Noisy MRI Reconstruction via MAP Estimation with an Implicit Deep-Denoiser Prior

TL;DR

This paper introduces ImMAP, a diffusion-based MRI reconstruction method that explicitly incorporates noise modeling into a MAP framework, improving reliability and interpretability over existing approaches.

Contribution

ImMAP is the first diffusion-based MRI reconstruction method that explicitly integrates the noise model into a MAP formulation, handling realistic measurement noise and MRI physics.

Findings

Outperforms state-of-the-art deep learning and diffusion methods on noisy datasets.

Provides a more reliable and interpretable MRI reconstruction under realistic noise conditions.

Clarifies the limitations of diffusion models in practical noisy MRI scenarios.

Abstract

Accelerating magnetic resonance imaging (MRI) remains challenging, particularly under realistic acquisition noise. While diffusion models have recently shown promise for reconstructing undersampled MRI data, many approaches lack an explicit link to the underlying MRI physics, and their parameters are sensitive to measurement noise, limiting their reliability in practice. We introduce Implicit-MAP (ImMAP), a diffusion-based reconstruction framework that integrates the acquisition noise model directly into a maximum a posteriori (MAP) formulation. Specifically, we build on the stochastic ascent method of Kadkhodaie et al. and generalize it to handle MRI encoding operators and realistic measurement noise. Across both simulated and real noisy datasets, ImMAP consistently outperforms state-of-the-art deep learning (LPDSNet) and diffusion-based (DDS) methods. By clarifying the practical behavior and limitations of diffusion models under realistic noise conditions, ImMAP establishes a more reliable and interpretable