# Accelerated MRI Reconstruction with Separable and Enhanced Low-Rank Hankel Regularization

arXiv: https://arxiv.org/abs/2107.11650 · HTML: https://mlsanity.com/paper/2107.11650/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2021.

## Built on by (most cited first, 18 of 18)

- [One-dimensional Deep Low-rank and Sparse Network for Accelerated MRI](https://mlsanity.com/paper/2112.04721/) (2021)
- [IMJENSE: Scan-specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI](https://mlsanity.com/paper/2311.12892/) (2023)
- [One for Multiple: Physics-informed Synthetic Data Boosts Generalizable Deep Learning for Fast MRI Reconstruction](https://mlsanity.com/paper/2307.13220/) (2023)
- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [A Faithful Deep Sensitivity Estimation for Accelerated Magnetic Resonance Imaging](https://mlsanity.com/paper/2210.12723/) (2022)
- [Deep Separable Spatiotemporal Learning for Fast Dynamic Cardiac MRI](https://mlsanity.com/paper/2402.15939/) (2024)
- [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024)
- [Cloud-Magnetic Resonance Imaging System: In the Era of 6G and Artificial Intelligence](https://mlsanity.com/paper/2310.11641/) (2023)
- [MCU-Net: A Multi-prior Collaborative Deep Unfolding Network with Gates-controlled Spatial Attention for Accelerated MR Image Reconstruction](https://mlsanity.com/paper/2402.03383/) (2024)
- [Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2212.05503/) (2022)
- [A Dynamics Theory of Implicit Regularization in Deep Low-Rank Matrix Factorization](https://mlsanity.com/paper/2212.14150/) (2022)
- [AliasNet: Alias Artefact Suppression Network for Accelerated Phase-Encode MRI](https://mlsanity.com/paper/2302.08861/) (2023)
- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [Multi-Weight Respecification of Scan-specific Learning for Parallel Imaging](https://mlsanity.com/paper/2204.01979/) (2022)
- [Convex Dual Theory Analysis of Two-Layer Convolutional Neural Networks with Soft-Thresholding](https://mlsanity.com/paper/2304.06959/) (2023)
- [A plug-and-play synthetic data deep learning for undersampled magnetic resonance image reconstruction](https://mlsanity.com/paper/2309.06681/) (2023)
- [PhyMRI-SR: Toward Physics-Aware MRI Image Super-Resolution](https://mlsanity.com/paper/2607.06238/) (2026)
- [Hankel Subspace Self-Supervised Learning for Parallel MRI Reconstruction](https://mlsanity.com/paper/2610.11560/) (2026)

## Abstract (arXiv)

The combination of the sparse sampling and the low-rank structured matrix reconstruction has shown promising performance, enabling a significant reduction of the magnetic resonance imaging data acquisition time. However, the low-rank structured approaches demand considerable memory consumption and are time-consuming due to a noticeable number of matrix operations performed on the huge-size block Hankel-like matrix. In this work, we proposed a novel framework to utilize the low-rank property but meanwhile to achieve faster reconstructions and promising results. The framework allows us to enforce the low-rankness of Hankel matrices constructing from 1D vectors instead of 2D matrices from 1D vectors and thus avoid the construction of huge block Hankel matrix for 2D k-space matrices. Moreover, under this framework, we can easily incorporate other information, such as the smooth phase of the image and the low-rankness in the parameter dimension, to further improve the image quality. We built and validated two models for parallel and parameter magnetic resonance imaging experiments, respectively. Our retrospective in-vivo results indicate that the proposed approaches enable faster reconstructions than the state-of-the-art approaches, e.g., about 8x faster than STDLRSPIRiT, and faithful removal of undersampling artifacts.