mlsanityData to 14 Oct 2026

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

arXiv 2408.15015 ↗First posted 27 Aug 2024cs.IT cs.CV eess.SPcited by 1

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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.

Key facts. Cited by 1 paper 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

16 of 49 references.

References · 16

  1. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,908
  2. 2018Joint Autoregressive and Hierarchical Priors for Learned Image Compressioncited by 664
  3. 2020High-Fidelity Generative Image Compressioncited by 338
  4. 2018Generative Adversarial Networks for Extreme Learned Image Compressioncited by 219
  5. 2019Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoffcited by 211
  6. 2020Semantics-Empowered Communication for Networked Intelligent Systemscited by 63
  7. 2021Universal Rate-Distortion-Perception Representations for Lossy Compressioncited by 47
  8. 2021A coding theorem for the rate-distortion-perception functioncited by 30
  9. 2021Towards Empirical Sandwich Bounds on the Rate-Distortion Functioncited by 14
  10. 2023On the Choice of Perception Loss Function for Learned Video Compressioncited by 10
  11. 2023Computation of Rate-Distortion-Perception Function under f-Divergence Perception Constraintscited by 6
  12. 2023Estimating the Rate-Distortion Function by Wasserstein Gradient Descentcited by 5
4 more
  1. 2023On the Computation of the Gaussian Rate-Distortion-Perception Functioncited by 5
  2. 2018Deformation Aware Image Compressioncited by 4
  3. 2020Distributed Learning and Inference with Compressed Imagescited by 3
  4. 2021A Practical Approach for Rate-Distortion-Perception Analysis in Learned Image Compressioncited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Rate-Distortion-Perception Theory: Redefining the Fundamental Limits of Information Representationcited by 0