Computation of the Multivariate Gaussian Rate-Distortion-Perception Function 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). In this paper, we propose a generic method for computing the rate-distortion-perception function (RDPF) of a multivariate Gaussian source under tensorizable distortion and perception metrics. Through the assumption of a jointly Gaussian reconstruction, we establish that the optimal solution of the RDPF belongs to the vector space spanned by the eigenvector of the source covariance matrix. Consequently, the multivariate optimization problem can be expressed as a function of the scalar Gaussian RDPFs of the source marginals, constrained by global distortion and perception levels. Utilizing this result, we devise an alternating minimization scheme based on the block nonlinear Gauss-Seidel method. This scheme solves optimally the optimization problem while identifying the optimal stage-wise distortion and perception levels. Furthermore, the associated algorithmic embodiment is provided, along with the convergence and the rate of convergence characterization. Lastly, in the regime of “perfect realism”, we provide the analytical solution for the multivariate Gaussian RDPF. We corroborate our findings with numerical simulations and draw connections to existing results. 2025-04-01T12:20:03Z 2025-04-01T12:20:03Z 2024-07 conference output G. Serra, P. A. Stavrou and M. Kountouris, "Computation of the Multivariate Gaussian Rate-Distortion-Perception Function," 2024Serra, Giuseppe et al. Computation of the Multivariate Gaussian Rate-Distortion-Perception Function. IEEE International Symposium on Information Theory (ISIT), Athens, Greece, 2024, pp. 1077-1082, doi: 10.1109/ISIT57864.2024.10619375 https://hdl.handle.net/10481/103373 10.1109/ISIT57864.2024.10619375 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