Computation of Rate-Distortion-Perception Functions With Wasserstein Barycenter

The nascent field of Rate-Distortion-Perception (RDP) theory is seeing a surge of research interest due to the application of machine learning techniques in the area of lossy compression. The information RDP function characterizes the three-way trade-off between description rate, average distortion, and perceptual quality measured by discrepancy between probability distributions. However, computing RDP functions has been a challenge due to the introduction of the perceptual constraint, and existing research often resorts to data-driven methods. In this paper, we show that the information RDP function can be transformed into a Wasserstein Barycenter problem. The non-strictly convexity brought by the perceptual constraint can be regularized by an entropy regularization term. We prove that the entropy regularized model converges to the original problem. Furthermore, we propose an alternating iteration method based on the Sinkhorn algorithm to numerically solve the regularized optimization problem. Experimental results demonstrate the efficiency and accuracy of the proposed algorithm.