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
Submitted to ArXiV, 10 January 2025
Type:
Conférence
Date:
2025-01-10
Department:
Systèmes de Communication
Eurecom Ref:
8036
Copyright:
© EURECOM. Personal use of this material is permitted. The definitive version of this paper was published in Submitted to ArXiV, 10 January 2025 and is available at :
See also:
PERMALINK : https://www.eurecom.fr/publication/8036