{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T23:24:15Z","timestamp":1772839455943,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,1,20]],"date-time":"2017-01-20T00:00:00Z","timestamp":1484870400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100002486","name":"Hankuk University of Foreign Studies","doi-asserted-by":"publisher","award":["2016"],"award-info":[{"award-number":["2016"]}],"id":[{"id":"10.13039\/501100002486","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2016R1C1B1009808"],"award-info":[{"award-number":["2016R1C1B1009808"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2014R1A2A1A10050531"],"award-info":[{"award-number":["2014R1A2A1A10050531"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2015R1A5A1009350"],"award-info":[{"award-number":["2015R1A5A1009350"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003052","name":"Ministry of Trade, Industry and Energy","doi-asserted-by":"publisher","award":["10048720"],"award-info":[{"award-number":["10048720"]}],"id":[{"id":"10.13039\/501100003052","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003621","name":"Ministry of Science, ICT and Future Planning","doi-asserted-by":"publisher","award":["B0717-16-0107"],"award-info":[{"award-number":["B0717-16-0107"]}],"id":[{"id":"10.13039\/501100003621","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2013R1A1A3010416"],"award-info":[{"award-number":["2013R1A1A3010416"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2017,7]]},"DOI":"10.1007\/s10915-017-0357-3","type":"journal-article","created":{"date-parts":[[2017,1,20]],"date-time":"2017-01-20T14:17:19Z","timestamp":1484921839000},"page":"172-197","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Total Generalized Variation Based Denoising Models for Ultrasound Images"],"prefix":"10.1007","volume":"72","author":[{"given":"Myeongmin","family":"Kang","sequence":"first","affiliation":[]},{"given":"Myungjoo","family":"Kang","sequence":"additional","affiliation":[]},{"given":"Miyoun","family":"Jung","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,1,20]]},"reference":[{"issue":"4","key":"357_CR1","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1137\/060671814","volume":"68","author":"G Aubert","year":"2008","unstructured":"Aubert, G., Aujol, J.F.: A variational approach to removing multiplicative noise. SIAM J. Appl. Math. 68(4), 925\u2013946 (2008)","journal-title":"SIAM J. Appl. Math."},{"key":"357_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-44588-5","volume-title":"Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations","author":"G Aubert","year":"2006","unstructured":"Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, vol. 147. Springer, Berlin (2006)"},{"key":"357_CR3","doi-asserted-by":"crossref","unstructured":"Barcelos, C.A., Vieira, L.E.: Ultrasound speckle noise reduction via an adaptive edge-controlled variational method. In: 2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 145\u2013151 (2014)","DOI":"10.1109\/SMC.2014.6973898"},{"issue":"3","key":"357_CR4","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1080\/02664768900000049","volume":"16","author":"J Besag","year":"1989","unstructured":"Besag, J.: Digital image processing: towards Bayesian image analysis. J. Appl. Stat. 16(3), 395\u2013407 (1989)","journal-title":"J. Appl. Stat."},{"key":"357_CR5","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/978-3-642-38267-3_13","volume":"7893","author":"K Bredies","year":"2013","unstructured":"Bredies, K., Holler, M.: A TGV regularized wavelet based zooming model. Scale Space Var. Methods Comput. Vis. 7893, 149\u2013160 (2013)","journal-title":"Scale Space Var. Methods Comput. Vis."},{"issue":"3","key":"357_CR6","doi-asserted-by":"crossref","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)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"357_CR7","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.jmaa.2012.08.053","volume":"389","author":"K Bredies","year":"2013","unstructured":"Bredies, K., Kunisch, K., Valkonen, T.: Properties of $$L^1$$ L 1 - $$TGV^2$$ T G V 2 : The one-dimensional case. J. Math. Anal. Appl. 389(1), 438\u2013454 (2013)","journal-title":"J. Math. Anal. Appl."