Qingyong Zhu^{1}, Jing Cheng^{2}, Zhuo-Xu Cui^{1}, Yuanyuan Liu^{3}, Yanjie Zhu^{2}, and Dong Liang^{1}

^{1}Research Center for Medical AI, SIAT, Chinese Academy of Sciences, Shenzhen, China, ^{2}Paul C. Lauterbur Research Center for Biomedical Imaging, SIAT, Chinese Academy of Sciences, Shenzhen, China, ^{3}National Innovation Center for Advanced Medical Devices, Shenzhen, China, Shenzhen, China

The existing accelerated MRI methods have the limitations such as fine-structure loss in the cases of high reduction factors or noisy measurements. This work presents a novel mutual-structure filtering based half-quadratic splitting algorithm for accurate undersampled brain MRI reconstruction. Experimental results on in-vivo images have shown that the proposed approach has a superior ability to capture meaningful details compared with other state-of-the-art reference guided reconstruction technologies.

\begin{align}&u=\mathop{\arg\min}_{x\in\mathbb{C}^{N\times1}}\frac{1}{2}\!\parallel\!\mathcal{A}x-b\!\parallel_2^2+\frac{\mu}{2}\!\!\parallel\!x-g\!\parallel_2^2\\ &g=\mathop{\arg\min}_{g\in\mathbb{C}^{N\times1}}\frac{\mu}{2}\parallel\!g-u\!\parallel_2^2+\lambda\phi(g)\end{align}where the second sub-problem is uaually the proximal operator of the regularization $$$\phi(g)$$$, and it can reduce to the additive white gaussian noise (AWGN) based plug-and-play filtering of the updated $$$u$$$, deriving a class of boosting algorithms in HQS framework.

- Mila N and Michael K N. Analysis of half-quadratic minimization methods for signal and image recovery. SIAM J. Scientific Comput. 2005; 27(3):937–966.
- Shen X Y, Zhou C, Xu L, et al. Mutual-Structure for Joint Filtering. 2015 IEEE Int. Conf. on Computer Vision (ICCV). 2015.
- Wang Z, Bovik, A. C., Sheikh, H. R., et al. Image quality assess-ment: from error visibility to structural similarity. IEEE Trans. ImageProcess. 2004; 13: 600-612.
- Haldar J P, Hernando D, Song S K, et al. Anatomically con-strained reconstruction from noisy data. Magn. Reson. Med. 2008; 59(4): 810-818.
- Peng X, Zhu Q. Y, Wang S S, et al. Reference guided CS-MRI with gradient orientation priors. 2015 IEEE Int. Conf. in Medicineand Biology Society (EMBS). 2015.

Figure.1 T1-weighted image and PD-weighted image.

Figure.2 T1-weighted image and PD-weighted image.Figure.2 Reconstruction results of CS-wTV, CS-GOP and the proposed method using 1D under-sampling pattern at reduction factors of R=3, 4 and 5. The corresponding local regions of returned images are enlarged for better visualization.

Table.1 The quantitative comparisons of various reconstructions on different reduction factors. The running time (RT) is measured to evaluate the algorithm efficiency. The reconstruction quality is quantified with the relative \unboldmath $$${\textit{l}_{2}}$$$-norm error (RLNE) and peak signal to noise ratio (PSNR).

DOI: https://doi.org/10.58530/2022/4684