Renkuan Zhai1, Xiaoqian Huang2, Yawei Zhao1, Meiling Ji1, Xuyang Lv2, Mengyao Qian1, Shu Liao2, and Guobin Li1
1United Imaging Healthcare, Shanghai, China, 2United Imaging Intelligence, Shanghai, China
Synopsis
The
advantages of Convolutional Neural Networks (CNN) for MRI acceleration have
been widely reported, but one remaining problem is that the significantly
complex network makes itself less explainable than conventional model-based methods.
In this work, a novel deep learning assisted MRI acceleration method is
introduced to address the uncertainty of CNN by integrating its output as
another constraint into the framework of Compressed Sensing (CS).
Introduction
Convolutional
Neural Networks (CNN)1,
an architecture widely used in the field of Artificial Intelligence (AI), has
been recently demonstrated to have the potential to outperform conventional
image processing methods. Many researches reported superior image reconstruction
quality of CNN related methods (e.g. VN 2, U-Net 3) for MRI acceleration.
However, as the CNN network is a complicated black box, all related methods are
facing a predicament of ensuring their performance and reliability which is critical
in clinical scenarios 4. Although larger amount of training data can be helpful for improving
stability, the uncertainty could not be addressed as strictly as methods based
on mathematical models. Compressed Sensing (CS)5 uses the characteristics of sparse
transform to recover information from partially acquired data, however it is
difficult to reconstruct tiny anatomic structures perfectly without any prior knowledge. In this study, a novel acceleration
framework, AI-assisted Compressed Sensing (ACS), is introduced. By incorporating
AI as a regularization term, ACS maintains the advantages of AI while also mathematically
addressing the uncertainty of AI.Method
In Compressed Sensing, the
reconstruction procedure can be formulated as a minimization problem
$$argmin_{x}\|\mathbf{E}x-y\|_2^2+\lambda\|\Phi{x}\|_{1}$$Here, $$$x$$$ denotes the image to be reconstructed. $$$\mathbf{E}$$$ denotes the production of Fourier encoding
with binary k-space sampling mask. $$$y$$$ represents the acquired k-space data. $$$\Phi$$$ denotes the sparse transform, e.g. wavelet or
total variation.
The key of CS is to find a proper sparse
transform to recover information by promoting sparsity, however this is
usually not guaranteed in reality due to mismatch between actual anatomic
structures and chosen sparse transform. Given $$$x_{AI}$$$ the reconstructed
image of the trained AI Module with under-sampled k-space as input and based on the assumption that the predicted
image $$$x_{AI}$$$ is close to the true image $$$x$$$,
the subtraction operation $$$x-x_{AI}$$$ can actually be taken as a sparse
transform. In the spirit of compressed sensing, any significant errors in $$$x_{AI}$$$
due to imperfection in AI Module can be corrected through the use of L1-norm
constraint $$$ \|x-x_{AI}\|_{1}$$$.
Therefore, by adding one more regularization term from AI Module, formula above can be extended as
$$argmin_{x}\|\mathbf{E}x-y\|_2^2+\lambda_1\|\Phi{x}\|_{1}+\lambda_2\|x-x_{AI}\|_{1}$$Compared to conventional
compressed sensing, the introduction of L1 regularization term $$$
\|x-x_{AI}\|_{1}$$$ incorporates the information obtained from the AI Module
into iterative reconstruction procedure, which is able to inherit the advantage
of AI prediction as well as correct its errors.
Figure 1 shows the
flowchart of ACS. Under-sampled k-space
data with incoherent trajectories was input to AI Module, which was trained
with millions of data with under-sampled k-space
as input and corresponding fully-sampled data as ground truth, to generate predicted
image $$$x_{AI}$$$. In the final CS Module, both the $$$x_{AI}$$$ and k-space data $$$y$$$ will participate in the iterative reconstruction to produce the
final image by solving the function defined in the second formula above.
To
evaluate the performance of ACS, images reconstructed with ACS and CS under
different acceleration levels were compared. Moreover, to validate the
capability of ACS in correcting errors from AI output, artifacts (Gaussian
shaped dots) were manually created and inserted into the output from the AI
Module in the simulation test.
Volunteer
data were acquired on a 3T clinical MR scanner (uMR 780, United Imaging
Healthcare, Shanghai, China) with following parameters: T2 FSE 2D of knee with k-space matrix size of [320x288], TR/TE
= 3000ms/50ms, echo train length = 11; T2 FSE 2D hip with k-space matrix size of [320x235], TR/TE = 4000ms/120ms, echo train
length = 39.Results & Discussion
Fully-sampled data were used as golden standard.
Under-sampled data with net acceleration factor from 2.00x to 4.00x were
generated from this fully-sampled data and reconstructed using ACS as well as
CS. Results are displayed in Figure 2. ACS showed better performance than CS
especially under high acceleration levels.
The
simulation test results are shown in Figure 3. Artificial
Gaussian-shaped artifacts were added to the output of AI Module as shown in Figure 3(b).
ACS was able to correct the artifacts from the AI output, as shown in
Figure 3(c), and demonstrated good consistency as compared to the fully-sampled
golden standard in Figure 3(d). Conclusion
In conclusion, ACS benefits from AI-provided efficiency and inherits the advantage of CS for information recovery to realize superior MRI acceleration. More importantly, ACS provides a unique way to address the uncertainty of AI by incorporating the output of AI as one more regularization term of conventional compressed sensing.Acknowledgements
No acknowledgement found.References
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