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Accelerating Myelin Water Content Quantification using Deep Non-Local Sparse Model1School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China, 2Department of Radiology, Stanford University, Stanford, CA, United States
Synopsis
A grouping sparse coding (Group-SC) model is used in this study for the acceleration of myelin water content quantification. Images with improved quality are obtained using the Group-SC algorithm, in the aspect of minimal artefacts and good data consistency with fully-sampled labels. Myelin water fraction (MWF) maps reconstructed using Group-SC demonstrate more natural spatial distribution of myelin water in the brain. The proposed Group-SC algorithm has demonstrated its potential for the acceleration of the myelin water content quantification at R = 6.
Introduction
Myelin water imaging (MWI) can be used for the quantification of myelin water content [1]. Multi-echo T2* weighted images (T2*WIs) have been used to generate myelin water fraction (MWF) map for the whole brain, which typically takes a scan time for several minutes [2-4]. Several methods have been proposed for the acceleration of the T2*WIs [5-7], some of them have exploited the similarity information in images [6,7]. In this study, a method based on deep grouping sparse coding (Group-SC) [8] model is employed to exploit the non-local self-similarity information among patches for the quantification of myelin water content, using convolutional joint sparse coding based on a variant of LISTA algorithm [9]. The preliminary results in this study demonstrate that the acceleration of myelin water content quantification with improved image quality can be achieved using the proposed deep Group-SC method.Theory
The flowchart of the Group-SC network is illustrated in Figure 1. The Group-SC module and the data consistency module are combined in succession as a single unit, while multiple units are concatenated together. The T2*WIs are first fed to a centering operation, which means that the zero-frequency information is not processed by the model. The global self-similarity information is integrated in the model, where a $$$L_{1,2}$$$-norm is used to enforce that the group-wise sparsity is shared across similar patches. After being processed by the Group-SC module the mean value is added back, and the image as a whole will further be processed by DC module.The Group-SC and DC module in a single unit are defined as follow:
$$\min _{x, \theta} \tau\left\|Y^{C}-D A\right\|_{2}^{2}+\xi \psi(A)+\left\|F_{u} x-y\right\|_{2}^{2}\tag{1}$$
where $$$x$$$ are the desired images, $$$A$$$ represents sparse coding for a given dictionary $$$D$$$, $$$Y^{C}$$$ are the centered input patches, $$$y$$$ is the undersampled k-space data, $$$F_{u}$$$ is the undersampled Fourier operator, $$$\| \|_{2}^{2}$$$ is the Frobenius norm, and $$$\tau,\xi$$$ are the regularization parameters. $$$\psi(A)=\Lambda\|A\|_{1,2}$$$ is the group sparsity regularizer, $$$\Lambda$$$ represents different soft-thresholding parameters $$$\lambda_{i}$$$ in each inner iteration step. $$$\theta$$$ is the set of parameters to learn, including all dictionaries and the regularization parameters.
The optimization problem can then be solved by the following two consecutive steps:
$$\begin{gathered}\mathrm{B}=A_{k}+C^{T}\left(Y^{C}-D A_{k}\right), \\A_{k+1}=\max \left(1-\frac{\Lambda_{k} \sqrt{\|\Sigma\|_{1}}}{\left\|B(\Sigma)^{\frac{1}{2}}\right\|_{1,2}}, 0\right) B，\end{gathered} \tag{2}$$
where $$$C$$$ is a decoupled dictionary from $$$D$$$, and $$$\Sigma$$$ is the similarity matrix which is updated at a given frequency. The output patches are then generated using a dictionary, which is also decoupled from $$$D$$$.
Methods
Twelve healthy subjects were scanned using a multi-slice mGRE sequence on a 3T MRI scanner (uMR790, United Imaging Healthcare, Ltd., Shanghai, China). Written consent was obtained before each scan. The scanning parameters were: FOV = 240 mm × 240 mm, matrix = 176 × 176, flip angle = 90°, TR = 2 s, first TE = 1.95 ms, echo spacing = 1.16 ms, echo train length = 30, slice thickness = 3 mm, 25 slices were scanned with a 1.5 mm slice gap. The whole brain scan time was 5.9 min. A multishot variable density blipped mGRE trajectory [2] with R = 6 was used for retrospective undersampling. The data of 7 subjects were used for training, 1 subject for validation, and 4 subjects for testing. The proposed algorithm was compared to the state-of-the-art TDLLS [2] and the CRNN [10,2] algorithms. The non-negative jointly sparse (NNJS) [11] algorithm was used for MWF estimation.Results
As shown in Figure 2, results from Group-SC show good consistency with fully sampled references, which can be clearly observed from difference maps. Minimal artefacts are obtained from Group-SC reconstructed images, and the PSNR values of them are higher than that of other two algorithms. In Figure 3, the MWF maps from Group-SC outperform images from TDLLS and CRNN. The nRMSE from Group-SC are the lowest among three algorithms. Statistical results for four test subjects in Table 1 demonstrate improved performances using the proposed algorithm in comparison with other two algorithms.Discussion and Conclusion
Superior performances have been achieved using Group-SC algorithm, in the aspect of reduced artefacts and better consistency with the fully sampled references. The self-similarity information provides a powerful prior during reconstruction, which yields better reconstruction results. The Group-SC algorithm has demonstrated its potential for the acceleration of myelin water content quantification at R = 6.Acknowledgements
This study is supported by the National Key Research and Development Program (2016YFC0103905) and the National Natural Science Foundation of China (81627901).
References
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Figures
Figure 2. Comparative results of the first echo of T2*WIs in four different slices, reconstructed by TDLLS, CRNN and Group-SC algorithms with R = 6 from one subject. All difference maps are amplified 10-fold for visualization. The PSNR are showed at the bottom of each reconstructed image.
Figure 3. Comparative results for MWF map from TDLLS, CRNN and Group-SC reconstructions with R = 6 from one subject. The nRMSE are showed at the bottom of each image.
Table 1. Comparison of the statistical results from MWF maps reconstructed by TDLLS, CRNN and Group-SC algorithms of four test subjects. Four evaluations (nRMSE, PSNR, HFEN, SSIM) were calculated in terms of mean and standard deviation at R = 6.