Yiman Huang^{1}, Xinlin Zhang^{1}, Hua Guo^{2}, Huijun Chen^{2}, Di Guo^{3}, and Xiaobo Qu^{1}

^{1}Department of Electronic Science, Xiamen University, Xiamen, China, ^{2}School of Medicine, Tsinghua University, Beijing, China, ^{3}School of Computer and Information Engineering, Xiamen University of Technology, Xiamen, China

Multi-shot DWI improves the image resolution, while it induces phase variation at the same time. We introduce a smooth phase constraint of each shot image into multi-shot DWI reconstruction procedures by imposing the low-rankness of Hankel matrix constructed from the k-space data. The image is further improved with a partial sum of singular values in low-rank matrix reconstruction. Results on brain imaging data show that the proposed method outperforms the state-of-the-art methods in terms of artifacts removal and is compatible to partial Fourier sampling in accelerated DWI.

Besides, in the low rank matrix reconstruction, it has been found that the minimization of nuclear norm may lead to sub-optimal performance, and some researches try to minimize the partial sum of singular values

Figure 1 shows the reconstruction results of 8-shot fully sampled DWI. Directly inverse Fourier transformation induces severe aliasing artifacts (Figure 1 (a)). Much better images are obtained using POCS-ICE and MUSSELS but visible artifacts can be observed, as marked by red arrows in Figure 1. MUSSELS result looks dark in the center of image. While our result can effectively reconstruct the image without artifacts and with shaper edges than MUSSELS.

Figure 2 shows the reconstruction results of 4-shot partial Fourier sampled DWI with partial Fourier factor equals 55%. Directly inverse Fourier transformation induces strong aliasing artifacts. All other methods are able to recover artifact-free image. While POCS-ICE shows noisier than MUSSELS, MUSSELS cannot recover the uncollected part of partial Fourier sampled data at all, which cause blurred images using MUSSELS. Among all, our method leads to a sharper image and has the ability to recover the uncollected partial Fourier sampled data, indicating that the k-space conjugate symmetry property has inherently been exploited in our PLRHM model.

This work was supported in part by National Key R&D Program of China (2017YFC0108700), National Natural Science Foundation of China (61571380, 61971361, 61871341, and 61811530021), Natural Science Foundation of Fujian Province of China (2018J06018), Fundamental Research Funds for the Central Universities (20720180056), Science and Technology Program of Xiamen (3502Z20183053), and China Scholarship Council.

The correspondence should be sent to Dr. Xiaobo Qu (Email: quxiaobo@xmu.edu.cn)

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Figure 1. The
8-shot in vivo experiment using different reconstruction methods. (a) Direct
FFT, (b) POCS-ICE, (c) MUSSELS, (d) the proposed method, (e) reference
reconstructed by using navigators. The residual artifacts are marked by the red
arrows.

Figure 2. Reconstructed
images of 4-shot in vivo data. (a) Direct FFT, (b) POCS-ICE, (c) MUSSELS, (d)
the proposed method, (e)-(h) k-space of (a)-(e).