We present a new method to estimate the rate-distortion-perception function in the perfect realism regime (PR-RDPF), for multivariate continuous sources subject to a single-letter 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 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 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.

翻译：我们提出了一种新方法，用于在完美现实主义机制（PR-RDPF）下估计多元连续源在满足单字符平均失真约束时的率失真感知函数。该方案不仅能解决特定问题，还能处理两个相关问题：熵最优传输（EOT）和输出约束率失真函数（OC-RDF），其中PR-RDPF是其特例。利用Copula分布，我们证明OC-RDF可转化为凸集上的I-投影问题，并基于此开发了最优投影的参数化解，证明其参数可通过凸规划求解任意精度估计。随后，我们提出基于梯度方法的迭代方案来估计凸规划问题。最后，我们给出了均方误差（MSE）失真约束下PR-RDPF的香农下界（SLB）。通过数值算例，我们利用所提出的迭代方案结合不同源的SLB评估了PR-RDPF的估计性能，从而支持了理论发现。