# PINQI: An End-to-End Physics-Informed Approach to Learned Quantitative MRI Reconstruction

arXiv: https://arxiv.org/abs/2306.11023 · HTML: https://mlsanity.com/paper/2306.11023/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 72 references that are in the map.
- First posted on arXiv 19 Jun 2023.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Bag of Tricks for Image Classification with Convolutional Neural Networks](https://mlsanity.com/paper/1812.01187/) (2018)
- [Learning Spatio-Temporal Representation with Pseudo-3D Residual Networks](https://mlsanity.com/paper/1711.10305/) (2017)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization](https://mlsanity.com/paper/1607.05447/) (2016)
- [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017)
- [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Training Deeper Convolutional Networks with Deep Supervision](https://mlsanity.com/paper/1505.02496/) (2015)
- [MR fingerprinting Deep RecOnstruction NEtwork (DRONE)](https://mlsanity.com/paper/1710.05267/) (2017)
- [Model Adaptation for Inverse Problems in Imaging](https://mlsanity.com/paper/2012.00139/) (2020)
- [Taking a Deeper Look at the Inverse Compositional Algorithm](https://mlsanity.com/paper/1812.06861/) (2018)
- [An End-To-End-Trainable Iterative Network Architecture for Accelerated Radial Multi-Coil 2D Cine MR Image Reconstruction](https://mlsanity.com/paper/2102.00783/) (2021)
- [CoRRECT: A Deep Unfolding Framework for Motion-Corrected Quantitative R2* Mapping](https://mlsanity.com/paper/2210.06330/) (2022)
- [SSL-QALAS: Self-Supervised Learning for Rapid Multiparameter Estimation in Quantitative MRI Using 3D-QALAS](https://mlsanity.com/paper/2302.14240/) (2023)
- [Cram'er-Rao bound-informed training of neural networks for quantitative MRI](https://mlsanity.com/paper/2109.10535/) (2021)
- [Deep Unrolling for Magnetic Resonance Fingerprinting](https://mlsanity.com/paper/2201.09375/) (2022)

## Built on by (most cited first, 7 of 7)

- [PINNs for Medical Image Analysis: A Survey](https://mlsanity.com/paper/2408.01026/) (2024)
- [MRpro: open framework for model-based, learned, and quantitative MR imaging](https://mlsanity.com/paper/2507.23129/) (2025)
- [NoSENSE: Learned unrolled cardiac MRI reconstruction without explicit sensitivity maps](https://mlsanity.com/paper/2309.15608/) (2023)
- [PINNing Cerebral Blood Flow: Analysis of Perfusion MRI in Infants using Physics-Informed Neural Networks](https://mlsanity.com/paper/2410.19759/) (2024)
- [Low-Rank Augmented Implicit Neural Representation for Unsupervised High-Dimensional Quantitative MRI Reconstruction](https://mlsanity.com/paper/2506.09100/) (2025)
- [DA-UCT: Self-Supervised Domain-Adaptive Ultrasound Computed Tomography for Rapid Musculoskeletal Sound Speed Reconstruction](https://mlsanity.com/paper/2605.25024/) (2026)
- [CUPA-T2*: Covariance-Aware Uncertainty Propagation and Alignment for T2* Mapping in Accelerated MRI](https://mlsanity.com/paper/2608.08693/) (2026)

## Abstract (arXiv)

Quantitative Magnetic Resonance Imaging (qMRI) enables the reproducible measurement of biophysical parameters in tissue. The challenge lies in solving a nonlinear, ill-posed inverse problem to obtain the desired tissue parameter maps from acquired raw data. While various learned and non-learned approaches have been proposed, the existing learned methods fail to fully exploit the prior knowledge about the underlying MR physics, i.e. the signal model and the acquisition model. In this paper, we propose PINQI, a novel qMRI reconstruction method that integrates the knowledge about the signal, acquisition model, and learned regularization into a single end-to-end trainable neural network. Our approach is based on unrolled alternating optimization, utilizing differentiable optimization blocks to solve inner linear and non-linear optimization tasks, as well as convolutional layers for regularization of the intermediate qualitative images and parameter maps. This design enables PINQI to leverage the advantages of both the signal model and learned regularization. We evaluate the performance of our proposed network by comparing it with recently published approaches in the context of highly undersampled T1-mapping, using both a simulated brain dataset, as well as real scanner data acquired from a physical phantom and in-vivo data from healthy volunteers. The results demonstrate the superiority of our proposed solution over existing methods and highlight the effectiveness of our method in real-world scenarios.