{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T21:58:21Z","timestamp":1785880701896,"version":"3.56.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,11,25]],"date-time":"2023-11-25T00:00:00Z","timestamp":1700870400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,11,25]],"date-time":"2023-11-25T00:00:00Z","timestamp":1700870400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SIViP"],"published-print":{"date-parts":[[2024,3]]},"DOI":"10.1007\/s11760-023-02876-6","type":"journal-article","created":{"date-parts":[[2023,11,25]],"date-time":"2023-11-25T11:02:28Z","timestamp":1700910148000},"page":"1601-1608","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Image denoising based on the fractional-order total variation and the minimax-concave"],"prefix":"10.1007","volume":"18","author":[{"given":"Xiaohui","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ping","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,11,25]]},"reference":[{"issue":"4","key":"2876_CR1","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1016\/j.jvcir.2007.04.005","volume":"18","author":"F Li","year":"2007","unstructured":"Li, F., Shen, C., Fan, J., Shen, C.: Image restoration combining a total variational filter and a fourth-order filter. J. Vis. Commun. Image Represent. 18(4), 322\u2013330 (2007). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.jvcir.2007.04.005","journal-title":"J. Vis. Commun. Image Represent."},{"issue":"1","key":"2876_CR2","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 Nonlinear Phenomena 60(1), 259\u2013268 (1992). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/0167-2789(92)90242-F","journal-title":"Phys. D Nonlinear Phenomena"},{"issue":"1","key":"2876_CR3","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1049\/ipr2.12010","volume":"15","author":"Y Wang","year":"2021","unstructured":"Wang, Y., Wang, Z.: Image denoising method based on variable exponential fractional-integer-order total variation and tight frame sparse regularization. IET Image Process. 15(1), 101\u2013114 (2021)","journal-title":"IET Image Process."},{"issue":"8","key":"2876_CR4","doi-asserted-by":"publisher","first-page":"7250","DOI":"10.1002\/mma.7257","volume":"44","author":"F Kazemi Golbaghi","year":"2021","unstructured":"Kazemi Golbaghi, F., Eslahchi, M., Rezghi, M.: Image denoising by a novel variable-order total fractional variation model. Math. Methods Appl. Sci. 44(8), 7250\u20137261 (2021)","journal-title":"Math. Methods Appl. Sci."},{"issue":"10","key":"2876_CR5","doi-asserted-by":"publisher","first-page":"1723","DOI":"10.1109\/83.869184","volume":"9","author":"Y-L You","year":"2000","unstructured":"You, Y.-L., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 9(10), 1723\u20131730 (2000). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1109\/83.869184","journal-title":"IEEE Trans. Image Process."},{"issue":"3","key":"2876_CR6","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1137\/090769521","volume":"3","author":"K Bredies","year":"2010","unstructured":"Bredies, K., Kunisch, K., Pock, T.: Total generalized variation. SIAM J. Imaging Sci. 3(3), 492\u2013526 (2010). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1137\/090769521","journal-title":"SIAM J. Imaging Sci."},{"key":"2876_CR7","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1016\/j.ins.2014.10.041","volume":"295","author":"J Liu","year":"2015","unstructured":"Liu, J., Huang, T.-Z., Selesnick, I.W., Lv, X.-G., Chen, P.-Y.: Image restoration using total variation with overlapping group sparsity. Inf. Sci. 295, 232\u2013246 (2015). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.ins.2014.10.041","journal-title":"Inf. Sci."},{"issue":"11","key":"2876_CR8","doi-asserted-by":"publisher","first-page":"2512","DOI":"10.1049\/iet-ipr.2019.0467","volume":"14","author":"M Hacini","year":"2020","unstructured":"Hacini, M., Hachouf, F., Charef, A.: A bi-directional fractional-order derivative mask for image processing applications. IET Image Process. 14(11), 2512\u20132524 (2020)","journal-title":"IET Image Process."},{"issue":"10","key":"2876_CR9","doi-asserted-by":"publisher","first-page":"2492","DOI":"10.1109\/TIP.2007.904971","volume":"16","author":"J Bai","year":"2007","unstructured":"Bai, J., Feng, X.-C.: Fractional-order anisotropic diffusion for image denoising. IEEE Trans. Image Process. 16(10), 2492\u20132502 (2007). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1109\/TIP.2007.904971","journal-title":"IEEE Trans. Image Process."},{"key":"2876_CR10","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":"2876_CR11","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1109\/LSP.2017.2647948","volume":"24","author":"I Selesnick","year":"2017","unstructured":"Selesnick, I.: Total variation denoising via the Moreau envelope. IEEE Signal Process. Lett. 24(2), 216\u2013220 (2017). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1109\/LSP.2017.2647948","journal-title":"IEEE Signal Process. Lett."},{"key":"2876_CR12","doi-asserted-by":"publisher","first-page":"19539","DOI":"10.1007\/s11042-021-10586-9","volume":"80","author":"M Zhou","year":"2021","unstructured":"Zhou, M., Zhao, P.: Enhanced total generalized variation method based on Moreau envelope. Multimed. Tools Appl. 80, 19539\u201319566 (2021)","journal-title":"Multimed. Tools Appl."},{"issue":"6\u20137","key":"2876_CR13","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1007\/s10851-019-00937-5","volume":"62","author":"I Selesnick","year":"2020","unstructured":"Selesnick, I., Lanza, A., Morigi, S., Sgallari, F.: Non-convex total variation regularization for convex denoising of signals. J. Math. Imaging Vis. 62(6\u20137), 825\u2013841 (2020)","journal-title":"J. Math. Imaging Vis."},{"key":"2876_CR14","doi-asserted-by":"publisher","first-page":"1027","DOI":"10.1007\/s11760-018-1248-2","volume":"12","author":"H Du","year":"2018","unstructured":"Du, H., Liu, Y.: Minmax-concave total variation denoising. Signal Image Video Process. 12, 1027\u20131034 (2018)","journal-title":"Signal Image Video Process."},{"issue":"4","key":"2876_CR15","doi-asserted-by":"publisher","first-page":"1733","DOI":"10.1007\/s11760-022-02384-z","volume":"17","author":"M Ji","year":"2022","unstructured":"Ji, M., Zhao, P.: Image restoration based on the minimax-concave and the overlapping group sparsity. Signal Image Video Process. 17(4), 1733\u20131741 (2022)","journal-title":"Signal Image Video Process."},{"issue":"2","key":"2876_CR16","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1214\/09-AOS729","volume":"38","author":"C-H Zhang","year":"2010","unstructured":"Zhang, C.-H.: Nearly unbiased variable selection under minimax concave penalty. Ann. Stat. 38(2), 894\u2013942 (2010). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1214\/09-AOS729","journal-title":"Ann. Stat."},{"key":"2876_CR17","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.cam.2017.03.014","volume":"322","author":"Y Yu","year":"2017","unstructured":"Yu, Y., Peng, J.: The Moreau envelope based efficient first-order methods for sparse recovery. J. Comput. Appl. Math. 322, 109\u2013128 (2017)","journal-title":"J. Comput. Appl. Math."},{"key":"2876_CR18","doi-asserted-by":"publisher","first-page":"109463","DOI":"10.1016\/j.chaos.2019.109463","volume":"131","author":"Q Wang","year":"2020","unstructured":"Wang, Q., Ma, J., Yu, S., Tan, L.: Noise detection and image denoising based on fractional calculus. Chaos Solitons Fractals 131, 109463 (2020). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.chaos.2019.109463","journal-title":"Chaos Solitons Fractals"},{"key":"2876_CR19","doi-asserted-by":"publisher","unstructured":"Li, D., Jiang, T., Jin, Q., Zhang, B.: Adaptive fractional order total variation image denoising via the alternating direction method of multipliers. In: 2020 Chinese Control And Decision Conference (CCDC), pp. 3876\u20133881 (2020). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1109\/CCDC49329.2020.9164418","DOI":"10.1109\/CCDC49329.2020.9164418"},{"key":"2876_CR20","doi-asserted-by":"crossref","unstructured":"Dong, F., Chen, Y.: A fractional-order derivative based variational framework for image denoising. Inverse Problems Imaging 10(1) (2016)","DOI":"10.3934\/ipi.2016.10.27"},{"key":"2876_CR21","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s10851-011-0285-z","volume":"43","author":"J Zhang","year":"2012","unstructured":"Zhang, J., Wei, Z., Xiao, L.: Adaptive fractional-order multi-scale method for image denoising. J. Math. Imaging Vis. 43, 39\u201349 (2012)","journal-title":"J. Math. Imaging Vis."