Exploring Low-Dimensional Structures in Images Using Deep Fourier Machines

Abstract

The ground-breaking results achieved by Deep Generative Models, when given merely a dataset representing the desired distribution of generated images have caught the interest of scholars. In this work, we introduce a novel structure designed for image generation utilizing the idea behind Fourier Series and Deep Learning function composition. By composing low-dimensional structures, we will first compress a high-dimensional image, and then we will use this latent space to generate fake images. Our compression algorithm gives comparable results to the JPEG algorithm and even, in some cases, outperforms it. Also, our image generation model can generate decent fake images on MNIST and CIFAR-10 datasets and can surpass the first generation of Variational Autoencoders