# Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging

arXiv: https://arxiv.org/abs/2203.12215 · HTML: https://mlsanity.com/paper/2203.12215/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 111 references that are in the map.
- First posted on arXiv 23 Mar 2022.

## Builds on (most cited first, 30 of 49)

- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [Plug and play methods for magnetic resonance imaging (long version)](https://mlsanity.com/paper/1903.08616/) (2019)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Advancing machine learning for MR image reconstruction with an open competition: Overview of the 2019 fastMRI challenge](https://mlsanity.com/paper/2001.02518/) (2020)
- [Zero-Shot Self-Supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2102.07737/) (2021)
- [Uncertainty Quantification in Deep MRI Reconstruction](https://mlsanity.com/paper/1901.11228/) (2019)
- [Neural Proximal Gradient Descent for Compressive Imaging](https://mlsanity.com/paper/1806.03963/) (2018)
- [GrappaNet: Combining Parallel Imaging with Deep Learning for Multi-Coil MRI Reconstruction](https://mlsanity.com/paper/1910.12325/) (2019)
- [MR image reconstruction using deep density priors](https://mlsanity.com/paper/1711.11386/) (2017)
- [VS-Net: Variable splitting network for accelerated parallel MRI reconstruction](https://mlsanity.com/paper/1907.10033/) (2019)
- [Better than Real: Complex-valued Neural Nets for MRI Fingerprinting](https://mlsanity.com/paper/1707.00070/) (2017)
- [Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction](https://mlsanity.com/paper/2102.06665/) (2021)
- [B-spline Parameterized Joint Optimization of Reconstruction and K-space Trajectories (BJORK) for Accelerated 2D MRI](https://mlsanity.com/paper/2101.11369/) (2021)
- [Unpaired Deep Learning for Accelerated MRI using Optimal Transport Driven CycleGAN](https://mlsanity.com/paper/2008.12967/) (2020)
- [High-level Prior-based Loss Functions for Medical Image Segmentation: A Survey](https://mlsanity.com/paper/2011.08018/) (2020)
- [SHINE: SHaring the INverse Estimate from the forward pass for bi-level optimization and implicit models](https://mlsanity.com/paper/2106.00553/) (2021)

## Built on by (most cited first, 30 of 50)

- [A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noise](https://mlsanity.com/paper/2205.10278/) (2022)
- [MambaMIR: An Arbitrary-Masked Mamba for Joint Medical Image Reconstruction and Uncertainty Estimation](https://mlsanity.com/paper/2402.18451/) (2024)
- [Deep Learning for Retrospective Motion Correction in MRI: A Comprehensive Review](https://mlsanity.com/paper/2305.06739/) (2023)
- [One for Multiple: Physics-informed Synthetic Data Boosts Generalizable Deep Learning for Fast MRI Reconstruction](https://mlsanity.com/paper/2307.13220/) (2023)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [Zero-Shot Adaptation for Approximate Posterior Sampling of Diffusion Models in Inverse Problems](https://mlsanity.com/paper/2407.11288/) (2024)
- [Unsupervised reconstruction of accelerated cardiac cine MRI using Neural Fields](https://mlsanity.com/paper/2307.14363/) (2023)
- [Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Prediction](https://mlsanity.com/paper/2405.18527/) (2024)
- [Physics-Driven Autoregressive State Space Models for Medical Image Reconstruction](https://mlsanity.com/paper/2412.09331/) (2024)
- [PINQI: An End-to-End Physics-Informed Approach to Learned Quantitative MRI Reconstruction](https://mlsanity.com/paper/2306.11023/) (2023)
- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [K-band: Self-supervised MRI Reconstruction via Stochastic Gradient Descent over K-space Subsets](https://mlsanity.com/paper/2308.02958/) (2023)
- [PnP-CM: Consistency Models as Plug-and-Play Priors for Inverse Problems](https://mlsanity.com/paper/2509.22736/) (2025)
- [Robust Physics-based Deep MRI Reconstruction Via Diffusion Purification](https://mlsanity.com/paper/2309.05794/) (2023)
- [PISCO: Self-Supervised k-Space Regularization for Improved Neural Implicit k-Space Representations of Dynamic MRI](https://mlsanity.com/paper/2501.09403/) (2025)
- [Cardiac Digital Twins at Scale from MRI: Open Tools and Representative Models from ~55000 UK Biobank Participants](https://mlsanity.com/paper/2505.21019/) (2025)
- [Adapting model-based deep learning to multiple acquisition conditions: Ada-MoDL](https://mlsanity.com/paper/2304.11238/) (2023)
- [Deep learning of personalized priors from past MRI scans enables fast, quality-enhanced point-of-care MRI with low-cost systems](https://mlsanity.com/paper/2505.02470/) (2025)
- [Denoising Generalized Expectation-Consistent Approximation for MR Image Recovery](https://mlsanity.com/paper/2206.05049/) (2022)
- [Uncertainty Estimation and Out-of-Distribution Detection for Deep Learning-Based Image Reconstruction using the Local Lipschitz](https://mlsanity.com/paper/2305.07618/) (2023)
- [Non-Cartesian Self-Supervised Physics-Driven Deep Learning Reconstruction for Highly-Accelerated Multi-Echo Spiral fMRI](https://mlsanity.com/paper/2312.05707/) (2023)
- [Self-Supervised k-Space Regularization for Motion-Resolved Abdominal MRI Using Neural Implicit k-Space Representation](https://mlsanity.com/paper/2404.08350/) (2024)
- [Point Neuron Learning: A New Physics-Informed Neural Network Architecture](https://mlsanity.com/paper/2408.16969/) (2024)
- [Fast MRI for All: Bridging Access Gaps by Training without Raw Data](https://mlsanity.com/paper/2411.13022/) (2024)
- [An unsupervised method for MRI recovery: Deep image prior with structured sparsity](https://mlsanity.com/paper/2501.01482/) (2025)
- [Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems](https://mlsanity.com/paper/2505.09528/) (2025)
- [Automated Tuning for Diffusion Inverse Problem Solvers without Generative Prior Retraining](https://mlsanity.com/paper/2509.09880/) (2025)
- [Time-Embedded Algorithm Unrolling for Computational MRI](https://mlsanity.com/paper/2510.16321/) (2025)
- [Continuous K-space Recovery Network with Image Guidance for Fast MRI Reconstruction](https://mlsanity.com/paper/2411.11282/) (2024)
- [Rational Gaussian wavelets and corresponding model driven neural networks](https://mlsanity.com/paper/2502.01282/) (2025)

## Abstract (arXiv)

Physics-driven deep learning methods have emerged as a powerful tool for computational magnetic resonance imaging (MRI) problems, pushing reconstruction performance to new limits. This article provides an overview of the recent developments in incorporating physics information into learning-based MRI reconstruction. We consider inverse problems with both linear and non-linear forward models for computational MRI, and review the classical approaches for solving these. We then focus on physics-driven deep learning approaches, covering physics-driven loss functions, plug-and-play methods, generative models, and unrolled networks. We highlight domain-specific challenges such as real- and complex-valued building blocks of neural networks, and translational applications in MRI with linear and non-linear forward models. Finally, we discuss common issues and open challenges, and draw connections to the importance of physics-driven learning when combined with other downstream tasks in the medical imaging pipeline.