# Transform Learning for Magnetic Resonance Image Reconstruction: From Model-based Learning to Building Neural Networks

arXiv: https://arxiv.org/abs/1903.11431 · HTML: https://mlsanity.com/paper/1903.11431/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2019.

## Built on by (most cited first, 9 of 9)

- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond](https://mlsanity.com/paper/2103.14528/) (2021)
- [An unsupervised deep learning framework for medical image denoising](https://mlsanity.com/paper/2103.06575/) (2021)
- [Single-pass Object-adaptive Data Undersampling and Reconstruction for MRI](https://mlsanity.com/paper/2111.09212/) (2021)
- [Data and Physics Driven Learning Models for Fast MRI -- Fundamentals and Methodologies from CNN, GAN to Attention and Transformers](https://mlsanity.com/paper/2204.01706/) (2022)
- [Adaptive Local Neighborhood-based Neural Networks for MR Image Reconstruction from Undersampled Data](https://mlsanity.com/paper/2206.00775/) (2022)
- [AliasNet: Alias Artefact Suppression Network for Accelerated Phase-Encode MRI](https://mlsanity.com/paper/2302.08861/) (2023)
- [Robust MRI Reconstruction by Smoothed Unrolling (SMUG)](https://mlsanity.com/paper/2312.07784/) (2023)
- [Accelerated MRI With Deep Linear Convolutional Transform Learning](https://mlsanity.com/paper/2204.07923/) (2022)

## Abstract (arXiv)

Magnetic resonance imaging (MRI) is widely used in clinical practice, but it has been traditionally limited by its slow data acquisition. Recent advances in compressed sensing (CS) techniques for MRI reduce acquisition time while maintaining high image quality. Whereas classical CS assumes the images are sparse in known analytical dictionaries or transform domains, methods using learned image models for reconstruction have become popular. The model could be pre-learned from datasets, or learned simultaneously with the reconstruction, i.e., blind CS (BCS). Besides the well-known synthesis dictionary model, recent advances in transform learning (TL) provide an efficient alternative framework for sparse modeling in MRI. TL-based methods enjoy numerous advantages including exact sparse coding, transform update, and clustering solutions, cheap computation, and convergence guarantees, and provide high-quality results in MRI compared to popular competing methods. This paper provides a review of some recent works in MRI reconstruction from limited data, with focus on the recent TL-based methods. A unified framework for incorporating various TL-based models is presented. We discuss the connections between transform learning and convolutional or filter bank models and corresponding multi-layer extensions, with connections to deep learning. Finally, we discuss recent trends in MRI, open problems, and future directions for the field.