},{"key":"357_CR8","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1007\/s00041-008-9045-x","volume":"14","author":"EJ Cand\u00e9s","year":"2008","unstructured":"Cand\u00e9s, E.J., Wakin, M.B., Boyd, S.P.: Enhancing sparsity by reweighted $$\\ell _1$$ \u2113 1 minimization. J. Fourier Anal. Appl. 14, 877\u2013905 (2008)","journal-title":"J. Fourier Anal. Appl."},{"key":"357_CR9","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1023\/B:JMIV.0000011320.81911.38","volume":"20","author":"A Chambolle","year":"2004","unstructured":"Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20, 89\u201397 (2004)","journal-title":"J. Math. Imaging Vis."},{"issue":"2","key":"357_CR10","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s002110050258","volume":"76","author":"A Chambolle","year":"1997","unstructured":"Chambolle, A., Lions, P.: Image recovery via total variation minimization and related problems. Numer. Math. 76(2), 167\u2013188 (1997)","journal-title":"Numer. Math."},{"issue":"1","key":"357_CR11","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1007\/s10851-010-0251-1","volume":"40","author":"A Chambolle","year":"2011","unstructured":"Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120\u2013145 (2011)","journal-title":"J. Math. Imaging Vis."},{"issue":"2","key":"357_CR12","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1137\/S1064827598344169","volume":"22","author":"T Chan","year":"2000","unstructured":"Chan, T., Marquina, A., Mulet, P.: High-order total variation-based image restoration. SIAM J. Sci. Comput. 22(2), 503\u2013516 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"357_CR13","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1007\/s10915-015-0048-x","volume":"66","author":"W Deng","year":"2016","unstructured":"Deng, W., Yin, W.: On the global and linear convergence of the generalized alternating direction method of multipliers. J. Sci. Comput. 66, 889\u2013916 (2016)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"357_CR14","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1090\/S0002-9947-1956-0084194-4","volume":"82","author":"J Douglas","year":"1956","unstructured":"Douglas, J., Rachford, H.H.: On the numerical solution of heat conduction problems in two and three space variables. Trans. Am. Math. Soc. 82(2), 421\u2013439 (1956)","journal-title":"Trans. Am. Math. Soc."},{"key":"357_CR15","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/BF01581204","volume":"55","author":"J Eckstein","year":"1992","unstructured":"Eckstein, J., Bertsekas, D.P.: On the Douglas\u2013Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55, 293\u2013318 (1992)","journal-title":"Math. Program."},{"issue":"7","key":"357_CR16","doi-asserted-by":"crossref","first-page":"932","DOI":"10.1109\/83.392335","volume":"4","author":"D Geman","year":"1995","unstructured":"Geman, D., Yang, C.: Nonlinear image recovery with half-quadratic regularization. IEEE Trans. Image Process. 4(7), 932\u2013946 (1995)","journal-title":"IEEE Trans. Image Process."},{"issue":"6","key":"357_CR17","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","volume":"6","author":"S Geman","year":"1984","unstructured":"Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. PAMI 6(6), 721\u2013741 (1984)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell. PAMI"},{"key":"357_CR18","doi-asserted-by":"crossref","first-page":"147","DOI":"10.5201\/ipol.2012.g-tvi","volume":"2","author":"P Getreuer","year":"2012","unstructured":"Getreuer, P.: Total variation inpainting using split Bregman. Image Process. On Line 2, 147\u2013157 (2012)","journal-title":"Image Process. On Line"},{"key":"357_CR19","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1007\/s10915-009-9331-z","volume":"45","author":"T Goldstein","year":"2010","unstructured":"Goldstein, T., Bresson, X., Osher, S.: Geometric applications of the split Bregman method: segmentation and surface reconstruction. J. Sci. Comput. 45, 272\u2013293 (2010)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"357_CR20","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1137\/080725891","volume":"2","author":"T Goldstein","year":"2009","unstructured":"Goldstein, T., Osher, S.: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2(2), 323\u2013343 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"357_CR21","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1007\/s10851-010-0225-3","volume":"39","author":"Z Jin","year":"2011","unstructured":"Jin, Z., Yang, X.: A variational model to remove the multiplicative noise in ultrasound images. J. Math. Imaging Vis. 39, 62\u201374 (2011)","journal-title":"J. Math. Imaging Vis."