FOUNDS Seminar Series Talk 06 - Computation of the Rate-Distortion-Perception Function

Talk Abstract: In this talk, we study methods for the computation of a generalization of the rate-distortion function called the rate-distortion-perception function (RDPF). This generalization to the rate-distortion problem was defined by the computer vision and machine learning community in recent years, to give a mathematical interpretation to the observation that “low distortion” is not a synonym for “high perceptual quality”, and, from an optimization perspective, there is a tradeoff between the distortion and the perception. The RDPF is also a relevant semantic-based metric in compression. For discrete sources, with single-letter distortion and a perception constraint that belongs to the family of f-divergences, we compute the RDPF by proposing an approximate alternating minimization approach a la Blahut-Arimoto algorithm that converges to a globally optimal point. For scalar Gaussian sources with squared error distortion and a perception constraint that can be either the KL divergence, the squared Wasserstein distance, the squared Hellinger distance, or the geometric Jensen-Shannon divergence, we derive closed-form expressions under the assumption of jointly Gaussian processes. Our closed-form solutions are also supported by their corresponding test-channel forward realizations, the first of their kind. For vector Gaussian sources, we propose a generic alternating minimization algorithm using a block-coordinated descent method that can optimally compute the vector Gaussian RDPF. For the extreme case of the perfect-realism vector Gaussian RDPF, that is to say, when the Gaussian distribution of the source and the reconstruction are constrained to be the same, we derive in closed-form solution a new optimal adaptive reverse-water- filling solution. We corroborate our findings with various simulation studies.