{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:21:52Z","timestamp":1787329312293,"version":"build-2736575974"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We consider the problem of detecting edges\u2014jump discontinuities in piecewise smooth functions from their N-degree spectral content, which is assumed to be corrupted by noise. There are three scales involved: the \u201csmoothness\" scale of order $1\/N$, the noise scale of order $\\sqrt{\\eta}$, and the $\\mathcal{O}(1)$ scale of the jump discontinuities. We use concentration factors which are adjusted to the standard deviation of the noise $\\sqrt{\\eta} \\gg 1\/N$ in order to detect the underlying $\\mathcal{O}(1)$-edges, which are separated from the noise scale $\\sqrt{\\eta} \\ll 1$.<\/jats:p>","DOI":"10.1137\/070689899","type":"journal-article","created":{"date-parts":[[2008,7,10]],"date-time":"2008-07-10T14:11:44Z","timestamp":1215699104000},"page":"2620-2635","source":"Crossref","is-referenced-by-count":28,"title":["Recovery of Edges from Spectral Data with Noise\u2014A New Perspective"],"prefix":"10.1137","volume":"46","author":[{"given":"Shlomo","family":"Engelberg","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":[[2008,7,2]]},"reference":[{"key":"R1","first-page":"articl","volume":"3","author":"Cruz-Uribe D.","year":"2002","journal-title":"J. Inequal. Pure Appl. Math."},{"key":"R2","unstructured":"S. Engelberg,\n                      Edge detection using Fourier coefficients\n                      , Amer. Math. Monthly, to appear."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1999.0262"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142999359153"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-007-5298-0"},{"key":"R6","unstructured":"G. Polya and G. Szego,\n                      Problems and Theorems in Analysis\n                      , Vol. I, Springer-Verlag, New York, 1972."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-006-0015-y"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492906320016"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070689899","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:34Z","timestamp":1787325274000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070689899"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":8,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070689899"],"URL":"https:\/\/doi.org\/10.1137\/070689899","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}