Universal Rate-Distortion-Perception Representations for Lossy Compression

TL;DR

This paper introduces a universal rate-distortion-perception framework for lossy compression, demonstrating that a single encoder can approximate the entire tradeoff space, with practical ML models showing minimal performance loss.

Contribution

It establishes the theoretical achievability of universal representations in rate-distortion-perception tradeoffs and proposes practical approaches for fixed encoders in image compression.

Findings

Single encoder can achieve entire distortion-perception tradeoff asymptotically for Gaussian sources.

Universal representations perform nearly as well as variable encoders on MNIST and SVHN.

Theoretical results extend to arbitrary distributions under certain conditions.

Abstract

In the context of lossy compression, Blau & Michaeli (2019) adopt a mathematical notion of perceptual quality and define the information rate-distortion-perception function, generalizing the classical rate-distortion tradeoff. We consider the notion of universal representations in which one may fix an encoder and vary the decoder to achieve any point within a collection of distortion and perception constraints. We prove that the corresponding information-theoretic universal rate-distortion-perception function is operationally achievable in an approximate sense. Under MSE distortion, we show that the entire distortion-perception tradeoff of a Gaussian source can be achieved by a single encoder of the same rate asymptotically. We then characterize the achievable distortion-perception region for a fixed representation in the case of arbitrary distributions, identify conditions under which the aforementioned results continue to hold approximately, and study the case when the rate is not fixed in advance. This motivates the study of practical constructions that are approximately universal across the RDP tradeoff, thereby alleviating the need to design a new encoder for each objective. We provide experimental results on MNIST and SVHN suggesting that on image compression tasks, the operational tradeoffs achieved by machine learning models with a fixed encoder suffer only a small penalty when compared to their variable encoder counterparts.