# WKGM: Weight-K-space Generative Model for Parallel Imaging Reconstruction

arXiv: https://arxiv.org/abs/2205.03883 · HTML: https://mlsanity.com/paper/2205.03883/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 43 references that are in the map.
- First posted on arXiv 8 May 2022.

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (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)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstruction](https://mlsanity.com/paper/2203.03623/) (2022)
- [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)
- [MRI Reconstruction Using Deep Bayesian Estimation](https://mlsanity.com/paper/1909.01127/) (2019)
- [LORAKI: Autocalibrated Recurrent Neural Networks for Autoregressive MRI Reconstruction in k-Space](https://mlsanity.com/paper/1904.09390/) (2019)
- [Compressible Latent-Space Invertible Networks for Generative Model-Constrained Image Reconstruction](https://mlsanity.com/paper/2007.02462/) (2020)
- [Homotopic Gradients of Generative Density Priors for MR Image Reconstruction](https://mlsanity.com/paper/2008.06284/) (2020)
- [IFR-Net: Iterative Feature Refinement Network for Compressed Sensing MRI](https://mlsanity.com/paper/1909.10856/) (2019)
- [Highly Scalable Image Reconstruction using Deep Neural Networks with Bandpass Filtering](https://mlsanity.com/paper/1805.03300/) (2018)

## Built on by (most cited first, 8 of 8)

- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [High-Frequency Space Diffusion Models for Accelerated MRI](https://mlsanity.com/paper/2208.05481/) (2022)
- [Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstruction](https://mlsanity.com/paper/2309.00853/) (2023)
- [A Survey of Emerging Applications of Diffusion Probabilistic Models in MRI](https://mlsanity.com/paper/2311.11383/) (2023)
- [Physics-Informed DeepMRI: Bridging the Gap from Heat Diffusion to k-Space Interpolation](https://mlsanity.com/paper/2308.15918/) (2023)
- [Sub-DM:Subspace Diffusion Model with Orthogonal Decomposition for MRI Reconstruction](https://mlsanity.com/paper/2411.03758/) (2024)
- [Adaptive Mask-guided K-space Diffusion for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2506.18270/) (2025)
- [High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstruction](https://mlsanity.com/paper/2607.01176/) (2026)

## Abstract (arXiv)

Deep learning based parallel imaging (PI) has made great progresses in recent years to accelerate magnetic resonance imaging (MRI). Nevertheless, it still has some limitations, such as the robustness and flexibility of existing methods have great deficiency. In this work, we propose a method to explore the k-space domain learning via robust generative modeling for flexible calibration-less PI reconstruction, coined weight-k-space generative model (WKGM). Specifically, WKGM is a generalized k-space domain model, where the k-space weighting technology and high-dimensional space augmentation design are efficiently incorporated for score-based generative model training, resulting in good and robust reconstructions. In addition, WKGM is flexible and thus can be synergistically combined with various traditional k-space PI models, which can make full use of the correlation between multi-coil data and realizecalibration-less PI. Even though our model was trained on only 500 images, experimental results with varying sampling patterns and acceleration factors demonstrate that WKGM can attain state-of-the-art reconstruction results with the well-learned k-space generative prior.