# Convolutional Analysis Operator Learning by End-To-End Training of Iterative Neural Networks

arXiv: https://arxiv.org/abs/2203.02166 · HTML: https://mlsanity.com/paper/2203.02166/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 4 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Model based learning for accelerated, limited-view 3D photoacoustic tomography](https://mlsanity.com/paper/1708.09832/) (2017)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [Convolutional Analysis Operator Learning: Acceleration and Convergence](https://mlsanity.com/paper/1802.05584/) (2018)
- [An End-To-End-Trainable Iterative Network Architecture for Accelerated Radial Multi-Coil 2D Cine MR Image Reconstruction](https://mlsanity.com/paper/2102.00783/) (2021)
- [Convolutional Dictionary Learning: Acceleration and Convergence](https://mlsanity.com/paper/1707.00389/) (2017)

## Built on by (most cited first, 1 of 1)

- [Convolutional Dictionary Learning by End-To-End Training of Iterative Neural Networks](https://mlsanity.com/paper/2206.04447/) (2022)

## Abstract (arXiv)

The concept of sparsity has been extensively applied for regularization in image reconstruction. Typically, sparsifying transforms are either pre-trained on ground-truth images or adaptively trained during the reconstruction. Thereby, learning algorithms are designed to minimize some target function which encodes the desired properties of the transform. However, this procedure ignores the subsequently employed reconstruction algorithm as well as the physical model which is responsible for the image formation process. Iterative neural networks - which contain the physical model - can overcome these issues. In this work, we demonstrate how convolutional sparsifying filters can be efficiently learned by end-to-end training of iterative neural networks. We evaluated our approach on a non-Cartesian 2D cardiac cine MRI example and show that the obtained filters are better suitable for the corresponding reconstruction algorithm than the ones obtained by decoupled pre-training.