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

arXiv: https://arxiv.org/abs/2511.11963 · HTML: https://mlsanity.com/paper/2511.11963/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 12 of its 16 references that are in the map.
- First posted on arXiv 15 Nov 2025.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 12 of 12)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [CDLNet: Noise-Adaptive Convolutional Dictionary Learning Network for Blind Denoising and Demosaicing](https://mlsanity.com/paper/2112.00913/) (2021)
- [GroupCDL: Interpretable Denoising and Compressed Sensing MRI via Learned Group-Sparsity and Circulant Attention](https://mlsanity.com/paper/2407.18967/) (2024)
- [Self-Supervised Noise Adaptive MRI Denoising via Repetition to Repetition (Rep2Rep) Learning](https://mlsanity.com/paper/2504.17698/) (2025)
- [Gabor is Enough: Interpretable Deep Denoising with a Gabor Synthesis Dictionary Prior](https://mlsanity.com/paper/2204.11146/) (2022)
- [Learned Primal Dual Splitting for Self-Supervised Noise-Adaptive MRI Reconstruction](https://mlsanity.com/paper/2504.15390/) (2025)

## Abstract (arXiv)

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