**Phase-Constrained Reconstruction of High-Resolution Multi-shot
Diffusion Weighted Image ( [****Chinese****] )**

Yiman Huang^{1},
Xinlin Zhang^{1}, Hua Guo^{2}, Huijun Chen^{2}, Di Guo^{3},
Feng Huang^{4}, Qin Xu^{4}, Xiaobo Qu^{1}*

^{1}Department of Electronic Science, Fujian Provincial Key Laboratory
of Plasma and Magnetic Resonance, School of Electronic Science and Engineering,
Xiamen University, Xiamen 361005, China.

^{2}Center for Biomedical Imaging Research, Department of Biomedical
Engineering, Tsinghua University, Beijing, 100084, China.

^{3}School of Computer and Information Engineering, Fujian Provincial
University Key Laboratory of Internet of Things Application Technology, Xiamen
University of Technology, Xiamen 361024, China.

^{4}Neusoft Medical System, Shanghai 200241, China.

**Contact**:
quxiaobo<|at|>xmu.edu.cn

**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

**Abstract**:

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.

**Methods:
**

1.
Background

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.

**Acknowledgments:**

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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