In this paper, we investigate the rate-distortionperception 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–Loeve 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 → ∞ as a function of the spectral density of the source process.
On the rate-distortion-perception function for Gaussian processes
ISIT 2025, IEEE International Symposium on Information Theory, 22-27 June 2025, Ann Arbor, USA
Type:
Conférence
City:
Ann Arbor
Date:
2025-06-22
Department:
Systèmes de Communication
Eurecom Ref:
8036
Copyright:
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PERMALINK : https://www.eurecom.fr/publication/8036