Autoencoder Image Generation with Multiscale Sparse Deconvolutions
Autoencoders and GAN's can synthesize remarkably complex images, although we still do not understand the mathematical properties of the generated random processes. We introduces a mathematical and algorithmic framework to analyze the principles of such image syntheses. In Wasserstein autoencoders, the coder is trained to transform the input random vector into a lower-dimensional nearly white noise. Images are synthesized from white noise with an inverse deep convolutional generator. We show that the encoder can be computed with a multiscale scattering transform, which mixes input variables at multiple scales. We prove that generating an image model then amounts to solve a sequence of linear deconvolutions at different scales. A deep convolutional generator regularizes this deconvolution by sparsity in dictionaries learned at each scale. Numerical image synthesis will be shown. Joint work with Tomas Anglès.