# Alternating Minimization Schemes for Computing Rate-Distortion-Perception Functions with f-Divergence Perception Constraints

arXiv: https://arxiv.org/abs/2408.15015 · HTML: https://mlsanity.com/paper/2408.15015/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 49 references that are in the map.
- First posted on arXiv 27 Aug 2024.

## Builds on (most cited first, 16 of 16)

- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [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)
- [Semantics-Empowered Communication for Networked Intelligent Systems](https://mlsanity.com/paper/2007.11579/) (2020)
- [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)
- [Towards Empirical Sandwich Bounds on the Rate-Distortion Function](https://mlsanity.com/paper/2111.12166/) (2021)
- [On the Choice of Perception Loss Function for Learned Video Compression](https://mlsanity.com/paper/2305.19301/) (2023)
- [Computation of Rate-Distortion-Perception Function under f-Divergence Perception Constraints](https://mlsanity.com/paper/2305.04604/) (2023)
- [Estimating the Rate-Distortion Function by Wasserstein Gradient Descent](https://mlsanity.com/paper/2310.18908/) (2023)
- [On the Computation of the Gaussian Rate-Distortion-Perception Function](https://mlsanity.com/paper/2311.09190/) (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)
- [A Practical Approach for Rate-Distortion-Perception Analysis in Learned Image Compression](https://mlsanity.com/paper/2104.14836/) (2021)

## Built on by (most cited first, 1 of 1)

- [Rate-Distortion-Perception Theory: Redefining the Fundamental Limits of Information Representation](https://mlsanity.com/paper/2607.17232/) (2026)

## Abstract (arXiv)

We study the computation of the rate-distortion-perception function (RDPF) for discrete memoryless sources subject to a single-letter average distortion constraint and a perception constraint belonging to the family of f-divergences. In this setting, the RDPF forms a convex programming problem for which we characterize optimal parametric solutions. We employ the developed solutions in an alternating minimization scheme, namely Optimal Alternating Minimization (OAM), for which we provide convergence guarantees. Nevertheless, the OAM scheme does not lead to a direct implementation of a generalized Blahut-Arimoto (BA) type of algorithm due to implicit equations in the iteration's structure. To overcome this difficulty, we propose two alternative minimization approaches whose applicability depends on the smoothness of the used perception metric: a Newton-based Alternating Minimization (NAM) scheme, relying on Newton's root-finding method for the approximation of the optimal solution of the iteration, and a Relaxed Alternating Minimization (RAM) scheme, based on relaxing the OAM iterates. We show, by deriving necessary and sufficient conditions, that both schemes guarantee convergence to a globally optimal solution. We also provide sufficient conditions on the distortion and perception constraints, which guarantee that the proposed algorithms converge exponentially fast in the number of iteration steps. We corroborate our theoretical results with numerical simulations and establish connections with existing results.