{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T00:49:05Z","timestamp":1787359745928,"version":"build-2736575974"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>A novel approach for multiscale image processing based on integro-differential equations (IDEs) was proposed in [E. Tadmor and P. Athavale, Inverse Probl. Imaging, 3 (2009), pp. 693\u2013710]. These IDEs, which stem naturally from multiscale $(BV,L^2)$ hierarchical decompositions, yield inverse scale representations of images in the sense that the $BV$-dual norms of their residuals are inversely proportional to the scaling parameters. Motivated by the fact that $(BV,L^1)$ decomposition is more suitable for extracting local scale-space features than $(BV,L^2)$, we introduce here the IDEs which arise from multiscale $(BV,L^1)$ hierarchical decompositions. We study several variants of this $(BV,L^1)$-based IDE model, depending on modifications to the curvature term.<\/jats:p>","DOI":"10.1137\/100795504","type":"journal-article","created":{"date-parts":[[2011,3,17]],"date-time":"2011-03-17T18:18:20Z","timestamp":1300385900000},"page":"300-312","source":"Crossref","is-referenced-by-count":12,"title":["Integro-Differential Equations Based on $(BV, L^1)$ Image Decomposition"],"prefix":"10.1137","volume":"4","author":[{"given":"Prashant","family":"Athavale","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eitan","family":"Tadmor","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,3,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/060662617"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/070698749"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/070711128"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/78.139258"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0729052"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"L. 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