Product of Gaussian Mixture Diffusion Model for Non-linear MRI Inversion
L. Nagler, M. Zach, T. Pock
Proceedings of the Tenth International Conference on Scale Space and Variational Methods in Computer Vision (SSVM'25), Totnes, United Kingdom, May 18-22, 2025, pp. 146–158.
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.
@INPROCEEDINGS(http://bigwww.epfl.ch/publications/nagler2501.html,
AUTHOR="Nagler, L. and Zach, M. and Pock, T.",
TITLE="Product of {G}aussian Mixture Diffusion Model for Non-linear
{MRI} Inversion",
BOOKTITLE="Proceedings of the Tenth International Conference on Scale
Space and Variational Methods in Computer Vision ({SSVM'25})",
YEAR="2025",
editor="",
volume="",
series="",
pages="146--158",
address="Totnes, United Kingdom",
month="May 18-22,",
organization="",
publisher="",
note="")