About the design of loss function.

[llstela]

It seems that the loss function exists no difference from WGAN-gp but only the l2-norm between the input and output of the generator. Is it the key term that makes OTUR draw such outstanding performance？ I also notice that the similar idea has appeared in simGAN (CVPR2017 Best Paper). So what's the difference between two of them?

[wangweiSJTU]

Sorry for not replying in time. Yes, the l2 transport cost term is critical for the performance, which is derived from the optimal transport criterion, which we propose to be the optimal criterion in the case without any prior model for the noise and signal. Note that, without the l2 transport cost, the formulation reduces to the standard conditional GAN, i.e. the CGAN method in the experiment comparison in the paper. Thanks for mentioning the simGAN work. I found that it also used GAN with a regularization term. But the core ideal of our work is fundamentally different form simGAN. Our method starts from the optimal transport criterion, which is proposed to be the optimal criterion for the restoration problem. In theory, our formulaiton can achieve optimal transport, see the derivation of our method and the analysis in our paper, but the simGAN formulation cannot. simGAN considers the data synthesization problem, optimal transport mapping is not necessary.