{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T02:06:18Z","timestamp":1768701978643,"version":"3.49.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,5,16]],"date-time":"2022-05-16T00:00:00Z","timestamp":1652659200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,5,16]],"date-time":"2022-05-16T00:00:00Z","timestamp":1652659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004055","name":"King Fahd University of Petroleum and Minerals","doi-asserted-by":"publisher","award":["SB181013"],"award-info":[{"award-number":["SB181013"]}],"id":[{"id":"10.13039\/501100004055","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s40314-022-01865-8","type":"journal-article","created":{"date-parts":[[2022,5,16]],"date-time":"2022-05-16T02:06:10Z","timestamp":1652666770000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["An effective algorithm for mean curvature-based image deblurring problem"],"prefix":"10.1007","volume":"41","author":[{"given":"Faisal","family":"Fairag","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9901-0924","authenticated-orcid":false,"given":"Shahbaz","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,5,16]]},"reference":[{"key":"1865_CR1","doi-asserted-by":"publisher","first-page":"1217","DOI":"10.1088\/0266-5611\/10\/6\/003","volume":"10","author":"R Acar","year":"1994","unstructured":"Acar R, Vogel CR (1994) Analysis of bounded variation penalty methods for ill-posed problems. Inverse Probl 10:1217\u20131229","journal-title":"Inverse Probl"},{"key":"1865_CR2","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1137\/S0895479802417106","volume":"26","author":"M Benzi","year":"2004","unstructured":"Benzi M, Golub GH (2004) A preconditioner for generalized saddle point problems. SIAM J Matrix Anal Appl 26:20\u201341","journal-title":"SIAM J Matrix Anal Appl"},{"key":"1865_CR3","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1137\/080737903","volume":"3","author":"C Brito-Loeza","year":"2010","unstructured":"Brito-Loeza C, Chen K (2010) Multigrid algorithm for high order denoising. SIAM J Imaging Sci 3:363\u2013389","journal-title":"SIAM J Imaging Sci"},{"key":"1865_CR4","doi-asserted-by":"publisher","first-page":"1066","DOI":"10.1002\/num.22042","volume":"32","author":"C Brito-Loeza","year":"2016","unstructured":"Brito-Loeza C, Chen K, Uc-Cetina V (2016) Image denoising using the Gaussian curvature of the image surface. Num Methods Partial Differ Equ 32:1066\u20131089","journal-title":"Num Methods Partial Differ Equ"},{"key":"1865_CR5","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1137\/0909051","volume":"9","author":"TF Chan","year":"1988","unstructured":"Chan TF (1988) An optimal circulant preconditioner for Toeplitz systems. SIAM J Sci Stat Comput 9:766\u2013771","journal-title":"SIAM J Sci Stat Comput"},{"key":"1865_CR6","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1093\/imanum\/11.3.333","volume":"11","author":"RH Chan","year":"1991","unstructured":"Chan RH (1991) Toeplitz preconditioners for Toeplitz systems with nonnegative generating functions. IMA J Numer Anal 11:333\u2013345","journal-title":"IMA J Numer Anal"},{"key":"1865_CR7","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/0024-3795(93)90226-E","volume":"190","author":"RH Chan","year":"1993","unstructured":"Chan RH, Ng K-P (1993) Toeplitz preconditioners for Hermitian Toeplitz systems. Linear Algebra Appl 190:181\u2013208","journal-title":"Linear Algebra Appl"},{"key":"1865_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/00207160.2012.757073","volume":"90","author":"K Chen","year":"2013","unstructured":"Chen K (2013) Introduction to variational image-processing models and applications. Int J Comput Math 90:1\u20138","journal-title":"Int J Comput Math"},{"key":"1865_CR9","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.aml.2014.12.001","volume":"43","author":"C Chen","year":"2015","unstructured":"Chen C, Ma C (2015) A generalized shift-splitting preconditioner for saddle