A Theory of the Distortion-Perception Tradeoff in Wasserstein Space

Dror Freirich, Tomer Michaeli, Ron Meir

פרסום מחקרי: פרק בספר / בדוח / בכנספרסום בספר כנסביקורת עמיתים

תקציר

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.

שפה מקוריתאנגלית
כותר פרסום המארחAdvances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
עורכיםMarc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
עמודים25661-25672
מספר עמודים12
מסת"ב (אלקטרוני)9781713845393
סטטוס פרסוםפורסם - 2021
אירוע35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online
משך הזמן: 6 דצמ׳ 202114 דצמ׳ 2021

סדרות פרסומים

שםAdvances in Neural Information Processing Systems
כרך31

כנס

כנס35th Conference on Neural Information Processing Systems, NeurIPS 2021
עירVirtual, Online
תקופה6/12/2114/12/21

ASJC Scopus subject areas

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