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

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.