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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.09254 |
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| _version_ | 1866908763956445184 |
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| author | Wang, Changshuo Liang, Zijian Niu, Kai Zhang, Ping |
| author_facet | Wang, Changshuo Liang, Zijian Niu, Kai Zhang, Ping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09254 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Theoretical Framework for Rate-Distortion Limits in Learned Image Compression Wang, Changshuo Liang, Zijian Niu, Kai Zhang, Ping Information Theory 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. |
| title | A Theoretical Framework for Rate-Distortion Limits in Learned Image Compression |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.09254 |