{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:15:08Z","timestamp":1762431308923,"version":"3.37.3"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2017,7,19]],"date-time":"2017-07-19T00:00:00Z","timestamp":1500422400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["91330101","11531005"],"award-info":[{"award-number":["91330101","11531005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["11501292"],"award-info":[{"award-number":["11501292"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Multidim Syst Sign Process"],"published-print":{"date-parts":[[2018,10]]},"DOI":"10.1007\/s11045-017-0512-x","type":"journal-article","created":{"date-parts":[[2017,7,19]],"date-time":"2017-07-19T09:52:13Z","timestamp":1500457933000},"page":"1459-1484","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Total generalized variation restoration with non-quadratic fidelity"],"prefix":"10.1007","volume":"29","author":[{"given":"Yiming","family":"Gao","sequence":"first","affiliation":[]},{"given":"Fang","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Xiaoping","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,7,19]]},"reference":[{"key":"512_CR1","volume-title":"Handbook of image and video processing","author":"A Bovik","year":"2000","unstructured":"Bovik, A. (2000). Handbook of image and video processing. New York: Academic."},{"key":"512_CR2","first-page":"44","volume":"8293","author":"K Bredies","year":"2014","unstructured":"Bredies, K. (2014). Recovering piecewise smooth multichannel images by minimization of convex functionals with total generalized variation penalty. Global Optimization Methods, LNCS, 8293, 44\u201377.","journal-title":"Global Optimization Methods, LNCS"},{"key":"512_CR3","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1137\/090769521","volume":"3","author":"K Bredies","year":"2010","unstructured":"Bredies, K., Kunisch, K., & Pock, T. (2010). Total generalized variation. SIAM Journal on Imaging Sciences, 3, 92\u2013526.","journal-title":"SIAM Journal on Imaging Sciences"},{"issue":"3","key":"512_CR4","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s10851-015-0564-1","volume":"52","author":"K Bredies","year":"2015","unstructured":"Bredies, K., & Sun, H. P. (2015). Preconditioned Douglas-Rachford algorithms for TV and TGV regularized variational imaging problems. Journal of Mathematical Imaging and Vision, 52(3), 317\u2013344.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"512_CR5","unstructured":"Bredies, K., & Valkonen, T. (2011). Inverse problems with second-order total generalized variation constraints. In Proceedings of SampTA 2011-9th international conference on sampling theory and applications, Singapore."},{"key":"512_CR6","doi-asserted-by":"crossref","first-page":"455","DOI":"10.3934\/ipi.2008.2.455","volume":"2","author":"X Bresson","year":"2008","unstructured":"Bresson, X., & Chan, T. F. (2008). Fast dual minimization of the vectorial total variation norm and applications to color image processing. Inverse Problems and Imaging, 2, 455\u2013484.","journal-title":"Inverse Problems and Imaging"},{"key":"512_CR7","first-page":"235","volume":"5567","author":"C Brune","year":"2009","unstructured":"Brune, C., Sawatzky, A., & Burger, M. (2009). Bregman-EM-TV methods with application to optical nanoscopy. LNCS, 5567, 235\u2013246.","journal-title":"LNCS"},{"key":"512_CR8","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. (2011). A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, 40, 120\u201345.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"512_CR9","doi-asserted-by":"crossref","first-page":"1817","DOI":"10.1137\/040604297","volume":"65","author":"TF Chan","year":"2005","unstructured":"Chan, T. F., & Esedoglu, S. (2005). Aspects of total variation regularized L1 function approximation. SIAM Journal on Applied Mathematics, 65, 1817\u20131837.","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"512_CR10","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1006\/jvci.2001.0491","volume":"12","author":"TF Chan","year":"2001","unstructured":"Chan, T. F., Kang, S. H., & Shen, J. H. (2001). Total variation denoising and enhancement of color images based on the CB and HSV color models. Journal of Visual Communication and Image Representation, 12, 422\u2013435.","journal-title":"Journal of Visual Communication and Image Representation"},{"key":"512_CR11","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1137\/S1064827598344169","volume":"22","author":"TF Chan","year":"2000","unstructured":"Chan, T. F., Marquina, A., & Mulet, P. (2000). High-order total variation-based image restoration. SIAM Journal on Scientific Computing, 22, 503\u2013516.","journal-title":"SIAM Journal on Scientific Computing"},{"key":"512_CR12","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1137\/100807247","volume":"4","author":"RH