},{"key":"357_CR22","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.jvcir.2015.08.006","volume":"32","author":"M Kang","year":"2015","unstructured":"Kang, M., Jung, M., Kang, M.: Nonconvex higher-order regularization based Rician noise removal with spatially adaptive parameters. J. Vis. Commun. Image R. 32, 180\u2013193 (2015)","journal-title":"J. Vis. Commun. Image R."},{"key":"357_CR23","unstructured":"Krishnan, D., Fergus, R.: Fast image deconvolution using hyper-Laplacian priors. In: Proceedings of the Advances in Neural Information Processing Systems, pp. 1033\u20131041 (2009)"},{"key":"357_CR24","first-page":"547","volume":"2","author":"K Krissian","year":"2005","unstructured":"Krissian, K., Kikinis, R., Westin, C., Vosburgh, K.: Speckle constrained filtering of ultrasound images. IEEE Comput. Vis. Pattern Recogn. 2, 547\u2013552 (2005)","journal-title":"IEEE Comput. Vis. Pattern Recogn."},{"key":"357_CR25","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1109\/TASSP.1987.1165131","volume":"ASSP\u201335","author":"DT Kuan","year":"1987","unstructured":"Kuan, D.T., Sawchuk, A.A., Strand, T.C., Chavel, P.: Adaptive restoration of images with speckle. IEEE Trans. Acoust. Speech Signal Process. ASSP\u201335, 373\u2013383 (1987)","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"issue":"5","key":"357_CR26","first-page":"636","volume":"25","author":"JS Lee","year":"1999","unstructured":"Lee, J.S.: Speckle suppression and anaylsis for synthetic aperture radar. Opt. Eng. 25(5), 636\u2013643 (1999)","journal-title":"Opt. Eng."},{"issue":"4","key":"357_CR27","doi-asserted-by":"crossref","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 R. 18(4), 322\u2013330 (2007)","journal-title":"J. Vis. Commun. Image R."},{"issue":"1","key":"357_CR28","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/31.16577","volume":"36","author":"T Loupas","year":"1989","unstructured":"Loupas, T., McDicken, W.N., Allan, P.L.: An adaptive weighted median filter for speckle suppression in medical ultrasonic images. IEEE Trans. Circuits Syst. 36(1), 129\u2013135 (1989)","journal-title":"IEEE Trans. Circuits Syst."},{"issue":"12","key":"357_CR29","doi-asserted-by":"crossref","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 application 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":"357_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory Lectures on Convex Optimization: A Basic Course","author":"Y Nesterov","year":"2004","unstructured":"Nesterov, Y.: Introductory Lectures on Convex Optimization: A Basic Course, vol. 87. Kluwer, Boston (2004)"},{"issue":"12","key":"357_CR31","doi-asserted-by":"crossref","first-page":"3073","DOI":"10.1109\/TIP.2010.2052275","volume":"19","author":"M Nikolova","year":"2010","unstructured":"Nikolova, M., Ng, M.K., Tam, C.P.: Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction. IEEE Trans. Image Process. 19(12), 3073\u20133088 (2010)","journal-title":"IEEE Trans. Image Process."},{"issue":"1","key":"357_CR32","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1137\/070692285","volume":"1","author":"M Nikolova","year":"2008","unstructured":"Nikolova, M., Ng, M.K., Zhang, S., Ching, W.: Efficient reconstruction of piecewise constant images using nonsmooth nonconvex minimization. SIAM J. Imaging Sci. 1(1), 2\u201325 (2008)","journal-title":"SIAM J. Imaging Sci."},{"key":"357_CR33","volume-title":"Numerical Optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (2006)"},{"key":"357_CR34","doi-asserted-by":"crossref","unstructured":"Ochs, P., Dosovitskiy, A., Brox, T., Pock, T.: An iterated $$\\ell _1$$ \u2113 1 algorithm for non-smooth non-convex optimization in computer vision. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2013)","DOI":"10.1109\/CVPR.2013.230"},{"issue":"1","key":"357_CR35","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1137\/140971518","volume":"8","author":"P Ochs","year":"2015","unstructured":"Ochs, P., Dosovitskiy, A., Brox, T., Pock, T.: On iteratively reweighted algorithm for nonsmooth nonconvex optimization in computer vision. SIAM J. Imaging Sci. 8(1), 331\u2013372 (2015)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"357_CR36","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.jvcir.2013.01.010","volume":"24","author":"S Oh","year":"2013","unstructured":"Oh, S., Woo, H., Yun, S., Kang, M.: Non-convex hybrid total variation for image denoising. J. Vis. Commun. Image R. 24(3), 332\u2013344 (2013)","journal-title":"J. Vis. Commun. Image R."