{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T06:56:25Z","timestamp":1763535385037},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,2,11]],"date-time":"2016-02-11T00:00:00Z","timestamp":1455148800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2016,9]]},"DOI":"10.1007\/s10915-016-0175-z","type":"journal-article","created":{"date-parts":[[2016,2,11]],"date-time":"2016-02-11T09:00:21Z","timestamp":1455181221000},"page":"1200-1216","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Variational Multiplicative Noise Removal by DC Programming"],"prefix":"10.1007","volume":"68","author":[{"given":"Zhi","family":"Li","sequence":"first","affiliation":[]},{"given":"Yifei","family":"Lou","sequence":"additional","affiliation":[]},{"given":"Tieyong","family":"Zeng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,2,11]]},"reference":[{"issue":"11","key":"175_CR1","doi-asserted-by":"crossref","first-page":"2984","DOI":"10.1109\/TSP.2014.2315167","volume":"62","author":"A Alvarado","year":"2014","unstructured":"Alvarado, A., Scutari, G., Pang, J.S.: A new decomposition method for multiuser DC-programming and its applications. IEEE Trans. Signal Process. 62(11), 2984\u20132998 (2014)","journal-title":"IEEE Trans. Signal Process."},{"issue":"4","key":"175_CR2","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."},{"issue":"2","key":"175_CR3","first-page":"562","volume":"21","author":"J Cai","year":"2004","unstructured":"Cai, J., Ji, H., Liu, C., Shen, Z.: Framelet-based blind motion deblurring from a single image. IEEE Trans. Image Process. 21(2), 562\u2013572 (2004)","journal-title":"IEEE Trans. Image Process."},{"issue":"1\u20132","key":"175_CR4","first-page":"89","volume":"20","author":"A Chambolle","year":"2004","unstructured":"Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20(1\u20132), 89\u201397 (2004)","journal-title":"J. Math. Imaging Vis."},{"issue":"1","key":"175_CR5","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":"1","key":"175_CR6","first-page":"98","volume":"7","author":"R Chan","year":"2014","unstructured":"Chan, R., Yang, H., Zeng, T.: A two-stage image segmentation method for blurry images with poisson or multiplicative gamma noise. SIAM J. Sci. Comput. 7(1), 98\u2013127 (2014)","journal-title":"SIAM J. Sci. Comput."},{"key":"175_CR7","doi-asserted-by":"publisher","unstructured":"Chan, T.F., Shen, J.: Image processing and analysis: variational, PDE, wavelet, and stochastic methods. Society for Industrial and Applied Mathematics (2005). doi: 10.1137\/1.9780898717877","DOI":"10.1137\/1.9780898717877"},{"issue":"12","key":"175_CR8","doi-asserted-by":"crossref","first-page":"4709","DOI":"10.1109\/TIP.2012.2214051","volume":"21","author":"X Chen","year":"2012","unstructured":"Chen, X., Ng, M., Zhang, C.: Non-lipschitz-regularization and box constrained model for image restoration. IEEE Trans. Image Process. 21(12), 4709\u20134721 (2012)","journal-title":"IEEE Trans. Image Process."},{"issue":"4","key":"175_CR9","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1137\/080740167","volume":"3","author":"X Chen","year":"2010","unstructured":"Chen, X., Zhou, W.: Smoothing nonlinear conjugate gradient method for image restoration using nonsmooth nonconvex minimization. SIAM J. Imaging Sci. 3(4), 765\u2013790 (2010)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"175_CR10","doi-asserted-by":"crossref","first-page":"1598","DOI":"10.1137\/120870621","volume":"6","author":"Y Dong","year":"2013","unstructured":"Dong, Y., Zeng, T.: A convex variational model for restoring blurred images with multiplicative noise. SIAM J. Imaging Sci. 6(3), 1598\u20131625 (2013)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"175_CR11","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10107-012-0625-9","volume":"140","author":"M D\u00fcr","year":"2013","unstructured":"D\u00fcr, M., Hiriart-Urruty, J.B.: Testing copositivity with the help of difference-of-convex optimization. Math. Program. 140(1), 31\u201343 (2013)","journal-title":"Math. Program."},{"key":"175_CR12","doi-asserted-by":"publisher","unstructured":"Ekeland, I., T\u00e9mam, R.: Convex analysis and variational problems. Society for Industrial and Applied Mathematics (1999). doi: 10.1137\/1.9781611971088","DOI":"10.1137\/1.9781611971088"},{"issue":"2\u20133","key":"175_CR13","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s10107-005-0622-3","volume":"104","author":"J Harrington","year":"2005","unstructured":"Harrington, J., Hobbs, B.F., Pang, J.S., Liu, A., Roch, G.: Collusive game solutions via optimization. Math. Program. 