Rate-Distortion-Perception Trade-off with Strong Realism Constraints: Role of Side Information and Common Randomness

2025-07-20

AI Summary

This paper investigates the rate–distortion–perception tradeoff in image compression under strong perceptual realism constraints—specifically, requiring the reconstructed image and source image to have *exactly* matching joint distributions. For settings where side information is available at either the encoder or decoder, we characterize its dual role as both a source of common randomness and a secondary observation of the source at the receiver. We formalize three stringent perceptual constraints: marginal realism, joint realism, and near-perfect realism. Leveraging random coding arguments and information-theoretic analysis, we derive fundamental limits for jointly Gaussian sources under squared-error distortion. Key insight: Under strong realism, side information at the decoder alone incurs a rate penalty unless sufficient common randomness is shared between encoder and decoder. Our results establish the first rigorous theoretical framework for generative image compression under exact distributional fidelity constraints.

Technology Category

• Machine Learning: Information Theory
• Computer Vision: Other Foundations of Computer Vision
• Game Theory and Economic Paradigms: Imperfect Information

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In image compression, with recent advances in generative modeling, existence of a trade-off between the rate and perceptual quality has been brought to light, where the perceptual quality is measured by the closeness of the output and source distributions. We consider the compression of a memoryless source sequence $X^n=(X_1, ldots, X_n)$ in the presence of memoryless side information $Z^n=(Z_1, ldots, Z_n),$ originally studied by Wyner and Ziv, but elucidate the impact of a strong perfect realism constraint, which requires the joint distribution of output symbols $Y^n=(Y_1,...,Y_n)$ to match the distribution of the source sequence. We consider two cases: when $Z^n$ is available only at the decoder, or at both the encoder and decoder, and characterize the information theoretic limits under various scenarios. Previous works show the superiority of randomized codes under strong perceptual quality constraints. When $Z^n$ is available at both terminals, we characterize its dual role, as a source of common randomness, and as a second look on the source for the receiver. We also study different notions of strong perfect realism which we call marginal realism, joint realism and near-perfect realism. We derive explicit solutions when $X$ and $Z$ are jointly Gaussian under the squared error distortion measure. In traditional lossy compression, having $Z$ only at the decoder imposes no rate penalty in the Gaussian scenario. We show that, when strong perfect realism constraints are imposed this holds only when sufficient common randomness is available.

Problem

• Study rate-distortion-perception trade-off with realism constraints
• Analyze side information's dual role in encoder-decoder systems
• Characterize strong realism variants in Gaussian compression scenarios

Innovation

• Utilizes side information for compression enhancement
• Applies strong perfect realism constraints
• Leverages common randomness in encoding