Chan","year":"2011","unstructured":"Chan, R. H., Yang, J. F., & Yuan, X. M. (2011). Alternating direction method for image inpainting in wavelet domain. SIAM Journal on Imaging Sciences, 4, 807\u2013826.","journal-title":"SIAM Journal on Imaging Sciences"},{"issue":"1","key":"512_CR13","first-page":"57","volume":"155","author":"CH Chen","year":"2013","unstructured":"Chen, C. H., He, B. S., Ye, Y. Y., & Yuan, X. M. (2013). The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Mathematical Programming, 155(1), 57\u201379.","journal-title":"Mathematical Programming"},{"key":"512_CR14","doi-asserted-by":"crossref","unstructured":"Eckstein, J., & Bertsekas, D. (1992). On the Douglas\u2013Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming, 55.","DOI":"10.1007\/BF01581204"},{"key":"512_CR15","unstructured":"Esser, E. (2009). Applications of Lagrangian-based alternating direction methods and connections to split Bregman. UCLA CAM Report, 09-31"},{"key":"512_CR16","unstructured":"Goldstein, T., ODonoghue, B., & Setzer, S. (2012). Fast alternating direction optimization methods. CAM report, pp. 12\u201335."},{"key":"512_CR17","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1137\/080725891","volume":"2","author":"T Goldstein","year":"2009","unstructured":"Goldstein, T., & Osher, S. (2009). The split Bregman method for L1-regularized prolbems. SIAM Journal on Imaging Sciences, 2, 323\u2013343.","journal-title":"SIAM Journal on Imaging Sciences"},{"key":"512_CR18","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s10589-007-9109-x","volume":"42","author":"BS He","year":"2009","unstructured":"He, B. S. (2009). Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities. Computational Optimization and Applications, 42, 195\u2013212.","journal-title":"Computational Optimization and Applications"},{"key":"512_CR19","first-page":"349","volume":"106","author":"BS He","year":"2000","unstructured":"He, B. S., Yang, H., & Wang, S. L. (2000). Alternating directions method with self-adaptive penalty parameters for monotone variational inequalities. Journal of Optimization Theory and Applications, 106, 349\u2013368.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"512_CR20","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s10851-007-0652-y","volume":"27","author":"T Le","year":"2007","unstructured":"Le, T., Chartrand, R., & Asaki, T. J. (2007). A variational approach to reconstructing images corrupted by Poisson noise. Journal of Mathematical Imaging and Vision, 27, 257\u2013263.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"512_CR21","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. (2003). Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Transactions on Image Processing, 12, 1579\u20131590.","journal-title":"IEEE Transactions on Image Processing"},{"issue":"4","key":"512_CR22","doi-asserted-by":"crossref","first-page":"1643","DOI":"10.1137\/100807697","volume":"33","author":"MK Ng","year":"2011","unstructured":"Ng, M. K., Wang, F., & Yuan, X. M. (2011). Inexact alternating direction methods for image recovery. SIAM Journal on Scientific Computing, 33(4), 1643\u20131668.","journal-title":"SIAM Journal on Scientific Computing"},{"key":"512_CR23","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1023\/B:JMIV.0000011920.58935.9c","volume":"20","author":"M Nikolova","year":"2004","unstructured":"Nikolova, M. (2004). A variational approach to remove outliers and impulse noise. Journal of Mathematical Imaging and Vision, 20, 99\u2013120.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"512_CR24","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L Rudin","year":"1992","unstructured":"Rudin, L., Osher, S., & Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D, 60, 61\u201379.","journal-title":"Physica D"},{"key":"512_CR25","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1007\/978-3-642-02256-2_39","volume":"5567","author":"S Setzer","year":"2009","unstructured":"Setzer, S. (2009). Split Bregman algorithm, Douglas-Rachford splitting, and frame shrinkage. Lecture Notes in Computer Science, 5567, 464\u2013476.","journal-title":"Lecture Notes in Computer Science"},{"key":"512_CR26","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. (2010). Deblurring Poissonian images by split Bregman techniques. Journal of Visual Communication and Image Representation, 21, 193\u2013199.","journal-title":"Journal of Visual Communication and Image Representation"},{"key":"512_CR27","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. (2010). Removing multiplicative noise by Douglas-Rachford splitting methods. Journal of Mathematical Imaging and Vision, 36, 168\u2013184.