104(2\u20133), 407\u2013435 (2005)","journal-title":"Math. Program."},{"key":"175_CR14","doi-asserted-by":"publisher","unstructured":"Hiriart-Urruty, J.B., Lemar\u00e9chal, C.: Convex analysis and minimization algorithms. Springer-Verlag, Berlin, Heidelberg (1993). doi: 10.1007\/978-3-662-02796-7","DOI":"10.1007\/978-3-662-02796-7"},{"issue":"1","key":"175_CR15","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1137\/080712593","volume":"2","author":"YM Huang","year":"2009","unstructured":"Huang, Y.M., Ng, M., Wen, Y.W.: A new total variation method for multiplicative noise removal. SIAM J. Imaging Sci. 2(1), 20\u201340 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"175_CR16","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s101070050003","volume":"87","author":"HA Le-Thi","year":"2000","unstructured":"Le-Thi, H.A.: An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints. Math. Program. 87, 401\u2013426 (2000)","journal-title":"Math. Program."},{"issue":"1\u20134","key":"175_CR17","first-page":"23","volume":"133","author":"HA Le-Thi","year":"2005","unstructured":"Le-Thi, H.A., Pham-Dihn, T.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133(1\u20134), 23\u201346 (2005)","journal-title":"Ann. Oper. Res."},{"issue":"1","key":"175_CR18","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s40595-013-0010-5","volume":"1","author":"HA Le-Thi","year":"2014","unstructured":"Le-Thi, H.A., Pham-Dihn, T.: DC programming in communication systems: challenging problems and methods. Vietnam J. Comput. Sci. 1(1), 15\u201328 (2014)","journal-title":"Vietnam J. Comput. Sci."},{"key":"175_CR19","unstructured":"Long, X., Solna, K., Xin, J.: Two $$\\ell _{1}$$ \u2113 1 based nonconvex methods for constructing sparse mean reverting portfolios. Technical Report, Department of Mathematics, University of California, Los Angeles (2014)"},{"key":"175_CR20","first-page":"169","volume":"359","author":"Y Lou","year":"2015","unstructured":"Lou, Y., Osher, S., Xin, J.: Computational aspects of constrained $$\\ell _{1}$$ \u2113 1 - $$\\ell _{2}$$ \u2113 2 minimization for compressive sensing. Model. Comput. Optim. Inf. Syst. Manag. Sci. 359, 169\u2013180 (2015)","journal-title":"Model. Comput. Optim. Inf. Syst. Manag. Sci."},{"issue":"1","key":"175_CR21","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1007\/s10915-014-9930-1","volume":"64","author":"Y Lou","year":"2014","unstructured":"Lou, Y., Yin, P., He, Q., Xin, J.: Computing sparse representation in a highly coherent dictionary based on difference of L1 and L2. J. Sci. Comput. 64(1), 178\u2013196 (2014)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"175_CR22","doi-asserted-by":"crossref","first-page":"1798","DOI":"10.1137\/14098435X","volume":"8","author":"Y Lou","year":"2015","unstructured":"Lou, Y., Zeng, T., Osher, S., Xin, J.: A weighted difference of anisotropic and isotropic total variation model for image processing. SIAM J. Imaging Sci. 8(3), 1798\u20131823 (2015)","journal-title":"SIAM J. Imaging Sci."},{"issue":"2","key":"175_CR23","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/s10915-009-9320-2","volume":"42","author":"Y Lou","year":"2010","unstructured":"Lou, Y., Zhang, X., Osher, S., Bertozzi, A.: Image recovery via nonlocal operators. J. Sci. Comput. 42(2), 185\u2013197 (2010)","journal-title":"J. Sci. Comput."},{"issue":"10","key":"175_CR24","doi-asserted-by":"crossref","first-page":"7667","DOI":"10.1063\/1.463486","volume":"97","author":"CD Maranas","year":"1992","unstructured":"Maranas, C.D., Floudas, C.A.: A global optimization approach for Lennard\u2013Jones microclusters. J. Chem. Phys. 97(10), 7667\u20137678 (1992)","journal-title":"J. Chem. Phys."},{"issue":"1\u20133","key":"175_CR25","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s10994-005-1505-9","volume":"61","author":"J Neumann","year":"2005","unstructured":"Neumann, J., Schn\u00f6rr, C., Steidl, G.: Combined SVM-based feature selection and classification. Mach. Learn. 61(1\u20133), 129\u2013150 (2005)","journal-title":"Mach. Learn."},{"issue":"12","key":"175_CR26","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., 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."