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

2025-01-15

AI Summary

To address key challenges in MRI nonlinear reconstruction—namely, poor interpretability, low computational efficiency, and non-robust coil sensitivity estimation—this paper proposes a lightweight, highly interpretable joint reconstruction framework. The method introduces, for the first time, a product-form Gaussian Mixture Diffusion Model (GMDM) as an image prior, coupled with classical smoothness regularization (e.g., total variation), enabling end-to-end joint estimation of both image and coil sensitivities—eliminating the need for offline calibration and redundant per-coil computations. Built upon variational inference, it supports Bayesian posterior mean and variance estimation, yielding pixel-wise uncertainty quantification. Experiments demonstrate robust performance under out-of-distribution contrasts and arbitrary k-space sampling trajectories. With significantly fewer parameters and faster inference, the method achieves reconstruction quality comparable to conventional TV-based approaches while enhancing interpretability and statistical rigor.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Diffusion Models for Vision
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Magnetic Resonance Imaging
• Diffusion Models
• Parallel Imaging Reconstruction

Innovation

• Gaussian Mixture Diffusion Model
• MRI Image Reconstruction
• Pixel Stability Assessment