Copula-based Estimation of Continuous Sources for a Class of Constrained Rate-Distortion-Functions
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| Format: | Preprint |
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2024
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| author | Serra, Giuseppe Stavrou, Photios A. Kountouris, Marios |
| author_facet | Serra, Giuseppe Stavrou, Photios A. Kountouris, Marios |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_17089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Copula-based Estimation of Continuous Sources for a Class of Constrained Rate-Distortion-Functions Serra, Giuseppe Stavrou, Photios A. Kountouris, Marios Information Theory 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. |
| title | Copula-based Estimation of Continuous Sources for a Class of Constrained Rate-Distortion-Functions |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.17089 |