{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:16:10Z","timestamp":1760148970599,"version":"build-2065373602"},"reference-count":64,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T00:00:00Z","timestamp":1687910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Data-centric inverse problems are a process of inferring physical attributes from indirect measurements. Full-waveform inversion (FWI) is a non-linear inverse problem that attempts to obtain a quantitative physical model by comparing the wave equation solution with observed data, optimizing an objective function. However, the FWI is strenuously dependent on a robust objective function, especially for dealing with cycle-skipping issues and non-Gaussian noises in the dataset. In this work, we present an objective function based on the Kaniadakis \u03ba-Gaussian distribution and the optimal transport (OT) theory to mitigate non-Gaussian noise effects and phase ambiguity concerns that cause cycle skipping. We construct the \u03ba-objective function using the probabilistic maximum likelihood procedure and include it within a well-posed version of the original OT formulation, known as the Kantorovich\u2013Rubinstein metric. We represent the data in the graph space to satisfy the probability axioms required by the Kantorovich\u2013Rubinstein framework. We call our proposal the \u03ba-Graph-Space Optimal Transport FWI (\u03ba-GSOT-FWI). The results suggest that the \u03ba-GSOT-FWI is an effective procedure to circumvent the effects of non-Gaussian noise and cycle-skipping problems. They also show that the Kaniadakis \u03ba-statistics significantly improve the FWI objective function convergence, resulting in higher-resolution models than classical techniques, especially when \u03ba=0.6.<\/jats:p>","DOI":"10.3390\/e25070990","type":"journal-article","created":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T01:53:57Z","timestamp":1688003637000},"page":"990","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Graph-Space Optimal Transport Approach Based on Kaniadakis \u03ba-Gaussian Distribution for Inverse Problems Related to Wave Propagation"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6384-5049","authenticated-orcid":false,"given":"S\u00e9rgio Luiz E. F.","family":"da Silva","sequence":"first","affiliation":[{"name":"Department of Applied Science and Technology, Politecnico di Torino, 10129 Torino, Italy"},{"name":"Geoscience Institute, Fluminense Federal University, Niter\u00f3i 24210-346, RJ, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8462-4280","authenticated-orcid":false,"given":"Jo\u00e3o M.","family":"de Ara\u00fajo","sequence":"additional","affiliation":[{"name":"Department of Theoretical and Experimental Physics, Federal University of Rio Grande do Norte, Natal 59072-970, RN, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0625-4875","authenticated-orcid":false,"given":"Erick","family":"de la Barra","sequence":"additional","affiliation":[{"name":"School of Business, Universidad Cat\u00f3lica del Norte, Coquimbo 1780000, CO, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1748-4040","authenticated-orcid":false,"given":"Gilberto","family":"Corso","sequence":"additional","affiliation":[{"name":"Department of Theoretical and Experimental Physics, Federal University of Rio Grande do Norte, Natal 59072-970, RN, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Razavy, M. 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