Real or Fake? Fourier Analysis of Generative Adversarial Network Fundus Images

With the increasing use of deep learning methodologies in various biomedical applications, there is a need for a large number of labeled medical image datasets for training and validation purposes. However, the accumulation of labeled datasets is expensive and time consuming. Recently, generative adversarial networks (GAN) have been utilized to generate synthetic datasets. Currently, the accuracy of generative adversarial networks is calculated using a structural similarity index measure (SSIM). SSIM is not adequate for comparison of images as it underestimates the distortions near hard edges. In this paper, we compare the real DRIVE dataset to the synthetic FunSyn-Net using Fourier transform techniques and show that Fourier behavior is quite different in the two datasets, especially at high frequencies. It is observed that for real images, the amplitude of the Fourier components exponentially decreased with increasing frequency. For the synthesized images, the rate of decrease of the amplitude is much slower. If a linear function is fit to the high frequency components, the slope distributions for the two datasets are completely different with no offset. The average slope in the log scale for DRIVE dataset and FunSyn-Net were 0.0195, and 0.009 respectively. We also looked at auto correlations for the horizontal cut of the Fourier transform and again saw a statistically significant difference between the means for the two datasets. Finally, we also observed that Fourier transforms with real images have higher magnitude squared coherence as compared to the synthesized images. Fourier transform has shown great success for finding differences between real and synthesized images and can be used to improve the synthesized GAN models.