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As usual for many variational problems in image analysis and processing, the energy we minimize consists of two terms: a data-fitting term and a regularization term. The main feature of our approach consists of choosing parameters in the regularization term adaptively. Namely, the regularization term is given by a weighted<jats:inline-formula><jats:alternatives><jats:tex-math>$$p(\\cdot )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>p<\/mml:mi><mml:mo>(<\/mml:mo><mml:mo>\u00b7<\/mml:mo><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-Dirichlet-based energy<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\int \\!a({\\varvec{x}}){\\,\\!|\\,\\!}\\nabla u {\\,\\!|\\,\\!}^{p({\\varvec{x}})}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mo>\u222b<\/mml:mo><mml:mspace\/><mml:mi>a<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mrow><mml:mspace\/><mml:mspace\/><mml:mo>|<\/mml:mo><mml:mspace\/><mml:mspace\/><\/mml:mrow><mml:mi>\u2207<\/mml:mi><mml:mi>u<\/mml:mi><mml:msup><mml:mrow><mml:mspace\/><mml:mspace\/><mml:mo>|<\/mml:mo><mml:mspace\/><mml:mspace\/><\/mml:mrow><mml:mrow><mml:mi>p<\/mml:mi><mml:mo>(<\/mml:mo><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, where the weight and exponent functions are determined from an analysis of the spectral content of the image curvature. Our numerical experiments, both qualitative and quantitative, suggest that the proposed approach delivers better results than state-of-the-art methods for extracting the structure from textured and mosaic images, as well as competitive results on image enhancement problems.<\/jats:p>","DOI":"10.1007\/s00138-023-01432-z","type":"journal-article","created":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T13:02:01Z","timestamp":1691672521000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Variable exponent diffusion for image detexturing"],"prefix":"10.1007","volume":"34","author":[{"given":"Pierre-Alain","family":"Fayolle","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7043-8847","authenticated-orcid":false,"given":"Alexander G.","family":"Belyaev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,8,10]]},"reference":[{"issue":"2","key":"1432_CR1","doi-asserted-by":"publisher","first-page":"982","DOI":"10.1109\/TIP.2016.2639450","volume":"26","author":"X Guo","year":"2017","unstructured":"Guo, X., Li, Y., Ling, H.: LIME: low-light image enhancement via illumination map estimation. 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