point problems. Appl Math Lett 43:49\u201355","journal-title":"Appl Math Lett"},{"key":"1865_CR10","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1002\/nla.2040","volume":"23","author":"K Chen","year":"2016","unstructured":"Chen K, Fairag F, Al-Mahdi A (2016) Preconditioning techniques for an image deblurring problem. Numer Linear Algebra Appl 23:570\u2013584","journal-title":"Numer Linear Algebra Appl"},{"key":"1865_CR11","volume-title":"Circulant matrices","author":"P Davis","year":"2012","unstructured":"Davis P (2012) Circulant matrices. American Mathematical Society, Providence"},{"key":"1865_CR12","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1553\/etna_vol54s108","volume":"54","author":"F Fairag","year":"2021","unstructured":"Fairag F, Chen K, Ahmad S (2021) Analysis of the CCFD method for mc-based image denoising problems. Electron Trans Numer Anal 54:108\u2013127","journal-title":"Electron Trans Numer Anal"},{"key":"1865_CR13","doi-asserted-by":"crossref","unstructured":"Fairag F, Ahmad S (2019) A two-level method for image deblurring problem. In: 2019 8th International Conference on Modeling Simulation and Applied Optimization (ICMSAO), IEEE, pp.\u00a01\u20135","DOI":"10.1109\/ICMSAO.2019.8880433"},{"key":"1865_CR14","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1023\/A:1016674923507","volume":"26","author":"F-R Lin","year":"2001","unstructured":"Lin F-R (2001) Preconditioners for block Toeplitz systems based on circulant preconditioners. Numer Algorithms 26:365\u2013379","journal-title":"Numer Algorithms"},{"key":"1865_CR15","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1002\/nla.397","volume":"12","author":"F-R Lin","year":"2005","unstructured":"Lin F-R, Ching W-K (2005) Inverse Toeplitz preconditioners for Hermitian Toeplitz systems. Numer Linear Algebra Appl 12:221\u2013229","journal-title":"Numer Linear Algebra Appl"},{"key":"1865_CR16","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/s11075-011-9516-z","volume":"60","author":"F-R Lin","year":"2012","unstructured":"Lin F-R, Wang C-X (2012) BTTB preconditioners for BTTB systems. Numer Algorithms 60:153\u2013167","journal-title":"Numer Algorithms"},{"key":"1865_CR17","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1137\/140962164","volume":"8","author":"M Myllykoski","year":"2015","unstructured":"Myllykoski M, Glowinski R, Karkkainen T, Rossi T (2015) A new augmented Lagrangian approach for $${l}^{1}$$-mean curvature image denoising. SIAM J Imaging Sci 8:95\u2013125","journal-title":"SIAM J Imaging Sci"},{"key":"1865_CR18","volume-title":"Iterative methods for Toeplitz systems","author":"MK Ng","year":"2004","unstructured":"Ng MK (2004) Iterative methods for Toeplitz systems. Oxford University Press, London"},{"key":"1865_CR19","unstructured":"Riley KL (1999) Two-level preconditioners for regularized ill-posed problems. PhD Thesis, Montana State University"},{"key":"1865_CR20","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"LI Rudin","year":"1992","unstructured":"Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D 60:259\u2013268","journal-title":"Physica D"},{"key":"1865_CR21","doi-asserted-by":"publisher","first-page":"2612","DOI":"10.1137\/110858239","volume":"5","author":"H Rui","year":"2012","unstructured":"Rui H, Pan H (2012) A block-centered finite difference method for the Darcy-Forchheimer model. SIAM J Numer Anal 5:2612\u20132631","journal-title":"SIAM J Numer Anal"},{"key":"1865_CR22","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.aml.2015.02.026","volume":"48","author":"DK Salkuyeh","year":"2015","unstructured":"Salkuyeh DK, Masoudi M, Hezari D (2015) On the generalized shift-splitting preconditioner for saddle point problems. Appl Math Lett 48:55\u201361","journal-title":"Appl Math Lett"},{"key":"1865_CR23","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/s10543-013-0448-y","volume":"54","author":"L Sun","year":"2014","unstructured":"Sun L, Chen K (2014) A new iterative algorithm for