# T2LR-Net: An unrolling network learning transformed tensor low-rank prior for dynamic MR image reconstruction

arXiv: https://arxiv.org/abs/2209.03832 · HTML: https://mlsanity.com/paper/2209.03832/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 55 references that are in the map.
- First posted on arXiv 8 Sep 2022.

## Builds on (most cited first, 10 of 10)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [OCMR (v1.0)--Open-Access Multi-Coil k-Space Dataset for Cardiovascular Magnetic Resonance Imaging](https://mlsanity.com/paper/2008.03410/) (2020)
- [Deep Low-rank plus Sparse Network for Dynamic MR Imaging](https://mlsanity.com/paper/2010.13677/) (2020)
- [Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2105.14320/) (2021)
- [A New Convex Relaxation for Tensor Completion](https://mlsanity.com/paper/1307.4653/) (2013)

## Built on by (most cited first, 4 of 4)

- [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)
- [JotlasNet: Joint Tensor Low-Rank and Attention-based Sparse Unrolling Network for Accelerating Dynamic MRI](https://mlsanity.com/paper/2502.11749/) (2025)
- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [USCTNet: A deep unfolding nuclear-norm optimization solver for physically consistent HSI reconstruction](https://mlsanity.com/paper/2509.10651/) (2025)

## Abstract (arXiv)

The tensor low-rank prior has attracted considerable attention in dynamic MR reconstruction. Tensor low-rank methods preserve the inherent high-dimensional structure of data, allowing for improved extraction and utilization of intrinsic low-rank characteristics. However, most current methods are still confined to utilizing low-rank structures either in the image domain or predefined transformed domains. Designing an optimal transformation adaptable to dynamic MRI reconstruction through manual efforts is inherently challenging. In this paper, we propose a deep unrolling network that utilizes the convolutional neural network (CNN) to adaptively learn the transformed domain for leveraging tensor low-rank priors. Under the supervised mechanism, the learning of the tensor low-rank domain is directly guided by the reconstruction accuracy. Specifically, we generalize the traditional t-SVD to a transformed version based on arbitrary high-dimensional unitary transformations and introduce a novel unitary transformed tensor nuclear norm (UTNN). Subsequently, we present a dynamic MRI reconstruction model based on UTNN and devise an efficient iterative optimization algorithm using ADMM, which is finally unfolded into the proposed T2LR-Net. Experiments on two dynamic cardiac MRI datasets demonstrate that T2LR-Net outperforms the state-of-the-art optimization-based and unrolling network-based methods.