# Characterization of the Distortion-Perception Tradeoff for Finite Channels with Arbitrary Metrics

arXiv: https://arxiv.org/abs/2402.02265 · HTML: https://mlsanity.com/paper/2402.02265/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 24 references that are in the map.
- First posted on arXiv 3 Feb 2024.

## Builds on (most cited first, 13 of 13)

- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [A Theory of the Distortion-Perception Tradeoff in Wasserstein Space](https://mlsanity.com/paper/2107.02555/) (2021)
- [A coding theorem for the rate-distortion-perception function](https://mlsanity.com/paper/2104.13662/) (2021)
- [The Rate-Distortion-Perception Tradeoff: The Role of Common Randomness](https://mlsanity.com/paper/2202.04147/) (2022)
- [Deep Optimal Transport: A Practical Algorithm for Photo-realistic Image Restoration](https://mlsanity.com/paper/2306.02342/) (2023)
- [Optimally Controllable Perceptual Lossy Compression](https://mlsanity.com/paper/2206.10082/) (2022)
- [Information Constrained Optimal Transport: From Talagrand, to Marton, to Cover](https://mlsanity.com/paper/2008.10249/) (2020)
- [Computation of Rate-Distortion-Perception Function under f-Divergence Perception Constraints](https://mlsanity.com/paper/2305.04604/) (2023)
- [Perceptual Kalman Filters: Online State Estimation under a Perfect Perceptual-Quality Constraint](https://mlsanity.com/paper/2306.02400/) (2023)

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

- [Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization](https://mlsanity.com/paper/2409.02388/) (2024)

## Abstract (arXiv)

Whenever inspected by humans, reconstructed signals should not be distinguished from real ones. Typically, such a high perceptual quality comes at the price of high reconstruction error, and vice versa. We study this distortion-perception (DP) tradeoff over finite-alphabet channels, for the Wasserstein-1 distance induced by a general metric as the perception index, and an arbitrary distortion matrix. Under this setting, we show that computing the DP function and the optimal reconstructions is equivalent to solving a set of linear programming problems. We provide a structural characterization of the DP tradeoff, where the DP function is piecewise linear in the perception index. We further derive a closed-form expression for the case of binary sources.