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

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.