# Learned Discrepancy Reconstruction and Benchmark Dataset for Magnetic Particle Imaging

arXiv: https://arxiv.org/abs/2501.05583 · HTML: https://mlsanity.com/paper/2501.05583/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 58 references that are in the map.
- First posted on arXiv 9 Jan 2025.

## Builds on (most cited first, 5 of 5)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Bilevel approaches for learning of variational imaging models](https://mlsanity.com/paper/1505.02120/) (2015)
- [Shared Prior Learning of Energy-Based Models for Image Reconstruction](https://mlsanity.com/paper/2011.06539/) (2020)
- [L1 data fitting for robust reconstruction in magnetic particle imaging: quantitative evaluation on Open MPI dataset](https://mlsanity.com/paper/2001.06083/) (2020)
- [Equilibrium Model with Anisotropy for Model-Based Reconstruction in Magnetic Particle Imaging](https://mlsanity.com/paper/2403.00602/) (2024)

## Built on by (most cited first, 2 of 2)

- [Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspective](https://mlsanity.com/paper/2605.06172/) (2026)
- [MPISuperRes-PnP: A Super-Resolution Zero-Shot Plug-and-Play Reconstruction Algorithm for Magnetic Particle Imaging](https://mlsanity.com/paper/2608.09672/) (2026)

## Abstract (arXiv)

Magnetic Particle Imaging (MPI) is an emerging imaging modality based on the magnetic response of superparamagnetic iron oxide nanoparticles to achieve high-resolution and real-time imaging without harmful radiation. One key challenge in the MPI image reconstruction task arises from its underlying noise model, which does not fulfill the implicit Gaussian assumptions that are made when applying traditional reconstruction approaches. To address this challenge, we introduce the Learned Discrepancy Approach, a novel learning-based reconstruction method for inverse problems that includes a learned discrepancy function. It enhances traditional techniques by incorporating an invertible neural network to explicitly model problem-specific noise distributions. This approach does not rely on implicit Gaussian noise assumptions, making it especially suited to handle the sophisticated noise model in MPI and also applicable to other inverse problems. To further advance MPI reconstruction techniques, we introduce the MPI-MNIST dataset - a large collection of simulated MPI measurements derived from the MNIST dataset of handwritten digits. The dataset includes noise-perturbed measurements generated from state-of-the-art model-based system matrices and measurements of a preclinical MPI scanner device. This provides a realistic and flexible environment for algorithm testing. Validated against the MPI-MNIST dataset, our method demonstrates significant improvements in reconstruction quality in terms of structural similarity when compared to classical reconstruction techniques.