# Homotopic Gradients of Generative Density Priors for MR Image Reconstruction

arXiv: https://arxiv.org/abs/2008.06284 · HTML: https://mlsanity.com/paper/2008.06284/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2020.

## Built on by (most cited first, 14 of 14)

- [ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformer](https://mlsanity.com/paper/2201.09376/) (2022)
- [Generative Modeling in Sinogram Domain for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2211.13926/) (2022)
- [Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstruction](https://mlsanity.com/paper/2309.00853/) (2023)
- [One-shot Generative Prior in Hankel-k-space for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2208.07181/) (2022)
- [Wavelet Transform-assisted Adaptive Generative Modeling for Colorization](https://mlsanity.com/paper/2107.04261/) (2021)
- [WKGM: Weight-K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2205.03883/) (2022)
- [K-space and Image Domain Collaborative Energy based Model for Parallel MRI Reconstruction](https://mlsanity.com/paper/2203.10776/) (2022)
- [DP-MDM: Detail-Preserving MR Reconstruction via Multiple Diffusion Models](https://mlsanity.com/paper/2405.05763/) (2024)
- [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024)
- [Universal Generative Modeling for Calibration-free Parallel Mr Imaging](https://mlsanity.com/paper/2201.10210/) (2022)
- [High-dimensional Assisted Generative Model for Color Image Restoration](https://mlsanity.com/paper/2108.06460/) (2021)
- [Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2212.05503/) (2022)
- [Multi-Weight Respecification of Scan-specific Learning for Parallel Imaging](https://mlsanity.com/paper/2204.01979/) (2022)
- [Diffusion-Assisted Frequency Attention Model for Whole-body Low-field MRI Reconstruction](https://mlsanity.com/paper/2507.17764/) (2025)

## Abstract (arXiv)

Deep learning, particularly the generative model, has demonstrated tremendous potential to significantly speed up image reconstruction with reduced measurements recently. Rather than the existing generative models that often optimize the density priors, in this work, by taking advantage of the denoising score matching, homotopic gradients of generative density priors (HGGDP) are proposed for magnetic resonance imaging (MRI) reconstruction. More precisely, to tackle the low-dimensional manifold and low data density region issues in generative density prior, we estimate the target gradients in higher-dimensional space. We train a more powerful noise conditional score network by forming high-dimensional tensor as the network input at the training phase. More artificial noise is also injected in the embedding space. At the reconstruction stage, a homotopy method is employed to pursue the density prior, such as to boost the reconstruction performance. Experiment results imply the remarkable performance of HGGDP in terms of high reconstruction accuracy; only 10% of the k-space data can still generate images of high quality as effectively as standard MRI reconstruction with the fully sampled data.