Blind Proximal Diffusion Model for Joint Image and Sensitivity Estimation in Parallel MRI

Parallel imaging (PI) has demonstrated notable efficiency in accelerating magnetic resonance imaging (MRI) using deep learning techniques. However, these models often face challenges regarding their adaptability and robustness across varying data acquisition. In this work, we introduce a novel joint estimation framework for MR image reconstruction and multi-channel sensitivity maps utilizing denoising diffusion models under blind settings, termed Blind Proximal Diffusion Model in Parallel MRI (BPDM-PMRI). BPDM-PMRI formulates the reconstruction problem as a non-convex optimization task for simultaneous estimation of MR images and sensitivity maps across multiple channels. We employ the proximal alternating linearized minimization (PALM) to iteratively update the reconstructed MR images and sensitivity maps. Distinguished from the traditional proximal operators, our diffusion-based proximal operators provide a more generalizable and stable prior characterization. Once the diffusion model is trained, it can be applied to various sampling trajectories. Comprehensive experiments conducted on publicly available MR datasets demonstrate that BPDM-PMRI outperforms existing methods in terms of denoising effectiveness and generalization capability, while keeping clinically acceptable inference times.