Copula-based Estimation of Continuous Sources for a Class of Constrained Rate-Distortion-Functions Serra, Giuseppe Stavrou, Photios A. Kountouris, Marios This work is part of a project that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 101003431). We present a new method to estimate the ratedistortion-perception function in the perfect realism regime (PR-RDPF), for multivariate continuous sources subject to a singleletter average distortion constraint. The proposed approach is not only able to solve the specific problem but also two related problems: the entropic optimal transport (EOT) and the outputconstrained rate-distortion function (OC-RDF), of which the PR-RDPF represents a special case. Using copula distributions, we show that the OC-RDF can be cast as an I-projection problem on a convex set, based on which we develop a parametric solution of the optimal projection proving that its 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 characterize a Shannon lower bound (SLB) for the PR-RDPF under a mean squared error (MSE) distortion constraint. We support our theoretical findings with numerical examples by assessing the estimation performance of our iterative scheme using the PR-RDPF with the obtained SLB for various sources. 2025-04-01T10:14:58Z 2025-04-01T10:14:58Z 2024-01-30 journal article Published version: G. Serra, P. A. Stavrou and M. Kountouris, "Copula-Based Estimation of Continuous Sources for a Class of Constrained Rate-Distortion Functions," 2024 IEEE International Symposium on Information Theory (ISIT), Athens, Greece, 2024, pp. 1089-1094, doi: 10.1109/ISIT57864.2024.10619503 https://hdl.handle.net/10481/103369 10.1109/ISIT57864.2024.10619503 eng info:eu-repo/grantAgreement/EC/H2020/101003431 http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional IEEE