{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T05:34:36Z","timestamp":1788845676747,"version":"build-2803163510"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T00:00:00Z","timestamp":1581033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009068","name":"Consejo Nacional de Innovaci\u00f3n, Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["11190116"],"award-info":[{"award-number":["11190116"]}],"id":[{"id":"10.13039\/501100009068","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008745","name":"UNAB","doi-asserted-by":"publisher","award":["DI-03-19\/R"],"award-info":[{"award-number":["DI-03-19\/R"]}],"id":[{"id":"10.13039\/501100008745","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282\u2013288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the R\u00e9nyi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case,     \u03b1 = 2    ) self-similar processes.<\/jats:p>","DOI":"10.3390\/e22020196","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T11:50:28Z","timestamp":1581076228000},"page":"196","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields"],"prefix":"10.3390","volume":"22","author":[{"given":"Orietta","family":"Nicolis","sequence":"first","affiliation":[{"name":"Facultad de Ingenieria, Universidad Andres Bello, Vi\u00f1a del Mar 2520000, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2868-7604","authenticated-orcid":false,"given":"Jorge","family":"Mateu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universitat Jaume I, E-12071 Castellon, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1172-5456","authenticated-orcid":false,"given":"Javier E.","family":"Contreras-Reyes","sequence":"additional","affiliation":[{"name":"Departamento de Estadistica, Universidad del Bio-Bio, Concepcion 4081112, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1002\/andp.18501550403","article-title":"On the motive power of heat, and on the laws which may be deduced from it for the theory of heat","volume":"368","author":"Clausius","year":"1850","journal-title":"Annalen der Physick"},{"key":"ref_2","first-page":"679","article-title":"Einige allgemeine Satze iiber Warmegleichgewicht unter Gas- molekulen","volume":"63","author":"Boltzmann","year":"1871","journal-title":"Sitzungsber. 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