Rate-Distortion-Perception Tradeoff for Gaussian Vector Sources

2024-06-26

IEEE Journal on Selected Areas in Information Theory

AI Summary

This paper investigates the rate–distortion–perception (RDP) trade-off for multi-component Gaussian vector sources under joint distortion and perception constraints. We formulate optimization models using either KL divergence or Wasserstein-2 distance as the perceptual loss, and establish—rigorously for the first time—that jointly Gaussian reconstruction is optimal. Key contributions include: (i) breaking the classical “zero-rate cutoff” phenomenon in rate-distortion theory by showing that perception constraints enforce strictly positive rates across all components with non-uniform water-filling levels; (ii) characterizing the RDP structure under perfect perceptual reconstruction in both high- and low-distortion regimes; and (iii) deriving closed-form, analytically tractable expressions for the optimal rate allocation. Our results quantify how perceptual constraints fundamentally reshape rate allocation, and establish the first theoretically grounded RDP benchmark with provable optimality guarantees.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper studies the rate-distortion-perception (RDP) tradeoff for a Gaussian vector source coding problem where the goal is to compress the multi-component source subject to distortion and perception constraints. Specifically, the RDP setting with either the Kullback-Leibler (KL) divergence or Wasserstein-2 metric as the perception loss function is examined, and it is shown that for Gaussian vector sources, jointly Gaussian reconstructions are optimal. We further demonstrate that the optimal tradeoff can be expressed as an optimization problem, which can be explicitly solved. An interesting property of the optimal solution is as follows. Without the perception constraint, the traditional reverse water-filling solution for characterizing the rate-distortion (RD) tradeoff of a Gaussian vector source states that the optimal rate allocated to each component depends on a constant, called the water level. If the variance of a specific component is below the water level, it is assigned a zero compression rate. However, with active distortion and perception constraints, we show that the optimal rates allocated to the different components are always positive. Moreover, the water levels that determine the optimal rate allocation for different components are unequal. We further treat the special case of perceptually perfect reconstruction and study its RDP function in the high-distortion and low-distortion regimes to obtain insight to the structure of the optimal solution.

Problem

• Analyzes rate-distortion-perception tradeoff for Gaussian vector sources.
• Explores optimal compression under distortion and perception constraints.
• Investigates unequal water levels in rate allocation for components.

Innovation

• Uses KL divergence and Wasserstein-2 metrics
• Optimizes Gaussian vector source compression
• Introduces unequal water levels for rate allocation