dorsal/arxiv
View SchemaA Theoretical Framework for Rate-Distortion Limits in Learned Image Compression
| Authors | Changshuo Wang, Zijian Liang, Kai Niu, Ping Zhang |
|---|---|
| Categories | |
| ArXiv ID | 2601.09254vv1 |
| URL | https://arxiv.org/abs/2601.09254 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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.
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"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.",
"arxiv_id": "2601.09254",
"authors": [
"Changshuo Wang",
"Zijian Liang",
"Kai Niu",
"Ping Zhang"
],
"categories": [
"cs.IT",
"math.IT"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "A Theoretical Framework for Rate-Distortion Limits in Learned Image Compression",
"url": "https://arxiv.org/abs/2601.09254",
"version": "v1"
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