# Measurement Score-Based MRI Reconstruction with Automatic Coil Sensitivity Estimation

arXiv: https://arxiv.org/abs/2509.18402 · HTML: https://mlsanity.com/paper/2509.18402/

## 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 9 of its 13 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Placed in

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

## Builds on (most cited first, 9 of 9)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data](https://mlsanity.com/paper/2403.08728/) (2024)
- [SPICER: Self-Supervised Learning for MRI with Automatic Coil Sensitivity Estimation and Reconstruction](https://mlsanity.com/paper/2210.02584/) (2022)
- [Measurement Score-Based Diffusion Model](https://mlsanity.com/paper/2505.11853/) (2025)

## Abstract (arXiv)

Diffusion-based inverse problem solvers (DIS) have recently shown outstanding performance in compressed-sensing parallel MRI reconstruction by combining diffusion priors with physical measurement models. However, they typically rely on pre-calibrated coil sensitivity maps (CSMs) and ground truth images, making them often impractical: CSMs are difficult to estimate accurately under heavy undersampling and ground-truth images are often unavailable. We propose Calibration-free Measurement Score-based diffusion Model (C-MSM), a new method that eliminates these dependencies by jointly performing automatic CSM estimation and self-supervised learning of measurement scores directly from k-space data. C-MSM reconstructs images by approximating the full posterior distribution through stochastic sampling over partial measurement posterior scores, while simultaneously estimating CSMs. Experiments on the multi-coil brain fastMRI dataset show that C-MSM achieves reconstruction performance close to DIS with clean diffusion priors -- even without access to clean training data and pre-calibrated CSMs.