# Quantitative Susceptibility Mapping through Model-based Deep Image Prior (MoDIP)

arXiv: https://arxiv.org/abs/2308.09467 · HTML: https://mlsanity.com/paper/2308.09467/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 58 references that are in the map.
- First posted on arXiv 18 Aug 2023.

## Builds on (most cited first, 10 of 10)

- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Quantitative Susceptibility Mapping using Deep Neural Network: QSMnet](https://mlsanity.com/paper/1803.05627/) (2018)
- [Fidelity Imposed Network Edit (FINE) for Solving Ill-Posed Image Reconstruction](https://mlsanity.com/paper/1905.07284/) (2019)
- [Exploring linearity of deep neural network trained QSM: QSMnet+](https://mlsanity.com/paper/1909.07716/) (2019)
- [QSMGAN: Improved Quantitative Susceptibility Mapping using 3D Generative Adversarial Networks with Increased Receptive Field](https://mlsanity.com/paper/1905.03356/) (2019)
- [Learned Proximal Networks for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2008.05024/) (2020)
- [MoDL-QSM: Model-based Deep Learning for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2101.08413/) (2021)
- [Instant tissue field and magnetic susceptibility mapping from MR raw phase using Laplacian enabled deep neural networks](https://mlsanity.com/paper/2111.07665/) (2021)
- [Affine Transformation Edited and Refined Deep Neural Network for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2211.13942/) (2022)
- [Meta-QSM: An Image-Resolution-Arbitrary Network for QSM Reconstruction](https://mlsanity.com/paper/1908.00206/) (2019)

## Built on by (most cited first, 4 of 4)

- [A Learnable Prior Improves Inverse Tumor Growth Modeling](https://mlsanity.com/paper/2403.04500/) (2024)
- [IR2QSM: Quantitative Susceptibility Mapping via Deep Neural Networks with Iterative Reverse Concatenations and Recurrent Modules](https://mlsanity.com/paper/2406.12300/) (2024)
- [Chemical Shift Encoding based Double Bonds Quantification in Triglycerides using Deep Image Prior](https://mlsanity.com/paper/2407.01926/) (2024)
- [Self-supervised physics-informed generative networks for phase retrieval from a single X-ray hologram](https://mlsanity.com/paper/2508.15530/) (2025)

## Abstract (arXiv)

The data-driven approach of supervised learning methods has limited applicability in solving dipole inversion in Quantitative Susceptibility Mapping (QSM) with varying scan parameters across different objects. To address this generalization issue in supervised QSM methods, we propose a novel training-free model-based unsupervised method called MoDIP (Model-based Deep Image Prior). MoDIP comprises a small, untrained network and a Data Fidelity Optimization (DFO) module. The network converges to an interim state, acting as an implicit prior for image regularization, while the optimization process enforces the physical model of QSM dipole inversion. Experimental results demonstrate MoDIP's excellent generalizability in solving QSM dipole inversion across different scan parameters. It exhibits robustness against pathological brain QSM, achieving over 32% accuracy improvement than supervised deep learning and traditional iterative methods. It is also 33% more computationally efficient and runs 4 times faster than conventional DIP-based approaches, enabling 3D high-resolution image reconstruction in under 4.5 minutes.