Phase-Constrained Reconstruction of High-Resolution Multi-shot Diffusion Weighted Image ( [Chinese] )
Yiman Huang1, Xinlin Zhang1, Hua Guo2, Huijun Chen2, Di Guo3, Feng Huang4, Qin Xu4, Xiaobo Qu1*
1Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, School of Electronic Science and Engineering, Xiamen University, Xiamen 361005, China.
2Center for Biomedical Imaging Research, Department of Biomedical Engineering, Tsinghua University, Beijing, 100084, China.
3School of Computer and Information Engineering, Fujian Provincial University Key Laboratory of Internet of Things Application Technology, Xiamen University of Technology, Xiamen 361024, China.
4Neusoft Medical System, Shanghai 200241, China.
Citations: Yiman Huang, Xinlin Zhang, Hua Guo, Huijun Chen, Di Guo, Feng Huang, Qin Xu, Xiaobo Qu*, Phase-constrained reconstruction of high-resolution multi-shot diffusion weighted magnetic resonance image, Journal of Magnetic Resonance, DOI: 10.1016/j.jmr.2020.106690, 2020.
Access to full text：https://authors.elsevier.com/a/1aZ%7EG3u0yjN80o
Diffusion weighted imaging (DWI) is a unique examining method in tumor diagnosis, acute stroke evaluation. Single-shot echo planar imaging is currently conventional method for DWI. However, single-shot DWI suffers from image distortion, blurring and low spatial resolution. Although multi-shot DWI improves image resolution, it brings phase variations among different shots at the same time. We introduce a smooth phase constraint of each shot image into multi-shot navigator-free DWI reconstruction by imposing the low-rankness of Hankel matrix constructed from the k-space data. Furthermore, we exploit the partial sum minimization of singular values to constrain the low-rankness of Hankel matrix. Results on brain imaging data show that the proposed method outperforms the state-of-the-art methods in terms of artifacts removal and our method potentially has the ability to reconstruct high number of shot of DWI.
KEYWORDS: Diffusion weighted imaging, Hankel matrix, image reconstruction, low-rankness, magnetic resonance imaging.
Diffusion weighted magnetic resonance imaging (MRI) is a unique examining method noninvasively detecting the Brownian motion of water molecules in the tissues in biomedical imaging. It is widely used in tumor diagnosis, acute stroke evaluation and neuroscience research. As a conventional method of diffusion weighted imaging (DWI) acquisition, single-shot echo-planar imaging (EPI) has the advantages of motion immunity and short acquisition time, but suffers from image distortion, blurring and low spatial resolution. some methods were proposed to overcome the distortion in DWI, such as spatiotemporal encoding and multi-shot EPI.
The multi-shot interleaved EPI fully acquires the k-space data by sampling different segment in each shot, as shown in Figure 1. Multi-shot EPI provides higher spatial resolution than single-shot EPI. However, multi-shot is sensitive to physiological motions, which will induce phase variations from shot to shot. Directly interleaving multi-shot data together into fully sampled k-space will lead to severe artifacts in image.
Figure 1. A schematic diagram of 3-shot interleaved DWI. Note: The solid lines represent the collecting lines in the k-space (Fourier space) of images, and the dotted lines denote the lines where signals are not sampled.
2. Phase-constrained Low Rank Hankel Matrix reconstruction (PLRHM)
We exploit the partial sum of singular values to constrain low-rankness, the proposed rank minimization model is:
where denotes concatenated matrices of k-space data of shots, , is an operator that converts into so called matrix in LORAKS the Fourier transform operator, the inverse Fourier transform operator, the channel coil sensitivity map, an operator that under-samples k-space data and zero-fills the non-sampled data points, the channel sampled k-space data, where is the rank of , the matrix size of , a regularization parameter that balances the data consistency and low-rankness constraint.
3. Main results
The proposed method was compared with two state-of-the-art navigator-free DWI image reconstruction methods, including the POCS-ICE and MUSSELS. Figure 2 show two slices reconstructions of 8-shot head DWI. Figure 2(d) exhibit the references reconstructed by IRIS. Slight artifacts still remain in the reconstructions of POCS-ICE (Figure 2(a)), as marked by red arrows. POCS-MUSSELS reconstructions (Figure 2(b)) show no obvious artifacts but they look dark in the center of images, as marked by yellow arrows. While our results (Figure 2(c)) can effectively reconstruct the image with minimal artifacts.
Figure 2. Reconstructions of slice 9 of 8-shot in vivo head DWI using different reconstruction methods. (a) POCS-ICE, (b) POCS-MUSSELS, (c) the proposed method, (d) reference reconstructed by IRIS. The residual artifact is marked by the red arrow and the dark region is marked by yellow arrow.
Figure 3 shows the reconstructions of 3 slices of 12-shot head DWI. Directly inverse Fourier transformation induces severe aliasing artifacts (Figure 3(a)). POCS-ICE fails to remove the severe aliasing artifacts (Figure 3(b)). POCS-MUSSELS removes the artifacts to some extent but slight artifacts still remain in the image (Figure 3(c)). While the proposed method can effectively reconstruct the image with minimal artifacts and shaper edges than POCS-MUSSELS, as shown in Figure 3(d). In this case, the shot number is up to 12, which is an aggressive high shot number for reconstruction. POCS-ICE and POCS-MUSSELS have difficulty to recover the artifact-free image, while the proposed method has the potential to handle the case with high number of shots.
Figure 3. Reconstructions of 3 slices of 12-shot in vivo head DWI using different reconstruction methods. (a) direct reconstruction without correction, (b) POCS-ICE, (c) POCS-MUSSELS, (d) the proposed method.
This work was supported in part by National Key R&D Program of China (2017YFC0108700), National Natural Science Foundation of China (61971361, 61871341, 61811530021 and 61672335), 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 authors would like to thank Dr. Guobin Li in United Imaging Company for providing the 12-shot head DWI data in this paper.
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