，et al.Plug-and-play methods provably converge with properly trained denoisers[C]//36th International Conference on Machine Learning，2019，97：5546-5557.
[18] AHMAD R，BOUMAN C A，Buzzard G T，et al.Plug-and-play methods for magnetic resonance imaging：using denoisers for image recovery[J].IEEE Signal Processing Magazine，2020，37（1）：105-116.
[19] CHAN S H，WANG X，ELGENDY O A.Plug-and-play ADMM for image restoration：fixed-point convergence and applications[J].IEEE Transactions on Computational Imaging，2016，3（1）：84-98.
[20] YANG Y，SUN J，LI H B，et al.Deep ADMM-Net for compressive sensing MRI[C]//30th Conference on Neural Information Processing Systems，Barcelona，2016：1-9.
[21] EKSIOGLU，ENDER M.Decoupled algorithm for MRI reconstruction using nonlocal block matching model：BM3D-MRI[J].Journal of Mathematical Imaging & Vision，2016，56（3）：430-440.
[22] ZHANG K，ZUO W，CHEN Y，et al.Beyond a Gaussian denoiser：residual learning of deep CNN for image denoising[J].IEEE Transactions on Image Processing，2016，26（7）：3142-3155.
[23] ZHANG K，ZUO W，ZHANG L.FFDNet：toward a fast and flexible solution for CNN based image denoising[J].IEEE Transactions on Image Processing，2018，27（9）：4608-4622.
[24] ZHANG K，ZUO W，GU S，et al.Learning deep CNN denoiser prior for image restoration[C]//2017 IEEE Conference on Computer Vision and Pattern Recognition，Honolulu，Jul 21-26，2017：3929-3938.
[25] ZHANG K，LI Y，ZUO W，et al.Plug-and-play image restoration with deep denoiser prior[J].arXiv：2008.13751，2020.
[26] RONNEBERGER O，FISCHER P，BROX T.U-Net：convolutional networks for biomedical image segmentation[C]//18th International Conference on Medical Image Computing and Computer-Assisted Intervention.Cham：Springer，2015：234-241.
[27] HE K，ZHANG X，REN S，et al.Deep residual learning for image recognition[C]//2016 IEEE Conference on Computer Vision and Pattern Recognition，2016：770-778.