Product-of-Gaussian-mixture diffusion models for joint nonlinear MRI reconstruction

Recently, diffusion models have attracted considerable attention for magnetic resonance image reconstruction due to their high sample quality. However, most existing methods rely on large networks with opaque time conditioning mechanisms and require offline coil sensitivity estimation. This results in limited interpretability of the reconstruction process and reduced flexibility in the acquisition setup. To address these limitations, we jointly reconstruct the image and the coil sensitivities by combining the parameter-efficient product-of-Gaussian-mixture diffusion model as an image prior with a classical smoothness prior on the coil sensitivities. The proposed method is fast and robust to both contrast and anatomical distribution shifts as well as changing k-space trajectories. Finally, we propose a more expressive parameterization of the image prior which improves results in denoising and magnetic resonance image reconstruction.