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"512_CR28","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1137\/100803730","volume":"4","author":"XC Tai","year":"2011","unstructured":"Tai, X. C., Hahn, J., & Chung, G. J. (2011). A fast algorithm for Eulers elastica model using augmented lagrangian method. SIAM Journal on Imaging Sciences, 4, 313\u2013344.","journal-title":"SIAM Journal on Imaging Sciences"},{"key":"512_CR29","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1137\/120867172","volume":"6","author":"T Valkonen","year":"2013","unstructured":"Valkonen, T., Bredies, K., & Knoll, F. (2013). Total generalized variation in diffusion tensor imaging. SIAM Journal on Imaging Sciences, 6, 487\u2013525.","journal-title":"SIAM Journal on Imaging Sciences"},{"key":"512_CR30","doi-asserted-by":"crossref","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. (2004). Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 13, 600\u2013612.","journal-title":"IEEE Transactions on Image Processing"},{"key":"512_CR31","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1137\/090767558","volume":"3","author":"CL Wu","year":"2010","unstructured":"Wu, C. L., & Tai, X. C. (2010). Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models. SIAM Journal on Imaging Sciences, 3, 300\u2013339.","journal-title":"SIAM Journal on Imaging Sciences"},{"issue":"1","key":"512_CR32","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s10915-011-9477-3","volume":"50","author":"C Wu","year":"2012","unstructured":"Wu, C., Zhang, J. Y., Duan, Y. P., & Tai, X. C. (2012). Augmented Lagrangian method for total variation based image restoration and segmentation over triangulated surfaces. Journal of Scientific Computing, 50(1), 145\u2013166.","journal-title":"Journal of Scientific Computing"},{"key":"512_CR33","doi-asserted-by":"crossref","first-page":"237","DOI":"10.3934\/ipi.2011.5.237","volume":"5","author":"CL Wu","year":"2011","unstructured":"Wu, C. L., Zhang, J. Y., & Tai, X. C. (2011). Augmented Lagrangian method for Total Variation Restoration with Non-quadratic Fidelity. Inverse Problems and Imaging, 5, 237\u2013261.","journal-title":"Inverse Problems and Imaging"},{"key":"512_CR34","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1137\/080730421","volume":"2","author":"JF Yang","year":"2009","unstructured":"Yang, J. F., Yin, W. T., Zhang, Y., & Wang, Y. L. (2009). A fast algorithm for edge-preserving variational multichannel image restoration. SIAM Journal on Imaging Sciences, 2, 569\u2013592.","journal-title":"SIAM Journal on Imaging Sciences"},{"issue":"1","key":"512_CR35","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1137\/090777761","volume":"33","author":"JF Yang","year":"2011","unstructured":"Yang, J. F., & Zhang, Y. (2011). Alternating direction method for l1-problems in compressive sensing. SIAM Journal on Scientific Computing, 33(1), 250\u2013278.","journal-title":"SIAM Journal on Scientific Computing"},{"key":"512_CR36","doi-asserted-by":"crossref","first-page":"2842","DOI":"10.1137\/080732894","volume":"31","author":"JF Yang","year":"2009","unstructured":"Yang, J. F., Zhang, Y., & Yin, W. T. (2009). An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise. SIAM Journal on Scientific Computing, 31, 2842\u20132865.","journal-title":"SIAM Journal on Scientific Computing"},{"key":"512_CR37","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1137\/060663027","volume":"6","author":"W Yin","year":"2007","unstructured":"Yin, W., Goldfarb, D., & Osher, S. (2007). The total variation regularized L1 model for multiscale decomposition. Multiscale Modeling and Simulation, 6, 190\u2013211.","journal-title":"Multiscale Modeling and Simulation"},{"key":"512_CR38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/110822268","volume":"5","author":"W Zhu","year":"2012","unstructured":"Zhu, W., & Chan, T. F. (2012). Image denoising using mean curvature of image surface. SIAM Journal on Imaging Sciences, 5, 1\u201332.","journal-title":"SIAM Journal on Imaging Sciences"}],"container-title":["Multidimensional Systems and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11045-017-0512-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-017-0512-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-017-0512-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,9,12]],"date-time":"2018-09-12T13:05:43Z","timestamp":1536757543000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11045-017-0512-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,19]]},"references-count":38,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,10]]}},"alternative-id":["512"],"URL":"https:\/\/doi.org\/10.1007\/s11045-017-0512-x","relation":{},"ISSN":["0923-6082","1573-0824"],"issn-type":[{"type":"print","value":"0923-6082"},{"type":"electronic","value":"1573-0824"}],"subject":[],"published":{"date-parts":[[2017,7,19]]}}}