# Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction

arXiv: https://arxiv.org/abs/2212.05503 · HTML: https://mlsanity.com/paper/2212.05503/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 11 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstruction](https://mlsanity.com/paper/2203.03623/) (2022)
- [MRI Reconstruction Using Deep Bayesian Estimation](https://mlsanity.com/paper/1909.01127/) (2019)
- [ADMM-Net: A Deep Learning Approach for Compressive Sensing MRI](https://mlsanity.com/paper/1705.06869/) (2017)
- [One-dimensional Deep Low-rank and Sparse Network for Accelerated MRI](https://mlsanity.com/paper/2112.04721/) (2021)
- [Accelerated MRI Reconstruction with Separable and Enhanced Low-Rank Hankel Regularization](https://mlsanity.com/paper/2107.11650/) (2021)
- [SDnDTI: Self-supervised deep learning-based denoising for diffusion tensor MRI](https://mlsanity.com/paper/2111.07220/) (2021)
- [Homotopic Gradients of Generative Density Priors for MR Image Reconstruction](https://mlsanity.com/paper/2008.06284/) (2020)
- [Image Reconstruction with Low-rankness and Self-consistency of k-space Data in Parallel MRI](https://mlsanity.com/paper/1909.02846/) (2019)
- [IFR-Net: Iterative Feature Refinement Network for Compressed Sensing MRI](https://mlsanity.com/paper/1909.10856/) (2019)
- [A Generative Word Embedding Model and its Low Rank Positive Semidefinite Solution](https://mlsanity.com/paper/1508.03826/) (2015)
- [High-dimensional Assisted Generative Model for Color Image Restoration](https://mlsanity.com/paper/2108.06460/) (2021)

## Built on by (most cited first, 1 of 1)

- [Adaptive Mask-guided K-space Diffusion for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2506.18270/) (2025)

## Abstract (arXiv)

Although recent deep learning methods, especially generative models, have shown good performance in fast magnetic resonance imaging, there is still much room for improvement in high-dimensional generation. Considering that internal dimensions in score-based generative models have a critical impact on estimating the gradient of the data distribution, we present a new idea, low-rank tensor assisted k-space generative model (LR-KGM), for parallel imaging reconstruction. This means that we transform original prior information into high-dimensional prior information for learning. More specifically, the multi-channel data is constructed into a large Hankel matrix and the matrix is subsequently folded into tensor for prior learning. In the testing phase, the low-rank rotation strategy is utilized to impose low-rank constraints on tensor output of the generative network. Furthermore, we alternately use traditional generative iterations and low-rank high-dimensional tensor iterations for reconstruction. Experimental comparisons with the state-of-the-arts demonstrated that the proposed LR-KGM method achieved better performance.