# Deep Geometric Distillation Network for Compressive Sensing MRI

arXiv: https://arxiv.org/abs/2107.04943 · HTML: https://mlsanity.com/paper/2107.04943/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 18 references that are in the map.
- First posted on arXiv 11 Jul 2021.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)

## Built on by (most cited first, 6 of 6)

- [An Interpretable MRI Reconstruction Network with Two-grid-cycle Correction and Geometric Prior Distillation](https://mlsanity.com/paper/2205.07062/) (2022)
- [Nest-DGIL: Nesterov-optimized Deep Geometric Incremental Learning for CS Image Reconstruction](https://mlsanity.com/paper/2308.03807/) (2023)
- [PRISTA-Net: Deep Iterative Shrinkage Thresholding Network for Coded Diffraction Patterns Phase Retrieval](https://mlsanity.com/paper/2309.04171/) (2023)
- [A Progressive Image Restoration Network for High-order Degradation Imaging in Remote Sensing](https://mlsanity.com/paper/2412.07195/) (2024)
- [A Multi-scale Generalized Shrinkage Threshold Network for Image Blind Deblurring in Remote Sensing](https://mlsanity.com/paper/2309.07524/) (2023)
- [MVMS-RCN: A Dual-Domain Unfolding CT Reconstruction with Multi-sparse-view and Multi-scale Refinement-correction](https://mlsanity.com/paper/2405.17141/) (2024)

## Abstract (arXiv)

Compressed sensing (CS) is an efficient method to reconstruct MR image from small sampled data in k-space and accelerate the acquisition of MRI. In this work, we propose a novel deep geometric distillation network which combines the merits of model-based and deep learning-based CS-MRI methods, it can be theoretically guaranteed to improve geometric texture details of a linear reconstruction. Firstly, we unfold the model-based CS-MRI optimization problem into two sub-problems that consist of image linear approximation and image geometric compensation. Secondly, geometric compensation sub-problem for distilling lost texture details in approximation stage can be expanded by Taylor expansion to design a geometric distillation module fusing features of different geometric characteristic domains. Additionally, we use a learnable version with adaptive initialization of the step-length parameter, which allows model more flexibility that can lead to convergent smoothly. Numerical experiments verify its superiority over other state-of-the-art CS-MRI reconstruction approaches. The source code will be available at urlhttps://github.com/fanxiaohong/Deep-Geometric-Distillation-Network-for-CS-MRI