{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:42Z","timestamp":1787337222673,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>Many applications show that nonconvex nonsmooth regularization has advantages for restoring images with neat edges. This phenomenon has been provided as a mathematical explanation for the anisotropic model through establishing a uniform lower bound for nonzero gradients of recovered images. For nonconvex and nonsmooth regularization using potential functions composed of the $\\ell_2$ norm of the image gradient, i.e., the isotropic model, there lack reasonable theoretical results in the literature. Based on some properties of image gradient fields not considered previously, we obtain a uniform lower bound for the nonzero gradients of recovered images for the isotropic model, which implies the edge recovery property of this model. Our theoretical results are illustrated using a numerical experiment.<\/jats:p>","DOI":"10.1137\/17m1123687","type":"journal-article","created":{"date-parts":[[2018,4,26]],"date-time":"2018-04-26T12:10:09Z","timestamp":1524744609000},"page":"1168-1182","source":"Crossref","is-referenced-by-count":28,"title":["On the Edge Recovery Property of Noncovex Nonsmooth Regularization in Image Restoration"],"prefix":"10.1137","volume":"56","author":[{"given":"Chao","family":"Zeng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chunlin","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,4,26]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2009.2031231"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/140985639"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1561\/2200000016"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1017\/S096249291600009X"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2014.2329274"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2012.2214051"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/090761471"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/080740167"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/11085997X"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2015.9.337"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2011.05.002"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/110854746"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-014-9860-y"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/040619582"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2010.2052275"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/10080172X"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/070692285"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/130942954"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/140971518"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90242-F"},{"key":"atypb22","volume-title":"Solutions of ill-posed problems","author":"Tikhonov A. 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