Analysis of Output-Constrained Lossy Source Coding with Rate-Distortion-Perception Theory

Konsep Inti

Distortion-rate function analysis for output-constrained source coding with Gaussian distributions.

Abstrak

The content delves into the distortion-rate function analysis of output-constrained lossy source coding, focusing on Gaussian distributions. It explores the connection between rate-distortion-perception coding and output-constrained source coding, highlighting the impact of common randomness on the fundamental limit of rate-distortion-perception coding. The paper provides insights into the tradeoff among compression rate, reconstruction distortion, and perceptual quality in image compression. It discusses various perception measures such as Kullback-Leibler divergence and squared quadratic Wasserstein distance. The study aims to characterize the information-theoretic limit of quadratic Gaussian rate-distortion-perception coding under different perception measures.
Section I: Introduction

Image compression quality not solely based on distortion.
Perception measure focuses on statistical properties.
Comparison of pre- and post-compression image distributions.
Section II: Problem Definition

Encoder-decoder system for lossy source coding.
Achievable distortion level with rate and common randomness constraints.
Section III: General Case

Uniformly integrable tuple for distortion-rate function characterization.
Distortion-rate function under squared error measure bounds established.
Section IV: Gaussian Case

Fundamental limit characterization for Gaussian distributions.
Impact of common randomness on distortion-rate tradeoff discussed.
Section V: Conclusion

Bounds on rate-distortion-perception tradeoff presented.
Future work on joint-distribution-based perception constraint proposed.

Statistik

arXiv:2403.14849v1 [cs.IT] 21 Mar 2024

Kutipan

Wawasan Utama Disaring Dari

Output-Constrained Lossy Source Coding With Application to Rate-Distortion-Perception Theory

by Li Xie,Liang... pada arxiv.org 03-25-2024

https://arxiv.org/pdf/2403.14849.pdf

Pertanyaan yang Lebih Dalam

How does the presence or absence of common randomness affect the distortion-rate tradeoff

The presence or absence of common randomness can significantly impact the distortion-rate tradeoff in rate-distortion-perception theory. When there is unlimited common randomness available, the distortion-rate tradeoff tends to be more favorable as it allows for a greater level of control over the reconstruction process. This results in a tighter bound on the achievable distortion levels. On the other hand, when there is limited or no common randomness, achieving low distortion levels while maintaining a certain rate becomes more challenging. In such cases, compromises may need to be made between reconstruction quality and compression efficiency.

What are the implications of using different perception measures in rate-distortion-perception theory

Using different perception measures in rate-distortion-perception theory can lead to varying outcomes and insights into the fundamental tradeoffs involved. For example, employing Kullback-Leibler divergence as a perception measure focuses on capturing differences in statistical properties between source and reconstruction distributions. This measure emphasizes information gain or loss during compression and can provide valuable insights into how well perceptual quality aligns with reconstruction accuracy.
On the other hand, utilizing squared quadratic Wasserstein distance as a perception measure emphasizes geometric aspects related to distributional similarity between source and reconstructed data points. This metric considers optimal transport plans for moving mass from one distribution to another efficiently while minimizing costs associated with these movements.
By incorporating different perception measures, researchers can gain a comprehensive understanding of how various factors influence the overall performance of rate-distortion-perception systems and make informed decisions about optimizing these systems based on specific requirements or constraints.

How can joint-distribution-based perception constraints impact the fundamental rate-distortion-perception tradeoff

Joint-distribution-based perception constraints have significant implications for the fundamental rate-distortion-perception tradeoff in coding systems. By considering joint distributions rather than just marginal distributions, these constraints aim to enforce sequence-level distributional consistency between source and reconstructed data at every time step.
One key implication is that joint-distribution-based constraints offer a more stringent criterion for evaluating perceptual quality compared to marginal-distribution-based constraints alone. By focusing on entire sequences rather than individual symbols independently, this approach ensures that not only are individual symbols accurately represented but also that their sequential relationships are preserved throughout encoding and decoding processes.
Additionally, joint-distribution-based perception constraints may introduce additional complexity into system design due to increased computational requirements for handling joint distributions effectively. However, by incorporating such constraints intelligently into coding schemes, researchers can potentially achieve higher levels of fidelity in reconstructing data sequences while balancing compression efficiency with perceptual quality considerations.