Universal Rate-Distortion-Perception Representations for Lossy Compression and Applications using Generative Models

In the context of lossy compression, Blau \ Michaeli \cite{blau2019rethinking} adopt a mathematical notion of perceptual quality and define the information rate-distortion-perception (RDP) function. We consider the notion of universal representations in which one fixes an encoder and varies the decoder to achieve a collection of distortion-perception constraints. We prove that the corresponding information-theoretic universal RDP function is operationally achievable in an approximate sense. Under MSE distortion, we show that the entire distortion-perception tradeoff for Gaussian sources is achieved by a single encoder asymptotically. We then characterize the achievable distortion-perception region for a fixed representation for arbitrary distributions. This motivates the study of practical constructions that are approximately universal, alleviating the need to design an encoder for each objective. We provide experiments on MNIST/SVHN suggesting that for image compression, the operational tradeoffs achieved by fixed-encoder machine learning models are comparable to their variable encoder counterparts.M.A.S