{"ID":2862157,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.01015","arxiv_id":"2510.01015","title":"Quantifying the noise sensitivity of the Wasserstein metric for images","abstract":"Wasserstein metrics are increasingly being used as similarity scores for images treated as discrete measures on a grid, yet their behavior under noise remains poorly understood. In this work, we consider the sensitivity of the signed Wasserstein distance with respect to pixel-wise additive noise and derive non-asymptotic upper bounds. Among other results, we prove that the error in the signed 2-Wasserstein distance scales with the square root of the noise standard deviation, whereas the Euclidean norm scales linearly. We present experiments that support our theoretical findings and point to a peculiar phenomenon where increasing the level of noise can decrease the Wasserstein distance. A case study on cryo-electron microscopy images demonstrates that the Wasserstein metric can preserve the geometric structure even when the Euclidean metric fails to do so.","short_abstract":"Wasserstein metrics are increasingly being used as similarity scores for images treated as discrete measures on a grid, yet their behavior under noise remains poorly understood. In this work, we consider the sensitivity of the signed Wasserstein distance with respect to pixel-wise additive noise and derive non-asymptot...","url_abs":"https://arxiv.org/abs/2510.01015","url_pdf":"https://arxiv.org/pdf/2510.01015v2","authors":"[\"Erik Lager\",\"Gilles Mordant\",\"Amit Moscovich\"]","published":"2025-10-01T15:22:12Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}