{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T04:27:32Z","timestamp":1649219252042},"reference-count":35,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2007,11]]},"abstract":"<jats:p> In this paper we present a new efficient iterative nonlinear scheme for recovering of a piecewise constant image from an observed image containing additive noise. We apply an adaptive neighborhood filter which comes from robust statistics and completely rejects outliers being greater than a certain constant. We prove that the iterated application of the scheme leads to a piecewise constant image. This observation generalizes the known results on convergence of nonlinear diffusion schemes to a constant steady-state. Moreover, we show that the partition of the image determining the piecewise constant steady-state after an infinite iteration process can already be found after a finite number of iteration steps. This result can be used for a fast approximation of the piecewise constant image by a mean value procedure. We examine the relations of our scheme to average and bilateral filtering, diffusion filtering and wavelet shrinkage. Numerical experiments illustrate the performance of the algorithm. <\/jats:p>","DOI":"10.1142\/s0219691307002142","type":"journal-article","created":{"date-parts":[[2007,11,5]],"date-time":"2007-11-05T05:38:21Z","timestamp":1194241101000},"page":"975-995","source":"Crossref","is-referenced-by-count":2,"title":["CONVERGENCE OF AN ITERATIVE NONLINEAR SCHEME FOR DENOISING OF PIECEWISE CONSTANT IMAGES"],"prefix":"10.1142","volume":"05","author":[{"given":"GERLIND","family":"PLONKA","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Duisburg-Essen, Campus Duisburg, 47048 Duisburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JIANWEI","family":"MA","sequence":"additional","affiliation":[{"name":"Laboratoire LMC-IMAG, University Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/S003614299529230X"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2002.1008390"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/83.661192"},{"key":"rf4","first-page":"60","volume":"2","author":"Buades A.","journal-title":"Comput. 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