Copula-based Estimation of Continuous Sources for a Class of Constrained Rate-Distortion Functions

We propose a novel method for estimating the rate-distortion-perception function in perfect realism regime (PR-RDPF) for a multivariate continuous source subject to a single-letter average distortion constraint. Our approach leads to a general computation scheme able to solve two related problems, the entropic optimal transport (EOT) and the output-constrained rate-distortion function (OC-RDF), of which the PR-RDPF represents a special case. Using copula distributions, we show that the OC-RDF is equivalent to an $I$-projection problem on a convex set, which allows us to recover the parametric solution of the optimal projection whose parameters can be estimated, up to an arbitrary precision, via the solution of a convex program. Subsequently, we propose an iterative scheme via gradient methods to estimate the convex program. Lastly, we support our theoretical findings with numerical examples by assessing the estimation performance of our scheme.