A Theoretical Framework for Rate-Distortion Limits in Learned Image Compression

2026-01-14

AI Summary

This work proposes a structurally interpretable rate-distortion analysis framework for neural image compression, addressing the lack of clear characterization of theoretical performance limits in existing methods. By decomposing the overall distortion into three components—variance estimation, quantization strategy, and context modeling—the framework derives, under Gaussian assumptions, the first closed-form expression for the optimal latent variance. It achieves a tight and tractable approximation to the rate-distortion bound by integrating second-moment-based variance estimation, quantization analysis guided by the reverse water-filling theorem, and mean prediction with entropy reduction in context modeling. This principled approach not only quantifies the gap between current neural codecs and information-theoretic optimality but also provides a theoretical foundation and concrete optimization directions for designing efficient neural image compression systems.

Technology Category

• Machine Learning: Information Theory
• Computer Vision: Learning & Optimization for CV
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We present a novel systematic theoretical framework to analyze the rate-distortion (R-D) limits of learned image compression. While recent neural codecs have achieved remarkable empirical results, their distance from the information-theoretic limit remains unclear. Our work addresses this gap by decomposing the R-D performance loss into three key components: variance estimation, quantization strategy, and context modeling. First, we derive the optimal latent variance as the second moment under a Gaussian assumption, providing a principled alternative to hyperprior-based estimation. Second, we quantify the gap between uniform quantization and the Gaussian test channel derived from the reverse water-filling theorem. Third, we extend our framework to include context modeling, and demonstrate that accurate mean prediction yields substantial entropy reduction. Unlike prior R-D estimators, our method provides a structurally interpretable perspective that aligns with real compression modules and enables fine-grained analysis. Through joint simulation and end-to-end training, we derive a tight and actionable approximation of the theoretical R-D limits, offering new insights into the design of more efficient learned compression systems.

Problem

• rate-distortion
• learned image compression
• information-theoretic limit
• neural codecs
• R-D limits

Innovation

• rate-distortion theory
• learned image compression
• variance estimation
• quantization gap
• context modeling