mean curvature-based variational image denoising. BIT Numer Math 54:523\u2013553","journal-title":"BIT Numer Math"},{"key":"1865_CR24","first-page":"1624","volume":"4","author":"AN Tikhonov","year":"1963","unstructured":"Tikhonov AN (1963) Regularization of incorrectly posed problems. Soviet Math Dokl 4:1624\u20131627","journal-title":"Soviet Math Dokl"},{"key":"1865_CR25","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1109\/83.679423","volume":"7","author":"CR Vogel","year":"1998","unstructured":"Vogel CR, Oman ME (1998) Fast, robust total variation-based reconstruction of noisy, blurred images. IEEE Trans Image Process 7:813\u2013824","journal-title":"IEEE Trans Image Process"},{"key":"1865_CR26","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1137\/090767558","volume":"3","author":"C Wu","year":"2010","unstructured":"Wu C, Tai X-C (2010) Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial tv, and high order models. SIAM J Imaging Sci 3:300\u2013339","journal-title":"SIAM J Imaging Sci"},{"key":"1865_CR27","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.apnum.2011.12.001","volume":"62","author":"F Yang","year":"2012","unstructured":"Yang F, Chen K, Yu B (2012) Homotopy method for a mean curvature-based denoising model. Appl Numer Math 62:185\u2013200","journal-title":"Appl Numer Math"},{"key":"1865_CR28","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1080\/10556788.2013.788650","volume":"29","author":"F Yang","year":"2014","unstructured":"Yang F, Chen K, Yu B, Fang D (2014) A relaxed fixed point method for a mean curvature-based denoising model. Optim Methods Softw 29:274\u2013285","journal-title":"Optim Methods Softw"},{"key":"1865_CR29","doi-asserted-by":"publisher","first-page":"463","DOI":"10.4208\/eajam.010817.160218","volume":"8","author":"J Zhang","year":"2018","unstructured":"Zhang J, Deng C, Shi Y, Wang S, Zhu Y (2018) A fast linearised augmented Lagrangian method for a mean curvature based model. East Asian J Appl Math 8:463\u2013476","journal-title":"East Asian J Appl Math"},{"key":"1865_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/110822268","volume":"5","author":"W Zhu","year":"2012","unstructured":"Zhu W, Chan T (2012) Image denoising using mean curvature of image surface. SIAM J Imaging Sci 5:1\u201332","journal-title":"SIAM J Imaging Sci"},{"key":"1865_CR31","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.3934\/ipi.2013.7.1409","volume":"7","author":"W Zhu","year":"2013","unstructured":"Zhu W, Tai X-C, Chan T (2013) Augmented Lagrangian method for a mean curvature based image denoising model. Inverse Probl Imaging 7:1409\u20131432","journal-title":"Inverse Probl Imaging"},{"key":"1865_CR32","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1007\/978-3-642-54774-4_5","volume-title":"Efficient algorithms for global optimization methods in computer vision","author":"W Zhu","year":"2014","unstructured":"Zhu W, Tai X-C, Chan T (2014) A fast algorithm for a mean curvature based image denoising model using augmented lagrangian method. In: Bruhn A, Pock T, Tai XC (eds) Efficient algorithms for global optimization methods in computer vision. Springer, Berlin, pp 104\u2013118"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01865-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-022-01865-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01865-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T20:52:50Z","timestamp":1654807970000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-022-01865-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,16]]},"references-count":32,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["1865"],"URL":"https:\/\/doi.org\/10.1007\/s40314-022-01865-8","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,16]]},"assertion":[{"value":"26 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 March 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 March 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"176"}}