Product of Gaussian Mixture Diffusion Model for non-linear MRI Inversion

TL;DR

This paper introduces a lightweight, interpretable Gaussian mixture diffusion model for MRI reconstruction that jointly estimates images and coil sensitivities, offering fast, robust results with uncertainty quantification.

Contribution

It proposes a novel product of Gaussian mixture diffusion model for joint MRI image and coil sensitivity reconstruction, improving interpretability and efficiency.

Findings

Achieves fast inference comparable to classical methods.

Demonstrates robustness to contrast and sampling variations.

Provides pixel-wise uncertainty estimates.

Abstract

Diffusion models have recently shown remarkable results in magnetic resonance imaging reconstruction. However, the employed networks typically are black-box estimators of the (smoothed) prior score with tens of millions of parameters, restricting interpretability and increasing reconstruction time. Furthermore, parallel imaging reconstruction algorithms either rely on off-line coil sensitivity estimation, which is prone to misalignment and restricting sampling trajectories, or perform per-coil reconstruction, making the computational cost proportional to the number of coils. To overcome this, we jointly reconstruct the image and the coil sensitivities using the lightweight, parameter-efficient, and interpretable product of Gaussian mixture diffusion model as an image prior and a classical smoothness priors on the coil sensitivities. The proposed method delivers promising results while allowing for fast inference and demonstrating robustness to contrast out-of-distribution data and sampling trajectories, comparable to classical variational penalties such as total variation. Finally, the probabilistic formulation allows the calculation of the posterior expectation and pixel-wise variance.