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Abstract #4625

Fractional-Order Diffusion Equation Driven White-Box Transformers for Accelerated MRI

Taofeng Xie1, Chen Luo2, Xuemei Wang3, Li Cao1, Yuanzhi Zhang4, Liming Tang5, Jianping Zhang6, Zhuoxu Cui7, and Dong Liang7
1School of Computer and Information Science, Inner Mongolia Medical University, Hohhot, China, 2Inner Mongolia University, Hohhot, China, 3Department of Nuclear Medicine, The Affiliated Hospital of Inner Mongolia Medical University, Hohhot, China, 4Intelligent Medical Engineering Research Center, The Second Affiliated Hospital of Inner Mongolia Medical University, Hohhot, China, 5Hubei Minzu University, Enshi, China, 6School of Mathematics and Computational Science, Xiangtan University, Xiangtan, China, 7Research Center for Medical AI, Shenzhen Institutes of Advanced Technology, Shenzhen, China

Synopsis

Keywords: Image Reconstruction, Diffusion Reconstruction

Motivation: An insufficiently theoretical relationship between optimization theory and Transformer architecture design.

Goal(s): Improved MRI reconstruction integrates Transformer and nonlinear diffusion model achieving white-box in deep learning.

Approach: By leveraging the properties of fractional Laplacian operators to effectively capture global information in images, we constructed a Transformer-like architecture as a fractional-order nonlinear diffusion model serving as a regularization term.

Results: Since the learning parameters in the Transformer-like architecture are the weight coefficients of the fractional Laplacian operator, this method exhibits strong interpretability. Numerical experiments demonstrate that the reconstruction performance of the proposed method is superior.

Impact: We constructed a Transformer-like architecture using fractional Laplacian operators to establish an MRI reconstruction model. The parameters of the Transformer-like architecture can be interpreted as coefficients of the fractional Laplacian operator, making the model a fully interpretable deep learning reconstruction.

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Keywords