{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:42Z","timestamp":1740123942785,"version":"3.37.3"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T00:00:00Z","timestamp":1671667200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T00:00:00Z","timestamp":1671667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100017142","name":"GNCS","doi-asserted-by":"crossref","award":["2021"],"award-info":[{"award-number":["2021"]}],"id":[{"id":"10.13039\/100017142","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s10444-022-10000-4","type":"journal-article","created":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T11:37:48Z","timestamp":1671709068000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Ternary image decomposition with automatic parameter selection via auto- and cross-correlation"],"prefix":"10.1007","volume":"49","author":[{"given":"Laura","family":"Girometti","sequence":"first","affiliation":[]},{"given":"Alessandro","family":"Lanza","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8334-8798","authenticated-orcid":false,"given":"Serena","family":"Morigi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,12,22]]},"reference":[{"key":"10000_CR1","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s10851-005-4783-8","volume":"22","author":"JF Aujol","year":"2005","unstructured":"Aujol, J.F., Aubert, G., Blanc-Feraud, L., Chambolle, A.: Image decomposition into a bounded variation component and an oscillating component. J. Math. Imaging Vis. 22, 71\u201388 (2005)","journal-title":"J. Math. Imaging Vis."},{"key":"10000_CR2","first-page":"84","volume":"63","author":"JF Aujol","year":"2005","unstructured":"Aujol, J.F., Chambolle, A.: Dual norms and image decomposition models. J. Math. Imaging Vis. 63, 84\u2013104 (2005)","journal-title":"J. Math. Imaging Vis."},{"key":"10000_CR3","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s11263-006-4331-z","volume":"67","author":"JF Aujol","year":"2006","unstructured":"Aujol, J.F., Gilboa, G., Chan, T., Osher, S.: Structure-texture image decomposition\u2014modeling, algorithms, and parameter selection. Int. J. Comput. Vision 67, 111\u2013136 (2006)","journal-title":"Int. J. Comput. Vision"},{"issue":"3","key":"10000_CR4","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1007\/s00211-017-0916-4","volume":"138","author":"R Chan","year":"2018","unstructured":"Chan, R., Lanza, A., Morigi, S., Sgallari, F.: Convex non-convex image segmentation. Numer. Math. 138(3), 635\u2013680 (2018)","journal-title":"Numer. Math."},{"key":"10000_CR5","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/s10851-007-0020-y","volume":"28","author":"J Gilles","year":"2007","unstructured":"Gilles, J.: Noisy image decomposition: a new structure, texture and noise model based on local adaptivity. J. Math. Imaging Vis. 28, 285\u2013295 (2007)","journal-title":"J. Math. Imaging Vis."},{"key":"10000_CR6","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.1137\/120881579","volume":"10","author":"J Gilles","year":"2012","unstructured":"Gilles, J.: Noisy multiscale texture separation. Multiscale Model. Simul. 10, 1409\u20131427 (2012)","journal-title":"Multiscale Model. Simul."},{"key":"10000_CR7","doi-asserted-by":"publisher","first-page":"2793","DOI":"10.1109\/TIP.2010.2049946","volume":"19","author":"J Gilles","year":"2010","unstructured":"Gilles, J., Meyer, Y.: Properties of BV-G structures + textures decomposition models. Application to road detection in satellite images. IEEE Trans. Image Process. 19, 2793\u20132800 (2010)","journal-title":"IEEE Trans. Image Process."},{"key":"10000_CR8","doi-asserted-by":"publisher","first-page":"124008","DOI":"10.1088\/1361-6420\/ab2d44","volume":"35","author":"M Huska","year":"2019","unstructured":"Huska, M., Lanza, A., Morigi, S., Selesnick, I.: A convex-nonconvex variational method for the additive decomposition of functions on surfaces. Inverse Probl. 35, 124008 (2019)","journal-title":"Inverse Probl."},{"issue":"4","key":"10000_CR9","doi-asserted-by":"publisher","first-page":"1749","DOI":"10.1137\/20M1355987","volume":"14","author":"M Huska","year":"2021","unstructured":"Huska, M., Kang, S.H., Lanza, A., Morigi, S.: A variational approach to additive image decomposition into structure, harmonic, and oscillatory components. SIAM J. Imaging Sci. 14(4), 1749\u20131789 (2021)","journal-title":"SIAM J. Imaging Sci."},{"key":"10000_CR10","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s10851-014-0549-5","volume":"53","author":"A Lanza","year":"2015","unstructured":"Lanza, A., Morigi, S., Sgallari, F.: Variational image restoration with constraints on noise whiteness. J. Math Imaging Vis 53, 61\u201377 (2015)","journal-title":"J. Math Imaging Vis"},{"key":"10000_CR11","doi-asserted-by":"publisher","first-page":"1503","DOI":"10.1007\/s10851-018-0845-6","volume":"60","author":"A Lanza","year":"2018","unstructured":"Lanza, A., Morigi, S., Sciacchitano, F., Sgallari, F.: Whiteness constraints in a unified variational framework for image restoration. J. Math. Imaging Vis. 60, 1503\u20131526 (2018)","journal-title":"J. Math. Imaging Vis."