# Constrained Gaussian Wasserstein Optimal Transport with Commutative Covariance Matrices

arXiv: https://arxiv.org/abs/2503.03744 · HTML: https://mlsanity.com/paper/2503.03744/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 41 references that are in the map.
- First posted on arXiv 5 Mar 2025.

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

- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [DeepJSCC-f: Deep Joint Source-Channel Coding of Images with Feedback](https://mlsanity.com/paper/1911.11174/) (2019)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Generative Joint Source-Channel Coding for Semantic Image Transmission](https://mlsanity.com/paper/2211.13772/) (2022)
- [Universal Rate-Distortion-Perception Representations for Lossy Compression](https://mlsanity.com/paper/2106.10311/) (2021)
- [DeepWiVe: Deep-Learning-Aided Wireless Video Transmission](https://mlsanity.com/paper/2111.13034/) (2021)
- [Bandwidth-Agile Image Transmission with Deep Joint Source-Channel Coding](https://mlsanity.com/paper/2009.12480/) (2020)
- [A coding theorem for the rate-distortion-perception function](https://mlsanity.com/paper/2104.13662/) (2021)
- [On the advantages of stochastic encoders](https://mlsanity.com/paper/2102.09270/) (2021)
- [On Perceptual Lossy Compression: The Cost of Perceptual Reconstruction and An Optimal Training Framework](https://mlsanity.com/paper/2106.02782/) (2021)
- [On the Choice of Perception Loss Function for Learned Video Compression](https://mlsanity.com/paper/2305.19301/) (2023)
- [Rate-Distortion-Perception Tradeoff Based on the Conditional-Distribution Perception Measure](https://mlsanity.com/paper/2401.12207/) (2024)
- [The Rate-Distortion-Perception Trade-off: The Role of Private Randomness](https://mlsanity.com/paper/2404.01111/) (2024)
- [On the Computation of the Gaussian Rate-Distortion-Perception Function](https://mlsanity.com/paper/2311.09190/) (2023)
- [Output-Constrained Lossy Source Coding With Application to Rate-Distortion-Perception Theory](https://mlsanity.com/paper/2403.14849/) (2024)
- [Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization](https://mlsanity.com/paper/2409.02388/) (2024)

## Abstract (arXiv)

Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the destination while minimizing the expected distortion relative to a given random variable/vector at the source. However, in practice, certain constraints may render the optimal transport plan infeasible. In this work, we consider three types of constraints: rate constraints, dimension constraints, and channel constraints, motivated by perception-aware lossy compression, generative principal component analysis, and deep joint source-channel coding, respectively. Special attenion is given to the setting termed Gaussian Wasserstein optimal transport, where both the source and reconstruction variables are multivariate Gaussian, and the end-to-end distortion is measured by the mean squared error. We derive explicit results for the minimum achievable mean squared error under the three aforementioned constraints when the covariance matrices of the source and reconstruction variables commute.