| Title: |
The equivalence of Fourier-based and Wasserstein metrics on imaging problems |
| Authors: |
Gennaro Auricchio; Andrea Codegoni; Stefano Gualandi; Giuseppe Toscani; Marco Veneroni |
| Contributors: |
Auricchio, Gennaro; Codegoni, Andrea; Gualandi, Stefano; Toscani, Giuseppe; Veneroni, Marco |
| Publisher Information: |
European Mathematical Society Publishing House |
| Publication Year: |
2020 |
| Collection: |
Padua Research Archive (IRIS - Università degli Studi di Padova) |
| Subject Terms: |
Fourier transform; Fourier-based metric; Image analysi; Wasserstein distance |
| Description: |
We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At di erence with the original one, the new Fourier-based metrics are well-defined also for probability distributions with di erent centers of mass, and for discrete probability measures supported over a regular grid. Among other properties, it is shown that, in the discrete setting, these new Fourier-based metrics are equivalent either to the Euclidean-Wasserstein distance W2, or to the Kantorovich-Wasserstein distance W1, with explicit constants of equivalence. Numerical results then show that in benchmark problems of image processing, Fourier metrics provide a better runtime with respect to Wasserstein ones. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/wos/WOS:000587437700008; volume:31; issue:3; firstpage:627; lastpage:649; journal:ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI; https://hdl.handle.net/11577/3528341 |
| DOI: |
10.4171/RLM/908 |
| Availability: |
https://hdl.handle.net/11577/3528341; https://doi.org/10.4171/RLM/908 |
| Rights: |
info:eu-repo/semantics/openAccess ; license:Accesso libero ; license uri:iris.PUB01 |
| Accession Number: |
edsbas.FD871848 |
| Database: |
BASE |