{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T12:16:20Z","timestamp":1648988180857},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2009]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider image denoising as the problem of removing spurious\noscillations due to noise while preserving edges in the images. We will suggest here\nhow to directly make infinitesimal adjustment to standard variational methods of\nimage denoising, to enhance desirable target assumption of the noiseless image. The\nstandard regularization method is used to define a suitable energy functional to\npenalize the data fidelity and the smoothness of the solution. This energy functional\nis tailored so that the region with small gradient is isotropically smoothed whereas in\na neighborhood of an edge presented by a large gradient smoothing is allowed only\nalong the edge contour. The regularized solution that arises in this fashion is then the\nsolution of a variational principle.\nTo this end the associated Euler \u2014 Lagrange equation needs to be solved numerically\nand the half-quadratic minimization is generally used to linearize the equation and to\nderive an iterative scheme. We describe here a method to modify Euler \u2014 Largrange\nequation from commonly used energy functionals, in a way to enhance certain desirable\npreconceived assumptions of the image, such as edge preservation. From an algorithmic\npoint of view, we may deem this algorithm as a smoothing by a local average with an\nadaptive gradient-based weight. However, this algorithm may result in noisy edges\nalthough the edge is preserved and noise is suppressed in the low-gradient regions of\nthe image. The main focus here is to present an edge-preserving regularization in the\naforementioned view point, and to provide an alternative and simple way to modify the\nexisting algorithm to mitigate the phenomena of noisy edges without explicitly defining\nstep where we specify an energy functional to be minimized.<\/jats:p>","DOI":"10.2478\/cmam-2009-0019","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T15:50:32Z","timestamp":1366041032000},"page":"309-318","source":"Crossref","is-referenced-by-count":1,"title":["Image Edge Respecting Denoising with Edge Denoising by a Designer Nonisotropic Structure Tensor Method"],"prefix":"10.2478","volume":"9","author":[{"given":"N.","family":"Santitissadeekorn","sequence":"first","affiliation":[{"name":"1School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia."}]},{"given":"E.M.","family":"Bollt","sequence":"additional","affiliation":[{"name":"2Department of Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699-5815, USA."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/3\/article-p309.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2009-0019\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:29Z","timestamp":1619101289000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/3\/article-p309.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2009-0019","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}