},{"key":"175_CR27","doi-asserted-by":"crossref","unstructured":"Ochs, P., Dosovitskiy, A., Brox, T., Pock, T.: An iterated L1 algorithm for non-smooth non-convex optimization in computer vision. In: IEEE conference on computer vision and pattern recognition, pp. 1759\u20131766 (2013)","DOI":"10.1109\/CVPR.2013.230"},{"issue":"3","key":"175_CR28","first-page":"123","volume":"1","author":"N Parikh","year":"2013","unstructured":"Parikh, N., Boyd, S.: Proximal algorithms. Found. Trends Optim. 1(3), 123\u2013231 (2013)","journal-title":"Found. Trends Optim."},{"issue":"1","key":"175_CR29","first-page":"289","volume":"22","author":"T Pham-Dihn","year":"1997","unstructured":"Pham-Dihn, T., Le-Thi, H.A.: Convex analysis approach to DC programming: theory, algorithms and applications. Acta Math. Vietnam 22(1), 289\u2013355 (1997)","journal-title":"Acta Math. Vietnam"},{"issue":"2","key":"175_CR30","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1137\/S1052623494274313","volume":"8","author":"T Pham-Dihn","year":"1998","unstructured":"Pham-Dihn, T., Le-Thi, H.A.: A DC optimization algorithm for solving the trust-region subproblem. SIAM J. Optim. 8(2), 476\u2013505 (1998)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"175_CR31","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1137\/110850372","volume":"5","author":"K Punithakumar","year":"2012","unstructured":"Punithakumar, K., Yuan, J., Ayed, I.B., Li, S., Boykov, Y.: A convex max-flow approach to distribution-based figure-ground separation. SIAM J. Imaging Sci. 5(4), 1333\u20131354 (2012)","journal-title":"SIAM J. Imaging Sci."},{"key":"175_CR32","doi-asserted-by":"crossref","unstructured":"Repetti, A., Chouzenoux, E., Pesquet, J.C.: A nonconvex regularized approach for phase retrieval. In: IEEE international conference on image processing, pp. 1753\u20131757 (2014)","DOI":"10.1109\/ICIP.2014.7025351"},{"key":"175_CR33","doi-asserted-by":"crossref","unstructured":"Rudin, L., Lions, P.L., Osher, S.: Multiplicative denoising and deblurring: theory and algorithms. In: Geometric Level Set Methods in Imaging, Vision, and Graphics, pp. 103\u2013119. Springer, New York (2003)","DOI":"10.1007\/0-387-21810-6_6"},{"issue":"1","key":"175_CR34","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L Rudin","year":"1992","unstructured":"Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60(1), 259\u2013268 (1992)","journal-title":"Phys. D"},{"key":"175_CR35","doi-asserted-by":"crossref","unstructured":"Schn\u00f6rr, C., Sch\u00fcle, T., Weber, S.: Variational reconstruction with DC-programming. In: Advances in Discrete Tomography and Its Applications, pp. 227\u2013243. Springer, Berlin (2007)","DOI":"10.1007\/978-0-8176-4543-4_11"},{"issue":"3","key":"175_CR36","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."},{"key":"175_CR37","doi-asserted-by":"crossref","unstructured":"Tang, M., Ayed, I.B., Boykov,Y.: Pseudo-bound optimization for binary energies. In: European Conference on Computer Vision, pp. 691\u2013707. Springer (2014)","DOI":"10.1007\/978-3-319-10602-1_45"},{"issue":"2","key":"175_CR38","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/S0363012998338806","volume":"38","author":"P Tseng","year":"2000","unstructured":"Tseng, P.: A modified forward\u2013backward splitting method for maximal monotone mappings. SIAM J. Control Optim. 38(2), 431\u2013446 (2000)","journal-title":"SIAM J. Control Optim."},{"issue":"5","key":"175_CR39","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1109\/TIP.2015.2401430","volume":"24","author":"J Xiao","year":"2015","unstructured":"Xiao, J., Ng, M., Yang, Y.F.: On the convergence of nonconvex minimization methods for image recovery. IEEE Trans. Image Process. 24(5), 1587\u20131598 (2015)","journal-title":"IEEE Trans. Image Process."},{"issue":"1","key":"175_CR40","doi-asserted-by":"crossref","first-page":"A536","DOI":"10.1137\/140952363","volume":"37","author":"P Yin","year":"2015","unstructured":"Yin, P., Lou, Y., He, Q., Xin, J.: Minimization of L1\u2013L2 for compressed sensing. SIAM J. Sci. Comput. 37(1), A536\u2013A563 (2015)","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0175-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0175-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0175-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T04:45:55Z","timestamp":1559450755000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0175-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,11]]},"references-count":40,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,9]]}},"alternative-id":["175"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0175-z","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,11]]}}}