SIAM Journal on Imaging Sciences, Volume 13, Issue 4, Page 2281-2306, January 2020.
To improve the performance of classical generative adversarial networks (GANs), Wasserstein generative adversarial networks (WGANs) were 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 OT theory. Here we show that a novel CycleGAN architecture can be derived as a Kantorovich dual OT formulation if a penalized least squares (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, which we call the OT-CycleGAN, has 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.

中文翻译：

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逆问题中无监督学习的最优运输驱动CycleGAN

SIAM影像科学杂志，第13卷，第4期，第2281-2306页，2020年1月。
为了提高经典生成对抗网络（GAN）的性能，Wasserstein生成对抗网络（WGAN）被开发为使用Wasserstein-1距离的最优运输（OT）问题的Kantorovich对偶公式。但是，尚不清楚如何从旧时理论推导CycleGAN型生成模型。在这里我们表明，如果将基于深度学习的逆最小路径罚分的惩罚最小二乘（PLS）成本用作运输成本，则可以将一种新颖的CycleGAN架构推导为Kantorovich对偶OT公式。此公式最重要的优点之一是，根据对前向问题的了解，可以得出CycleGAN体系结构的不同变化：例如，一个具有两对生成器和一个鉴别器的，另一个则只有一对生成器和鉴别器。即使对于这两种生成器情况，我们也表明，前向运算符的结构知识可以导致生成器结构更简单，从而大大简化了神经网络训练。新的CycleGAN配方（我们称为OT-CycleGAN）已应用于各种生物医学成像问题，例如加速磁共振成像（MRI），超分辨率显微镜和低剂量X射线计算机断层扫描（CT）。实验结果证实了该理论的有效性和灵活性。我们将其称为OT-CycleGAN，已应用于各种生物医学成像问题，例如加速磁共振成像（MRI），超分辨率显微镜和低剂量X射线计算机断层扫描（CT）。实验结果证实了该理论的有效性和灵活性。我们将其称为OT-CycleGAN，已应用于各种生物医学成像问题，例如加速磁共振成像（MRI），超分辨率显微镜和低剂量X射线计算机断层扫描（CT）。实验结果证实了该理论的有效性和灵活性。