Congcong Liu1,2, Zhuoxu Cui1, Zhilang Qiu1, Haoxiang Li1,2, Yifan Guo1, Chentao Cao1,2, Xin Liu1,2, Hairong Zheng1,2, Dong Liang1,2,3, and Haifeng Wang1,2
1Shenzhen Institutes of Advanced Technology,Chinese Academy of Sciences, Shenzhen, China, 2Shenzhen College of Advanced Technology, University of Chinese Academy of Sciences, Shenzhen, China, 3Research Centre for Medical AI, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
Synopsis
CSM or kernel needs to be estimated in conventional parallel image, which is very time-consuming and the estimation process may be inaccurate. Here, wave coding model based on virtual conjugate coil using deep generative modes (WV-DGM) is proposed for the virtual conjugate coil (VCC) extended model based on wave coding. WV-DGM combined with deep DGM without training can realize advantages of wave encoding and introduce extra phase to reduce the ill-condition of the model via VCC. The results in vivo demonstrated that WV-DGM can achieve better quality compared with conventional SENSE while 10x times used to estimate CSM is reduced.
Introduction
In MRI reconstruction based on wave encoding,
the condition number of the system can be reduced by using the re-encoded coil sensitivity
information of the readout direction. Coil sensitivity maps (CSM) need to be estimated
prior common reconstruction using SENSE[1-4] and kernels need to be calculated in
the GRAPPA[5-7] for calibration in k-space. The
process of calculation the CSM or kernel is laborious and inaccurate while
having requirement to the template. A large amount of training data needs to be
collected and preprocessed in using conventional deep learning reconstruction methos[8],[9], which is difficult to achieve in clinical[10]. Fortunately, deep generative models[11],[12] (DGM) are a kind of untrained net including CSM
free and calibration free. In addition, DGM maintains the equal reconstruction
accuracy while still maintaining a theory similar to CS to ensure that the physical
encoding process meets certain conditions[13],[14].
A new model based on wave coding
model[15] and combined with virtual conjugate coil (VCC) without untraning was
proposed in this work, named WV-DGM. WV-DGM not only contains wave encoding mechanism, but also has the efficiency and accuracy of
DGM. Furthermore, additional phase information is also considered to improve the reconstruction. WV-DGM has achieves the best
reconstruction quality in vivo data while having the shortest reconstruction time compared
to other reconstruction methods. We believe that WV-DGM will have greater
potential in clinical application to achieve rapid reconstruction.Methods
The
DGM (as shown in Fig. 1) employed in the WV-DGM is that presents a generative
convolutional neural network that provides a low-dimensional to high-dimensional
mapping method [8], i.e., $$$G: \mathbb{R}^p \to \mathbb{R}^{c \times w \times h }$$$, where $$$c$$$, $$$w$$$, and $$$h$$$ represent
the number of output channel, the width and height of the image each channel,
respectively. The input of DGM is fixed, chosen randomly. The VCC-based wave coding (Wave-VCC) can effectively utilize the physical properties in MRI and
increase the SNR of the reconstruction. WV-DGM is proposed combined with DGM as
follows, $$arg\min_{ \mathcal {G}_i} \frac {1} {2} \sum_{i=1}^{\mathcal {n}_\mathcal {c}} || \mathcal {M} \mathcal {F}_x^{-1} \mathcal {Psf}( \mathcal{k}_\mathcal{i}^{\ast}, \mathcal{y}) \mathcal {F}_\mathcal {x} \mathcal {G}_\mathcal{i}(\xi)- \mathcal {k}_\mathcal{i}^{\ast} ||_2^2$$.
Where, a set of $$$\mathcal {k}_\mathcal{i}^{\ast}$$$ k-space data consisted of $$$\mathcal {k}_1^{\ast}$$$, $$$\cdots$$$, $$$\mathcal {k}_\mathcal {n_c}^{\ast}$$$ of $$$\mathcal {n}_\mathcal{c}$$$ receiver coil is given with a given mask $$$\mathcal {M}$$$ of an unknown image, especially, $$$\mathcal{k}_\mathcal{i}^{\ast}$$$ were expanded from the original $$$\mathcal {k}_\mathcal {i}$$$ data via VCC. $$$\mathcal {Psf}(\mathcal {k}_\mathcal {i}^{\ast},\mathcal{y})$$$ was introduced as a kind of convolutional kernel in the readout direction
in MRI, which can effectively reduce the ill-condition of WV-DGM solution and
increase SNR.
The IRB (institutional review board) approved in vivo human brain experiments
were performed on a 3T uMR790 scanner (United Imaging, Shanghai, China). The WV-DGM
is introduced into the common PI based on
Wave-VCC physical encoding, which can greatly reduce the reconstruction complexity
and time due to the steps of CSM being estimated in SENSE, or kernel in GRAPPA are
eliminated. The knee data was encoded and expanded by using the process of simulated via wave
coding and the expend of VCC methods. The results show that WV-DGM achieves
better results compared with conventional SENSE reconstruction. The brain data of
the gradient field encoded by the actual wave was also collected and expanded
with the VCC. The results demonstrate
that WV-DGM proposed in this work has better performance compared to SENSE. In
addition, out method is more friendly to clinical realization.Results
In Fig. 2, the Psf
divided into original and extended via VCC was measured in the actual scanning
system. The 7-cycles wave were successfully implemented for the actual encoding
system, which can reduce the ill-condition in WV-DGM. The simulated Psf was generated to encode the knee
data (4x) to reconstruction, as shown in Fig. 3. The results show
that the reconstruction quality by using the DMG model has gradually improved
in V-DGM, W-DGM, and DGM, especially, WV-DGM can reconstruct the best image
quality including higher SNR and contrast while 10x times used to estimate CSM is reduced. The brain data in vivo encoded by wave was
reconstructed in scanner to verify the actual reconstruction quality of WV-DGM. WV-DGM shows that our proposed WV-DGM technique enhances
the reconstruction, as shown in Fig. 4. Conclusion
In summary, WV-DGM greatly reduces the complexity of reconstruction without needing to estimate CSM or kernel. This technology is friendly in clinical implementation.Acknowledgements
Congcong Liu and Zhuoxu Cui contributed equally to this work. The authors thank Prof. Berkin Bilgic and Mohammad Zalbagi Darestani for sharing the WaveCAIPI, and ConvDecoder reconstruction codes. Some of the work was partially supported by the National Natural Science Foundation of China (61871373, 81729003, and 81901736), the Strategic Priority Research Program of Chinese Academy of Sciences (No. XDB25000000), the Chinese Academy of Sciences Engineering Laboratory for Medical Imaging Technology and Equipment (No. KFJ-PTXM-012), the Pearl River Talent Recruitment Program of Guangdong Province (2019QN01Y986), the Shenzhen Science and Technology Program (JCYJ20210324115810030), the Shenzhen Peacock Plan Team Program (No. KQTD20180413181834876), and the Shenzhen Key Laboratory of Ultrasound Imaging and Therapy (No. ZDSYS201802061806314).References
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