Explicit Use of Fourier Spectrum in Generative Adversarial Networks

Generative Adversarial Networks have got the researcher's attention due to their state-of- the-art performance in generating new images with only a dataset of the target distribution. It has been shown that there is a dissimilarity between the spectrum of authentic images and fake ones. Since the Fourier transform is a bijective mapping, saying that the model has a significant problem in learning the original distribution is a fair conclusion. In this work, we investigate the possible reasons for the mentioned drawback in the architecture and mathematical theory of the current GANs. Then we propose a new model reducing the discrepancies between the spectrum of the actual and fake images. To that end, we design a brand new architecture for the frequency domain using the blueprint of geometric deep learning. Then, we experimentally show that promising improvements in the quality of the generated images by considering the Fourier domain representation of the original data as a principal feature in the training process.