Integrating data distribution prior via Langevin dynamics for end‐to‐end MR reconstruction

Purpose To develop a novel deep learning‐based method inheriting the advantages of data distribution prior and end‐to‐end training for accelerating MRI. Methods Langevin dynamics is used to formulate image reconstruction with data distribution before facilitate image reconstruction. The data distribution prior is learned implicitly through the end‐to‐end adversarial training to mitigate the hyper‐parameter selection and shorten the testing time compared to traditional probabilistic reconstruction. By seamlessly integrating the deep equilibrium model, the iteration of Langevin dynamics culminates in convergence to a fix‐point, ensuring the stability of the learned distribution. Results The feasibility of the proposed method is evaluated on the brain and knee datasets. Retrospective results with uniform and random masks show that the proposed method demonstrates superior performance both quantitatively and qualitatively than the state‐of‐the‐art. Conclusion The proposed method incorporating Langevin dynamics with end‐to‐end adversarial training facilitates efficient and robust reconstruction for MRI. Empirical evaluations conducted on brain and knee datasets compellingly demonstrate the superior performance of the proposed method in terms of artifact removing and detail preserving.