},{"key":"10000_CR12","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s10851-016-0655-7","volume":"56","author":"A Lanza","year":"2016","unstructured":"Lanza, A., Morigi, S., Sgallari, F.: Convex image denoising via non-convex regularization with parameter selection. J. Math. Imaging Vis. 56, 195\u2013220 (2016)","journal-title":"J. Math. Imaging Vis."},{"issue":"2","key":"10000_CR13","doi-asserted-by":"publisher","first-page":"1099","DOI":"10.1137\/18M1199149","volume":"12","author":"A Lanza","year":"2019","unstructured":"Lanza, A., Morigi, S., Selesnick, I.W., Sgallari, F.: Sparsity-inducing nonconvex nonseparable regularization for convex image processing. SIAM J. Imaging Sci. 12(2), 1099\u20131134 (2019)","journal-title":"SIAM J. Imaging Sci."},{"key":"10000_CR14","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1553\/etna_vol53s329","volume":"53","author":"A Lanza","year":"2020","unstructured":"Lanza, A., Pragliola, M., Sgallari, F.: Residual whiteness principle for parameter-free image restoration. Electron. Trans. Numer. Anal. 53, 329\u2013351 (2020)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"10000_CR15","volume-title":"Convex non-Convex Variational Models, Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging","author":"A Lanza","year":"2022","unstructured":"Lanza, A., Morigi, S., Selesnick, I.W., Sgallari, F.: Convex non-Convex Variational Models, Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Berlin (2022)"},{"issue":"12","key":"10000_CR16","doi-asserted-by":"publisher","first-page":"1450","DOI":"10.1109\/TIP.2002.806241","volume":"11","author":"F Malgouyres","year":"2002","unstructured":"Malgouyres, F.: Minimizing the total variation under a general convex constraint for image restoration. IEEE Trans. Image Process. 11(12), 1450\u20131456 (2002)","journal-title":"IEEE Trans. Image Process."},{"doi-asserted-by":"crossref","unstructured":"Meyer, Y.: Oscillating patterns in image processing and nonlinear evolution equations: the fifteenth Dean Jacqueline B. Lewis Memorial Lectures. American mathematical society, USA (2001)","key":"10000_CR17","DOI":"10.1090\/ulect\/022"},{"issue":"3","key":"10000_CR18","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1137\/S1540345902416247","volume":"1","author":"SJ Osher","year":"2003","unstructured":"Osher, S.J., Sole, A., Vese, L.A.: Image decomposition and restoration using total variation minimization and the H\u2212\u20091 norm. SIAM J. Multiscale Model. Simul. 1(3), 349\u2013370 (2003)","journal-title":"SIAM J. Multiscale Model. Simul."},{"key":"10000_CR19","volume-title":"Image decomposition using total variation and div(bmo)","author":"TM Le","year":"2004","unstructured":"Le, T.M., Vese, L.: Image decomposition using total variation and div(bmo). CAM04-76, UCLA (2004)"},{"issue":"1-3","key":"10000_CR20","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1023\/A:1025384832106","volume":"19","author":"LA Vese","year":"2003","unstructured":"Vese, L.A., Osher, S.J.: Modeling textures with total variation minimization and oscillating patterns in image processing. J. Sci. Comput. 19(1-3), 553\u2013572 (2003)","journal-title":"J. Sci. Comput."},{"key":"10000_CR21","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"LI Rudin","year":"1992","unstructured":"Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D. 60, 259\u2013268 (1992)","journal-title":"Phys. D."},{"issue":"10","key":"10000_CR22","doi-asserted-by":"publisher","first-page":"1570","DOI":"10.1109\/TIP.2005.852206","volume":"14","author":"JL Starck","year":"2005","unstructured":"Starck, J.L., Elad, M., Donoho, D.L.: Image decomposition via the combination of sparse representations and a variational approach. IEEE Trans Image Process 14(10), 1570\u201382 (2005)","journal-title":"IEEE Trans Image Process"},{"doi-asserted-by":"crossref","unstructured":"Tang, L., Wu, L., Fang, Z., Li, C.: A non-convex ternary variational decomposition and its application for image denoising. IET Signal Proc. (2021)","key":"10000_CR23","DOI":"10.1049\/sil2.12088"},{"issue":"2","key":"10000_CR24","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1214\/09-AOS729","volume":"38","author":"CH Zhang","year":"2010","unstructured":"Zhang, C.H.: Nearly unbiased variable selection under minimax concave penalty. Ann. Stat. 38(2), 894\u2013942 (2010)","journal-title":"Ann. Stat."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-022-10000-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-022-10000-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-022-10000-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T11:41:29Z","timestamp":1671709289000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-022-10000-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,22]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["10000"],"URL":"https:\/\/doi.org\/10.1007\/s10444-022-10000-4","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"type":"print","value":"1019-7168"},{"type":"electronic","value":"1572-9044"}],"subject":[],"published":{"date-parts":[[2022,12,22]]},"assertion":[{"value":"3 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 November 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 December 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that there are no conflicts of interest regarding the publication of this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of interest"}}],"article-number":"1"}}