  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
nonstrictly 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.