},{"issue":"1","key":"2876_CR22","doi-asserted-by":"publisher","first-page":"77","DOI":"10.3934\/ipi.2019064","volume":"14","author":"M Rahman Chowdhury","year":"2020","unstructured":"Rahman Chowdhury, M., Zhang, J., Qin, J., Lou, Y.: Poisson image denoising based on fractional-order total variation. Inverse Probl. Imaging 14(1), 77\u201396 (2020)","journal-title":"Inverse Probl. Imaging"},{"issue":"5","key":"2876_CR23","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1016\/S0362-546X(98)00299-5","volume":"41","author":"K Ito","year":"2000","unstructured":"Ito, K., Kunisch, K.: Augmented Lagrangian methods for Nonsmooth, convex optimization in Hilbert spaces. Nonlinear Anal. Theory Methods Appl. 41(5), 591\u2013616 (2000). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/S0362-546X(98)00299-5","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"issue":"3","key":"2876_CR24","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1137\/080724265","volume":"1","author":"Y Wang","year":"2008","unstructured":"Wang, Y., Yang, J., Yin, W., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imaging Sci. 1(3), 248\u2013272 (2008). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1137\/080724265","journal-title":"SIAM J. Imaging Sci."},{"key":"2876_CR25","doi-asserted-by":"crossref","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces (2017)","DOI":"10.1007\/978-3-319-48311-5"},{"issue":"4","key":"2876_CR26","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TIP.2003.819861","volume":"13","author":"Z Wang","year":"2004","unstructured":"Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600\u2013612 (2004). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1109\/TIP.2003.819861","journal-title":"IEEE Trans. Image Process."},{"issue":"12","key":"2876_CR27","doi-asserted-by":"publisher","first-page":"4954","DOI":"10.1109\/TIP.2014.2360133","volume":"23","author":"C He","year":"2014","unstructured":"He, C., Hu, C., Zhang, W., Shi, B.: A fast adaptive parameter estimation for total variation image restoration. IEEE Trans. Image Process. 23(12), 4954\u20134967 (2014). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1109\/TIP.2014.2360133","journal-title":"IEEE Trans. Image Process."},{"key":"2876_CR28","doi-asserted-by":"publisher","unstructured":"Che, J., Guan, Q., Wang, X.: Image denoising based on adaptive fractional partial differential equations. In: 2013 6th International Congress on Image and Signal Processing (CISP), vol. 01, pp. 288\u2013292 (2013). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1109\/CISP.2013.6744004","DOI":"10.1109\/CISP.2013.6744004"},{"issue":"12","key":"2876_CR29","doi-asserted-by":"publisher","first-page":"1579","DOI":"10.1109\/TIP.2003.819229","volume":"12","author":"M Lysaker","year":"2003","unstructured":"Lysaker, M., Lundervold, A., Tai, X.-C.: Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Trans. Image Process. 12(12), 1579\u20131590 (2003)","journal-title":"IEEE Trans. Image Process."},{"key":"2876_CR30","doi-asserted-by":"publisher","unstructured":"Yang, S., Wang, J., Fan, W., Zhang, X., Wonka, P., Ye, J.: An efficient admm algorithm for multidimensional anisotropic total variation regularization problems. In: Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. KDD \u201913, pp. 641\u2013649. Association for Computing Machinery, New York, NY, USA (2013). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1145\/2487575.2487586","DOI":"10.1145\/2487575.2487586"}],"container-title":["Signal, Image and Video Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/content\/pdf\/10.1007\/s11760-023-02876-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/article\/10.1007\/s11760-023-02876-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/content\/pdf\/10.1007\/s11760-023-02876-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T07:16:16Z","timestamp":1708413376000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/10.1007\/s11760-023-02876-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,25]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["2876"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s11760-023-02876-6","relation":{},"ISSN":["1863-1703","1863-1711"],"issn-type":[{"value":"1863-1703","type":"print"},{"value":"1863-1711","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,25]]},"assertion":[{"value":"15 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 June 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 October 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 November 2023","order":4,"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 no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}