# Accelerated MRI With Deep Linear Convolutional Transform Learning

arXiv: https://arxiv.org/abs/2204.07923 · HTML: https://mlsanity.com/paper/2204.07923/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 17 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Blind Super-Resolution Kernel Estimation using an Internal-GAN](https://mlsanity.com/paper/1909.06581/) (2019)
- [Adversarial and Perceptual Refinement for Compressed Sensing MRI Reconstruction](https://mlsanity.com/paper/1806.11216/) (2018)
- [Convolutional Analysis Operator Learning: Acceleration and Convergence](https://mlsanity.com/paper/1802.05584/) (2018)
- [Transform Learning for Magnetic Resonance Image Reconstruction: From Model-based Learning to Building Neural Networks](https://mlsanity.com/paper/1903.11431/) (2019)
- [FRIST - Flipping and Rotation Invariant Sparsifying Transform Learning and Applications](https://mlsanity.com/paper/1511.06359/) (2015)

## Abstract (arXiv)

Recent studies show that deep learning (DL) based MRI reconstruction outperforms conventional methods, such as parallel imaging and compressed sensing (CS), in multiple applications. Unlike CS that is typically implemented with pre-determined linear representations for regularization, DL inherently uses a non-linear representation learned from a large database. Another line of work uses transform learning (TL) to bridge the gap between these two approaches by learning linear representations from data. In this work, we combine ideas from CS, TL and DL reconstructions to learn deep linear convolutional transforms as part of an algorithm unrolling approach. Using end-to-end training, our results show that the proposed technique can reconstruct MR images to a level comparable to DL methods, while supporting uniform undersampling patterns unlike conventional CS methods. Our proposed method relies on convex sparse image reconstruction with linear representation at inference time, which may be beneficial for characterizing robustness, stability and generalizability.