},{"key":"357_CR37","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1007\/s10851-013-0445-4","volume":"48","author":"K Papafitsoros","year":"2014","unstructured":"Papafitsoros, K., Sch\u00f6nlieb, C.B.: A combined first and second order variational approach for image restoration. J. Math. Imaging Vis. 48, 308\u2013338 (2014)","journal-title":"J. Math. Imaging Vis."},{"issue":"10","key":"357_CR38","doi-asserted-by":"crossref","first-page":"2576","DOI":"10.1109\/TIP.2007.904975","volume":"16","author":"M Robini","year":"2007","unstructured":"Robini, M., Lachal, A., Magnin, I.: A stochastic continuation approach to piecewise constant reconstruction. IEEE Trans. Image Process. 16(10), 2576\u20132589 (2007)","journal-title":"IEEE Trans. Image Process."},{"issue":"1","key":"357_CR39","doi-asserted-by":"crossref","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 Phenom. 60(1), 259\u2013268 (1992)","journal-title":"Phys. D Nonlinear Phenom."},{"key":"357_CR40","unstructured":"Setzer, S., Steidl, G.: Variational methods with higher-order derivatives in image processing. In: Approximation Theory XII: San Antonio, pp. 360\u2013386 (2008)"},{"issue":"3","key":"357_CR41","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.jvcir.2009.10.006","volume":"21","author":"S Setzer","year":"2010","unstructured":"Setzer, S., Steidl, G., Teuber, T.: Deblurring Poissonian images by split Bregman techniques. J. Vis. Commun. Image R. 21(3), 193\u2013199 (2010)","journal-title":"J. Vis. Commun. Image R."},{"issue":"3","key":"357_CR42","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1137\/070689954","volume":"1","author":"J Shi","year":"2008","unstructured":"Shi, J., Osher, S.: A nonlinear inverse scale space method for a convex multiplicative noise model. SIAM J. Imaging Sci. 1(3), 294\u2013321 (2008)","journal-title":"SIAM J. Imaging Sci."},{"issue":"2","key":"357_CR43","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1007\/s10851-009-0179-5","volume":"36","author":"G Steidl","year":"2010","unstructured":"Steidl, G., Teuber, T.: Removing multiplicative noise by Douglas-Rachford splitting methods. J. Math. Imaging Vis. 36(2), 168\u2013184 (2010)","journal-title":"J. Math. Imaging Vis."},{"issue":"3","key":"357_CR44","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1109\/83.661189","volume":"7","author":"S Teboul","year":"1998","unstructured":"Teboul, S., Blanc-Feraud, L., Aubert, G., Barlaud, M.: Variational approach for edge-preserving regularization using coupled PDEs. IEEE Trans. Image Process. 7(3), 387\u2013397 (1998)","journal-title":"IEEE Trans. Image Process."},{"key":"357_CR45","unstructured":"Vese, L., Chan, T.: Redced non-convex functional approximations for image restoration and segmentation. UCLA CAM Report 97-56 (1997)"},{"issue":"2","key":"357_CR46","doi-asserted-by":"crossref","first-page":"B336","DOI":"10.1137\/11083811X","volume":"35","author":"H Woo","year":"2013","unstructured":"Woo, H., Yun, S.: Proximal linearized alternating direction method for multiplicative denoising. SIAM J. Sci. Comput. 35(2), B336\u2013B358 (2013)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"357_CR47","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1137\/090777761","volume":"33","author":"J Yang","year":"2011","unstructured":"Yang, J., Zhang, Y.: Alternating direction algorithms for $$\\ell _1$$ \u2113 1 problems in compressive sensing. SIAM J. Sci. Comput 33(1), 250\u2013278 (2011)","journal-title":"SIAM J. Sci. Comput"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0357-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0357-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0357-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,17]],"date-time":"2019-09-17T16:34:44Z","timestamp":1568738084000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0357-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,20]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["357"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0357-3","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,20]]}}}