Perceptual lossy compression rate for two correlated Gaussian sources

Official URL: https://dx.doi.org/10.1109/LCOMM.2025.3594598

Progress has been made in deriving analytical solutions for the Rate-Distortion Function (RDF) in the case of correlated sources. Extending these results to incorporate perceptual constraints yields the Rate-Distortion-Perception Function (RDPF) and presents persistent challenges even in the relatively simple case of Gaussian sources. The inherent asymmetry of perceptual constraints, commonly quantified by the Kullback-Leibler (KL) divergence, raises uncertainties about whether encoding a Gaussian source into Gaussian-distributed codewords is optimal. Restricting the search space without proof may overlook superior alternatives. In this study, we examine the case of two correlated Gaussian sources under individual fidelity constraints addressing both perceptual quality and distortion. In the presence of perception constraints (KL-divergence), we prove that the optimal strategy involves encoding the correlated Gaussian sources into a pair of Gaussian distributed codewords. Then, we explicitly express the correlation between the encoded messages. Moreover, we derive the RDPF as a solution to an optimization problem involving four variables intricately linked to encoded and source information statistics.