# On the Computation of the Gaussian Rate-Distortion-Perception Function

arXiv: https://arxiv.org/abs/2311.09190 · HTML: https://mlsanity.com/paper/2311.09190/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 44 references that are in the map.
- First posted on arXiv 15 Nov 2023.

## Builds on (most cited first, 19 of 19)

- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [High-Fidelity Generative Image Compression](https://mlsanity.com/paper/2006.09965/) (2020)
- [Generative Adversarial Networks for Extreme Learned Image Compression](https://mlsanity.com/paper/1804.02958/) (2018)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Lossy Compression with Gaussian Diffusion](https://mlsanity.com/paper/2206.08889/) (2022)
- [Semantics-Empowered Communication for Networked Intelligent Systems](https://mlsanity.com/paper/2007.11579/) (2020)
- [On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means](https://mlsanity.com/paper/1904.04017/) (2019)
- [Universal Rate-Distortion-Perception Representations for Lossy Compression](https://mlsanity.com/paper/2106.10311/) (2021)
- [A coding theorem for the rate-distortion-perception function](https://mlsanity.com/paper/2104.13662/) (2021)
- [ProxIQA: A Proxy Approach to Perceptual Optimization of Learned Image Compression](https://mlsanity.com/paper/1910.08845/) (2019)
- [The Rate-Distortion-Perception Tradeoff: The Role of Common Randomness](https://mlsanity.com/paper/2202.04147/) (2022)
- [Computation of Rate-Distortion-Perception Function under f-Divergence Perception Constraints](https://mlsanity.com/paper/2305.04604/) (2023)
- [Deformation Aware Image Compression](https://mlsanity.com/paper/1804.04593/) (2018)
- [Distributed Learning and Inference with Compressed Images](https://mlsanity.com/paper/2004.10497/) (2020)
- [Independent Gaussian Distributions Minimize the Kullback-Leibler (KL) Divergence from Independent Gaussian Distributions](https://mlsanity.com/paper/2011.02560/) (2020)
- [A Practical Approach for Rate-Distortion-Perception Analysis in Learned Image Compression](https://mlsanity.com/paper/2104.14836/) (2021)
- [Characterization and Computation of Matrices of Maximal Trace over Rotations](https://mlsanity.com/paper/1908.08824/) (2019)

## Built on by (most cited first, 5 of 5)

- [Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization](https://mlsanity.com/paper/2409.02388/) (2024)
- [Alternating Minimization Schemes for Computing Rate-Distortion-Perception Functions with f-Divergence Perception Constraints](https://mlsanity.com/paper/2408.15015/) (2024)
- [Constrained Gaussian Wasserstein Optimal Transport with Commutative Covariance Matrices](https://mlsanity.com/paper/2503.03744/) (2025)
- [Two tales for a geometric Jensen--Shannon divergence](https://mlsanity.com/paper/2508.05066/) (2025)
- [Rate-Distortion-Perception Theory: Redefining the Fundamental Limits of Information Representation](https://mlsanity.com/paper/2607.17232/) (2026)

## Abstract (arXiv)

In this paper, we study the computation of the rate-distortion-perception function (RDPF) for a multivariate Gaussian source under mean squared error (MSE) distortion and, respectively, Kullback-Leibler divergence, geometric Jensen-Shannon divergence, squared Hellinger distance, and squared Wasserstein-2 distance perception metrics. To this end, we first characterize the analytical bounds of the scalar Gaussian RDPF for the aforementioned divergence functions, also providing the RDPF-achieving forward "test-channel" realization. Focusing on the multivariate case, we establish that, for tensorizable distortion and perception metrics, the optimal solution resides on the vector space spanned by the eigenvector of the source covariance matrix. Consequently, the multivariate optimization problem can be expressed as a function of the scalar Gaussian RDPFs of the source marginals, constrained by global distortion and perception levels. Leveraging this characterization, we design an alternating minimization scheme based on the block nonlinear Gauss-Seidel method, which optimally solves the problem while identifying the Gaussian RDPF-achieving realization. Furthermore, the associated algorithmic embodiment is provided, as well as the convergence and the rate of convergence characterization. Lastly, for the "perfect realism" regime, the analytical solution for the multivariate Gaussian RDPF is obtained. We corroborate our results with numerical simulations and draw connections to existing results.