Efficient Computation and Analysis of Rate-Distortion-Perception Functions Using Wasserstein Barycenter

Concetti Chiave

The authors study the information rate-distortion-perception (RDP) function, which characterizes the three-way trade-off between description rate, average distortion, and perceptual quality. They reformulate the RDP problem as a Wasserstein Barycenter optimization problem, enabling the identification of critical transitions where constraints become inactive and the analysis of the interplay between distortion and perception measures. An entropy-regularized model and an improved Alternating Sinkhorn algorithm are proposed to efficiently solve the RDP problem.

Sintesi

The content discusses the information rate-distortion-perception (RDP) function, which extends the classical rate-distortion theory by incorporating perceptual quality as an additional constraint. The authors approach the RDP problem from the perspective of optimal transport and introduce the Wasserstein Barycenter model for RDP functions (WBM-RDP).
Key highlights:

The authors establish an equivalence between the RDP problem and the Wasserstein Barycenter optimization problem, which enables the identification of critical transitions where one of the constraints becomes inactive.
They prove the existence of critical transition functions that characterize the interplay between distortion and perception measures, and show how these critical transition curves can be effectively computed.
The authors construct an entropy-regularized formulation of the WBM-RDP, which admits a unique optimal solution and converges to the original problem.
An improved Alternating Sinkhorn (AS) algorithm is proposed, which effectively combines the advantages of the AS algorithm for RD functions and the entropy-regularized algorithm for Wasserstein Barycenter problems.
The authors apply their numerical methods to a reverse data hiding problem, demonstrating the effectiveness of incorporating perceptual measures in steganography techniques.

Statistiche

The authors use the following key metrics and figures in the content:

Distortion function Δ(x, y): a measurable function that satisfies non-negativity and Δ(x, y) = 0 if and only if x = y.
Perceptual measure d(p, r): a divergence measure that satisfies non-negativity and convexity in the second argument.
Wasserstein metric W(p, r): the optimal transport cost between distributions p and r.
Entropy-regularized parameter ε > 0 in the WBM-RDP optimization problem.

Citazioni

"The introduction of the perceptual quality constraint brings new challenges to the classical rate-distortion problem from several aspects."
"We approach the RDP problem from the perspective of Optimal Transport (OT). We introduce the Wasserstein Barycenter model for Rate-Distortion-Perception functions (WBM-RDP) and corresponding algorithms."
"With the reformulated Wasserstein Barycenter problem, we design an algorithm to tackle the WBM-RDP. One challenge is that the WBM-RDP is not strictly convex."

Approfondimenti chiave tratti da

Computation and Critical Transitions of Rate-Distortion-Perception Functions With Wasserstein Barycenter

by Chunhui Chen... alle arxiv.org 04-09-2024

https://arxiv.org/pdf/2404.04681.pdf

Domande più approfondite

How can the proposed Wasserstein Barycenter framework and algorithms be extended to other information-theoretic problems beyond the RDP function

The proposed Wasserstein Barycenter framework and algorithms can be extended to other information-theoretic problems beyond the RDP function by leveraging the principles of optimal transport and the Wasserstein metric. One potential application is in network information theory, where the optimization of information flow between nodes can benefit from the efficient computation of Wasserstein Barycenters. By formulating the problem in a similar manner to the RDP function, with appropriate constraints and objectives, the framework can be adapted to address various network communication scenarios. Additionally, the algorithms developed for the WBM-RDP model can be modified and optimized to suit the specific requirements of different information-theoretic problems, providing a versatile and powerful tool for researchers in the field.

What are the potential limitations or drawbacks of using the Wasserstein metric as the perceptual measure, and how could alternative perceptual measures be incorporated into the WBM-RDP model

While the Wasserstein metric offers valuable insights and computational advantages in measuring the discrepancy between probability distributions, it may have limitations in certain perceptual contexts. One potential drawback is the sensitivity of the Wasserstein metric to outliers or extreme values in the distributions, which can skew the perceptual quality assessment. To address this limitation, alternative perceptual measures such as the Total Variation (TV) distance or the Kullback-Leibler (KL) divergence could be incorporated into the WBM-RDP model. These measures provide different perspectives on the divergence between distributions and may offer more robust evaluations of perceptual quality in certain scenarios. By integrating a variety of perceptual measures into the model, researchers can enhance the flexibility and applicability of the framework to a wider range of problems and datasets.

Given the close connection between optimal transport and information theory revealed in this work, what other synergies between these two fields could be explored to advance the state-of-the-art in both areas

The close connection between optimal transport and information theory opens up a plethora of synergies that can be explored to advance both fields. One potential synergy is in the development of efficient data compression algorithms based on optimal transport principles. By leveraging the insights from Wasserstein Barycenter computations and applying them to data compression tasks, researchers can potentially improve the compression efficiency and perceptual quality of encoded data. Additionally, the integration of optimal transport concepts into machine learning models, such as generative adversarial networks (GANs) or reinforcement learning algorithms, could lead to novel approaches for data generation, anomaly detection, and reinforcement learning tasks. Exploring these synergies further could pave the way for innovative solutions in both information theory and optimal transport research.