# Optimal Transport driven CycleGAN for Unsupervised Learning in Inverse Problems

arXiv: https://arxiv.org/abs/1909.12116 · HTML: https://mlsanity.com/paper/1909.12116/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2019.

## Built on by (most cited first, 4 of 4)

- [Breaking the Dilemma of Medical Image-to-image Translation](https://mlsanity.com/paper/2110.06465/) (2021)
- [Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond](https://mlsanity.com/paper/2103.14528/) (2021)
- [Adaptive Local Neighborhood-based Neural Networks for MR Image Reconstruction from Undersampled Data](https://mlsanity.com/paper/2206.00775/) (2022)
- [Fine-grained MRI Reconstruction using Attentive Selection Generative Adversarial Networks](https://mlsanity.com/paper/2103.07672/) (2021)

## Abstract (arXiv)

To improve the performance of classical generative adversarial network (GAN), Wasserstein generative adversarial networks (W-GAN) was developed as a Kantorovich dual formulation of the optimal transport (OT) problem using Wasserstein-1 distance. However, it was not clear how cycleGAN-type generative models can be derived from the optimal transport theory. Here we show that a novel cycleGAN architecture can be derived as a Kantorovich dual OT formulation if a penalized least square (PLS) cost with deep learning-based inverse path penalty is used as a transportation cost. One of the most important advantages of this formulation is that depending on the knowledge of the forward problem, distinct variations of cycleGAN architecture can be derived: for example, one with two pairs of generators and discriminators, and the other with only a single pair of generator and discriminator. Even for the two generator cases, we show that the structural knowledge of the forward operator can lead to a simpler generator architecture which significantly simplifies the neural network training. The new cycleGAN formulation, what we call the OT-cycleGAN, have been applied for various biomedical imaging problems, such as accelerated magnetic resonance imaging (MRI), super-resolution microscopy, and low-dose x-ray computed tomography (CT). Experimental results confirm the efficacy and flexibility of the theory.