# Physics-Informed DeepMRI: Bridging the Gap from Heat Diffusion to k-Space Interpolation

arXiv: https://arxiv.org/abs/2308.15918 · HTML: https://mlsanity.com/paper/2308.15918/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 30 Aug 2023.

## Builds on (most cited first, 13 of 13)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Deep Generalization of Structured Low-Rank Algorithms (Deep-SLR)](https://mlsanity.com/paper/1912.03433/) (2019)
- [Structured Low-Rank Algorithms: Theory, MR Applications, and Links to Machine Learning](https://mlsanity.com/paper/1910.12162/) (2019)
- [WKGM: Weight-K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2205.03883/) (2022)
- [Linear Predictability in MRI Reconstruction: Leveraging Shift-Invariant Fourier Structure for Faster and Better Imaging](https://mlsanity.com/paper/1903.03141/) (2019)
- [A Nonconvex Nonsmooth Regularization Method for Compressed Sensing and Low-Rank Matrix Completion](https://mlsanity.com/paper/1605.00479/) (2016)

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

- [A Multi-scale Generalized Shrinkage Threshold Network for Image Blind Deblurring in Remote Sensing](https://mlsanity.com/paper/2309.07524/) (2023)
- [K-space Diffusion Model Based MR Reconstruction Method for Simultaneous Multislice Imaging](https://mlsanity.com/paper/2501.03293/) (2025)

## Abstract (arXiv)

In the field of parallel imaging (PI), alongside image-domain regularization methods, substantial research has been dedicated to exploring k-space interpolation. However, the interpretability of these methods remains an unresolved issue. Furthermore, these approaches currently face acceleration limitations that are comparable to those experienced by image-domain methods. In order to enhance interpretability and overcome the acceleration limitations, this paper introduces an interpretable framework that unifies both k-space interpolation techniques and image-domain methods, grounded in the physical principles of heat diffusion equations. Building upon this foundational framework, a novel k-space interpolation method is proposed. Specifically, we model the process of high-frequency information attenuation in k-space as a heat diffusion equation, while the effort to reconstruct high-frequency information from low-frequency regions can be conceptualized as a reverse heat equation. However, solving the reverse heat equation poses a challenging inverse problem. To tackle this challenge, we modify the heat equation to align with the principles of magnetic resonance PI physics and employ the score-based generative method to precisely execute the modified reverse heat diffusion. Finally, experimental validation conducted on publicly available datasets demonstrates the superiority of the proposed approach over traditional k-space interpolation methods, deep learning-based k-space interpolation methods, and conventional diffusion models in terms of reconstruction accuracy, particularly in high-frequency regions.