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To develop a deep learning‐based Bayesian estimation for MRI reconstruction.

We modeled the MRI reconstruction problem with Bayes’s theorem, following the recently proposed PixelCNN++ method. The image reconstruction from incomplete k‐space measurement was obtained by maximizing the posterior possibility. A generative network was utilized as the image prior, which was computationally tractable, and the k‐space data fidelity was enforced by using an equality constraint. The stochastic backpropagation was utilized to calculate the descent gradient in the process of maximum a posterior, and a projected subgradient method was used to impose the equality constraint. In contrast to the other deep learning reconstruction methods, the proposed one used the likelihood of prior as the training loss and the objective function in reconstruction to improve the image quality.

The …