{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:38:07Z","timestamp":1753886287670,"version":"3.41.2"},"reference-count":20,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2010,4,27]],"date-time":"2010-04-27T00:00:00Z","timestamp":1272326400000},"content-version":"vor","delay-in-days":116,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of\nanisotropic diffusion. By incorporating edges found at multiple scales\nvia an adaptive edge detector\u2010based indicator function, the proposed\nscheme removes noise while respecting salient boundaries. We create\na smooth transition region around probable edges found and reduce\nthe diffusion rate near it by a gradient\u2010based diffusion coefficient. In\ncontrast to the previous anisotropic diffusion schemes, we prove the\nwell\u2010posedness of our scheme in the space of bounded variation. The\nproposed scheme is general in the sense that it can be used with any\nof the existing diffusion equations. Numerical simulations on noisy\nimages show the advantages of our scheme when compared to other\nrelated schemes.<\/jats:p>","DOI":"10.1155\/2010\/763847","type":"journal-article","created":{"date-parts":[[2010,4,27]],"date-time":"2010-04-27T15:31:38Z","timestamp":1272382298000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Well\u2010Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising"],"prefix":"10.1155","volume":"2010","author":[{"given":"V. B. Surya","family":"Prasath","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arindama","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,4,27]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-44588-5"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/34.56205"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/83.541424"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/0729012"},{"key":"e_1_2_7_5_2","unstructured":"StrongD. 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