{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T11:56:17Z","timestamp":1714391777248},"reference-count":18,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T00:00:00Z","timestamp":1608508800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2021,8]]},"abstract":"Abstract<\/jats:title>Image denoising is a typical inverse problem and is hard to be solved. Fortunately, a powerful two\u2010phase method for restoring images corrupted by high\u2010level impulse noise has been proposed. The key point of the method is the computational efficiency of the second phase which requires the minimization of a smooth objective function defined on the terms of edge\u2010preserving potential function. In this paper, we propose an effective three\u2010term conjugate gradient method to restore the corrupted images in the second phase of two\u2010phase method. An attractive feature of the proposed method is that the search direction satisfies the sufficient descent property at each iteration without any line search. The global convergence is established for general smooth functions under the Armijo\u2010type line search. Preliminary numerical results are reported to indicate that the proposed method to be used for impulse noise removal is promising.<\/jats:p>","DOI":"10.1002\/nla.2358","type":"journal-article","created":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T22:58:46Z","timestamp":1608591526000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A gradient\u2010type iterative method for impulse noise removal"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-1400-7791","authenticated-orcid":false,"given":"Jinkui","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics Chongqing Three Gorges University Chongqing China"}]},{"given":"Haisong","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics North China University of Water Resources and Electric Power Zhengzhou China"}]},{"given":"Yongxiang","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics Chongqing Three Gorges University Chongqing China"}]},{"given":"Liqiao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Personnel Division Chongqing Three Gorges University Chongqing China"}]}],"member":"311","published-online":{"date-parts":[[2020,12,21]]},"reference":[{"key":"e_1_2_9_2_1","volume-title":"Fundamentals of nonlinear digital filtering","author":"Astola J","year":"1997"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/83.370679"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/31.83870"},{"issue":"8","key":"e_1_2_9_5_1","first-page":"784","article-title":"Space variant median filters for the restoration of impulse noise corrupted images","volume":"48","author":"Chen T","year":"2001","journal-title":"IEEE Trans Circuits\u2010II"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2002.804278"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1023\/B:JMIV.0000011920.58935.9c"},{"issue":"10","key":"e_1_2_9_8_1","first-page":"1479","article-title":"Salt\u2010and\u2010pepper noise removal by median\u2010type noise detector and edge\u2010preserving regularization","volume":"14","author":"Chan RH","year":"2005","journal-title":"J Math Imaging Vis"},{"key":"e_1_2_9_9_1","doi-asserted-by":"crossref","unstructured":"ChanRH HoCW LeungCY NikolovaM. 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