DeepAI AI Chat
Log In Sign Up

A Theory of the Distortion-Perception Tradeoff in Wasserstein Space

07/06/2021
by   Dror Freirich, et al.
Technion
0

The lower the distortion of an estimator, the more the distribution of its outputs generally deviates from the distribution of the signals it attempts to estimate. This phenomenon, known as the perception-distortion tradeoff, has captured significant attention in image restoration, where it implies that fidelity to ground truth images comes at the expense of perceptual quality (deviation from statistics of natural images). However, despite the increasing popularity of performing comparisons on the perception-distortion plane, there remains an important open question: what is the minimal distortion that can be achieved under a given perception constraint? In this paper, we derive a closed form expression for this distortion-perception (DP) function for the mean squared-error (MSE) distortion and the Wasserstein-2 perception index. We prove that the DP function is always quadratic, regardless of the underlying distribution. This stems from the fact that estimators on the DP curve form a geodesic in Wasserstein space. In the Gaussian setting, we further provide a closed form expression for such estimators. For general distributions, we show how these estimators can be constructed from the estimators at the two extremes of the tradeoff: The global MSE minimizer, and a minimizer of the MSE under a perfect perceptual quality constraint. The latter can be obtained as a stochastic transformation of the former.

READ FULL TEXT

page 9

page 20

page 21

01/23/2019

Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff

Lossy compression algorithms are typically designed and analyzed through...
08/24/2018

Introducing the Perception-Distortion Tradeoff into the Rate-Distortion Theory of General Information Sources

Blau and Michaeli recently introduced a novel concept for inverse proble...
04/12/2022

On the Rate-Distortion-Perception Function

Rate-distortion-perception theory generalizes Shannon's rate-distortion ...
04/18/2019

On The Classification-Distortion-Perception Tradeoff

Signal degradation is ubiquitous and computational restoration of degrad...
06/21/2022

Optimally Controllable Perceptual Lossy Compression

Recent studies in lossy compression show that distortion and perceptual ...
11/16/2017

The Perception-Distortion Tradeoff

Image restoration algorithms are typically evaluated by some distortion ...
12/16/2019

A Converse Bound Characterization on Zero-Delay Indirect RDF for Vector Gauss-Markov Sources

We consider a zero-delay remote source coding problem where a hidden sou...