# Deep Generalization of Structured Low-Rank Algorithms (Deep-SLR)

arXiv: https://arxiv.org/abs/1912.03433 · HTML: https://mlsanity.com/paper/1912.03433/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2019.

## Built on by (most cited first, 30 of 30)

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- [One for Multiple: Physics-informed Synthetic Data Boosts Generalizable Deep Learning for Fast MRI Reconstruction](https://mlsanity.com/paper/2307.13220/) (2023)
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- [Deep Algorithm Unrolling for Biomedical Imaging](https://mlsanity.com/paper/2108.06637/) (2021)
- [Equilibrated Zeroth-Order Unrolled Deep Networks for Accelerated MRI](https://mlsanity.com/paper/2112.09891/) (2021)
- [A Faithful Deep Sensitivity Estimation for Accelerated Magnetic Resonance Imaging](https://mlsanity.com/paper/2210.12723/) (2022)
- [Deep unfolding as iterative regularization for imaging inverse problems](https://mlsanity.com/paper/2211.13452/) (2022)
- [CL-MRI: Self-Supervised Contrastive Learning to Improve the Accuracy of Undersampled MRI Reconstruction](https://mlsanity.com/paper/2306.00530/) (2023)
- [Matrix Completion-Informed Deep Unfolded Equilibrium Models for Self-Supervised k-Space Interpolation in MRI](https://mlsanity.com/paper/2309.13571/) (2023)
- [Deep Separable Spatiotemporal Learning for Fast Dynamic Cardiac MRI](https://mlsanity.com/paper/2402.15939/) (2024)
- [DP-MDM: Detail-Preserving MR Reconstruction via Multiple Diffusion Models](https://mlsanity.com/paper/2405.05763/) (2024)
- [Adapting model-based deep learning to multiple acquisition conditions: Ada-MoDL](https://mlsanity.com/paper/2304.11238/) (2023)
- [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024)
- [Image Reconstruction for Accelerated MR Scan with Faster Fourier Convolutional Neural Networks](https://mlsanity.com/paper/2306.02886/) (2023)
- [Physics-Informed DeepMRI: Bridging the Gap from Heat Diffusion to k-Space Interpolation](https://mlsanity.com/paper/2308.15918/) (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)
- [Reconstruction and Segmentation of Parallel MR Data using Image Domain DEEP-SLR](https://mlsanity.com/paper/2102.01172/) (2021)
- [Joint Calibrationless Reconstruction and Segmentation of Parallel MRI](https://mlsanity.com/paper/2105.09220/) (2021)
- [K-UNN: k-Space Interpolation With Untrained Neural Network](https://mlsanity.com/paper/2208.05827/) (2022)
- [K-space Diffusion Model Based MR Reconstruction Method for Simultaneous Multislice Imaging](https://mlsanity.com/paper/2501.03293/) (2025)
- [PS-Net: Learned Partially Separable Model for Dynamic MR Imaging](https://mlsanity.com/paper/2205.04073/) (2022)
- [Edge-weighted pFISTA-Net for MRI Reconstruction](https://mlsanity.com/paper/2302.07468/) (2023)
- [Efficient MRI Parallel Imaging Reconstruction by K-Space Rendering via Generalized Implicit Neural Representation](https://mlsanity.com/paper/2309.06067/) (2023)
- [Towards Globally Predictable k-Space Interpolation: A White-box Transformer Approach](https://mlsanity.com/paper/2508.04051/) (2025)
- [Low-Rank Velocity Fields as a Structural Prior for Unsupervised 4D Medical Image Interpolation](https://mlsanity.com/paper/2608.24025/) (2026)
- [Hankel Subspace Self-Supervised Learning for Parallel MRI Reconstruction](https://mlsanity.com/paper/2610.11560/) (2026)

## Abstract (arXiv)

Structured low-rank (SLR) algorithms, which exploit annihilation relations between the Fourier samples of a signal resulting from different properties, is a powerful image reconstruction framework in several applications. This scheme relies on low-rank matrix completion to estimate the annihilation relations from the measurements. The main challenge with this strategy is the high computational complexity of matrix completion. We introduce a deep learning (DL) approach to significantly reduce the computational complexity. Specifically, we use a convolutional neural network (CNN)-based filterbank that is trained to estimate the annihilation relations from imperfect (under-sampled and noisy) k-space measurements of Magnetic Resonance Imaging (MRI). The main reason for the computational efficiency is the pre-learning of the parameters of the non-linear CNN from exemplar data, compared to SLR schemes that learn the linear filterbank parameters from the dataset itself. Experimental comparisons show that the proposed scheme can enable calibration-less parallel MRI; it can offer performance similar to SLR schemes while reducing the runtime by around three orders of magnitude. Unlike pre-calibrated and self-calibrated approaches, the proposed uncalibrated approach is insensitive to motion errors and affords higher acceleration. The proposed scheme also incorporates image domain priors that are complementary, thus significantly improving the performance over that of SLR schemes.