Optimal Transport driven CycleGAN for Unsupervised Learning in Inverse Problems
This work provides a theoretical framework for unsupervised learning in inverse problems, benefiting researchers in biomedical imaging and related fields, though it is incremental in extending optimal transport to cycleGANs.
The authors tackled the lack of a theoretical foundation for cycleGAN-type models in inverse problems by deriving a novel cycleGAN architecture from optimal transport theory, resulting in flexible model variations that simplify training and achieve state-of-the-art performance in biomedical imaging tasks like accelerated MRI and low-dose CT.
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.