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

TL;DR

This work addresses accelerated MRI reconstruction under realistic noise by marrying diffusion priors with explicit MRI physics through a maximum a posteriori (MAP) framework. It introduces ImMAP, an implicit prior diffusion-based method that uses Tweedie's formula to access the denoiser score and incorporates the measurement model via a likelihood term, solved with a coarse-to-fine stochastic ascent. Across synthetic and real scanner noise, ImMAP outperforms state-of-the-art diffusion and end-to-end methods and exhibits robustness with little hyperparameter tuning, offering improved interpretability over conventional diffusion approaches. The results suggest that physics-informed diffusion priors can deliver reliable, high-quality reconstructions for noisy MRI without the instability and tuning burden common to existing diffusion-based methods.

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

Figures (5)

• Figure 1: Quantitative performance of end-to-end (LPDSNet), and denoising diffusion based (DDS, ImMAP) reconstruction methods on the T1w brain test dataset. NRMSE/LPIPS/SSIM (%) shown at $8\times$ acceleration and across noise-levels $(\sigma_y)$. Noise is considered in two scenarios: simulated noise added to the coil-combined fully-sampled image data (i.e. ${(\bm{\Sigma}_y)_{cc} = \sigma_y \in (0.01,0.02,0.05)}$), and measurement noise (meas., $\bm{\Sigma}_y=\hat{\bm{\Sigma}}_y$) where the original fully-sampled k-space data is retrospectively undersampled. Error bars show standard-error of the mean over 16 test-volumes.
• Figure 2: Visual comparison of ImMAP joint denoising and reconstruction MRI at $8\times$ acceleration against classical reconstruction (SENSE espirit), end-to-end deep reconstruction (LPDSNet lpds2025), denoising diffusion model (DDS chung2024decomposed), across noise-levels $(\sigma_y)$. Quantitative metrics (NRMSE/LPIPS/SSIM (%)) are shown in yellow above each reconstruction.
• Figure 3: Ablation of ImMAP's noise-injection parameter $\beta \in (0, 1]$. Left: average NRMSE over the T1w brain test set vs. $\beta$, across noise-levels ${\sigma_y=(0.01,0.02,0.05, \text{meas.})}$. Standard error of the mean shown via shaded regions. Right: Corresponding average number of iterations vs. $\beta$, across noise-levels.
• Figure 4: DDS performance (average volume NRMSE) on $8\times$ accelerated T1w brain test-set with varying $\gamma$ hyperparameter over different noise levels ${\sigma_y=(0.01,0.02,0.05, \text{meas.})}$. Standard error of the mean shown via shaded regions. DDS takes 83 iterations.
• Figure 5: Visualization of $8\times$ reconstruction at $\sigma_y=0.02$ when changing hyperparameters for DDS ($\gamma$) and ImMAP ($\beta$) on a slice from the T1w brain test-set. NRMSE/LPIPS/SSIM $(\%)$ shown on each image as compared to the fully-sampled reconstruction.