Diffusion posterior sampling for magnetic resonance imaging

Score-based diffusion models have been utilized to solve inverse problems in magnetic resonance imaging (MRI) in the context of diffusion posterior sampling. Their training-free benefit over supervised learning is particularly promising when there is an anatomy shift in experimental configuration of MRI. The diffusion posterior sampling (DPS) alternates between unconditional generation and measurement-guided gradient descent step, derived from an approximation to the intractable measurement likelihood conditioned on the intermediate image estimate. To address the unknown likelihood, the conventional solution predicts the clean image from the intermediate image via Tweedie's formula. The primary drawback of such method is the computational expense of back-propagation through the network for gradient calculation. To alleviate the back-propagation, we propose a novel gradient descent iteration that eliminates the need for the complicated back-propagation. Compared to the existing annealed Langevin dynamics-based DPS for MRI, our approach offers enhanced performance in image reconstruction with a cleaner background. The significant performance of our approach is validated by experiments.