On the Rate-Distortion-Perception Function for Gaussian Processes
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916562673336320 |
|---|---|
| author | Serra, Giuseppe Stavrou, Photios A. Kountouris, Marios |
| author_facet | Serra, Giuseppe Stavrou, Photios A. Kountouris, Marios |
| contents | In this paper, we investigate the rate-distortion-perception function (RDPF) of a source modeled by a Gaussian Process (GP) on a measure space $Ω$ under mean squared error (MSE) distortion and squared Wasserstein-2 perception metrics. First, we show that the optimal reconstruction process is itself a GP, characterized by a covariance operator sharing the same set of eigenvectors of the source covariance operator. Similarly to the classical rate-distortion function, this allows us to formulate the RDPF problem in terms of the Karhunen-Loève transform coefficients of the involved GPs. Leveraging the similarities with the finite-dimensional Gaussian RDPF, we formulate an analytical tight upper bound for the RDPF for GPs, which recovers the optimal solution in the "perfect realism" regime. Lastly, in the case where the source is a stationary GP and $Ω$ is the interval $[0, T]$ equipped with the Lebesgue measure, we derive an upper bound on the rate and the distortion for a fixed perceptual level and $T \to \infty$ as a function of the spectral density of the source process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Rate-Distortion-Perception Function for Gaussian Processes Serra, Giuseppe Stavrou, Photios A. Kountouris, Marios Information Theory In this paper, we investigate the rate-distortion-perception function (RDPF) of a source modeled by a Gaussian Process (GP) on a measure space $Ω$ under mean squared error (MSE) distortion and squared Wasserstein-2 perception metrics. First, we show that the optimal reconstruction process is itself a GP, characterized by a covariance operator sharing the same set of eigenvectors of the source covariance operator. Similarly to the classical rate-distortion function, this allows us to formulate the RDPF problem in terms of the Karhunen-Loève transform coefficients of the involved GPs. Leveraging the similarities with the finite-dimensional Gaussian RDPF, we formulate an analytical tight upper bound for the RDPF for GPs, which recovers the optimal solution in the "perfect realism" regime. Lastly, in the case where the source is a stationary GP and $Ω$ is the interval $[0, T]$ equipped with the Lebesgue measure, we derive an upper bound on the rate and the distortion for a fixed perceptual level and $T \to \infty$ as a function of the spectral density of the source process. |
| title | On the Rate-Distortion-Perception Function for Gaussian Processes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.06363 |