# The quadratic Wasserstein metric for inverse data matching

arXiv: https://arxiv.org/abs/1911.06911 · HTML: https://mlsanity.com/paper/1911.06911/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2019.

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

- [Resistance Distance and Linearized Optimal Transport on Graphs](https://mlsanity.com/paper/2404.15261/) (2024)
- [A local squared Wasserstein-2 method for efficient reconstruction of models with uncertainty](https://mlsanity.com/paper/2406.06825/) (2024)
- [Measure-Theoretic Time-Delay Embedding](https://mlsanity.com/paper/2409.08768/) (2024)
- [A Generalized Weighted Optimization Method for Computational Learning and Inversion](https://mlsanity.com/paper/2201.09223/) (2022)
- [HV Metric For Time-Domain Full Waveform Inversion](https://mlsanity.com/paper/2508.17122/) (2025)

## Abstract (arXiv)

This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein (W2) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the infinite-dimensional setup, that the W2 distance has a smoothing effect on the inversion process, making it robust against high-frequency noise in the data but leading to a reduced resolution for the reconstructed objects at a given noise level. Second, we demonstrate that for some finite-dimensional problems, the W2 distance leads to optimization problems that have better convexity than the classical L2 and H-1 distances, making it a more preferred distance to use when solving such inverse matching problems.