{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,8]],"date-time":"2026-08-08T05:29:09Z","timestamp":1786166949993,"version":"3.56.0"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,7,3]],"date-time":"2013-07-03T00:00:00Z","timestamp":1372809600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2013,12]]},"DOI":"10.1007\/s10589-013-9576-1","type":"journal-article","created":{"date-parts":[[2013,7,2]],"date-time":"2013-07-02T12:48:41Z","timestamp":1372769321000},"page":"507-530","source":"Crossref","is-referenced-by-count":602,"title":["An efficient augmented Lagrangian method with applications to total variation minimization"],"prefix":"10.1007","volume":"56","author":[{"given":"Chengbo","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wotao","family":"Yin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hong","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yin","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2013,7,3]]},"reference":[{"key":"9576_CR1","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","volume":"8","author":"J. Barzilai","year":"1988","unstructured":"Barzilai, J., Borwein, J.M.: Two-point step size gradient methods. IMA J. Numer. Anal. 8, 141\u2013148 (1988)","journal-title":"IMA J. Numer. Anal."},{"key":"9576_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/090756855","volume":"4","author":"S. Becker","year":"2011","unstructured":"Becker, S., Bobin, J., Cand\u00e8s, E.: NESTA: a fast and accurate first-order method for sparse recovery. SIAM J. Imaging Sci. 4, 1\u201339 (2011)","journal-title":"SIAM J. Imaging Sci."},{"issue":"12","key":"9576_CR3","doi-asserted-by":"crossref","first-page":"2992","DOI":"10.1109\/TIP.2007.909319","volume":"16","author":"J. Bioucas-Dias","year":"2007","unstructured":"Bioucas-Dias, J., Figueiredo, M.: A new TwIST: two-step iterative thresholding algorithm for image restoration. IEEE Trans. Image Process. 16(12), 2992\u20133004 (2007)","journal-title":"IEEE Trans. Image Process."},{"key":"9576_CR4","volume-title":"IEEE International Conference on Image Processing\u2014ICIP 2007","author":"J. Bioucas-Dias","year":"2007","unstructured":"Bioucas-Dias, J., Figueiredo, M.: Two-step algorithms for linear inverse problems with non-quadratic regularization. In: IEEE International Conference on Image Processing\u2014ICIP 2007, San Antonio, TX, USA, September 2007"},{"issue":"11","key":"9576_CR5","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/34.969114","volume":"23","author":"Y. Boykov","year":"2001","unstructured":"Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23(11), 1222\u20131239 (2001)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"2","key":"9576_CR6","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/TIT.2005.862083","volume":"52","author":"E. Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489\u2013509 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"12","key":"9576_CR7","doi-asserted-by":"crossref","first-page":"5406","DOI":"10.1109\/TIT.2006.885507","volume":"52","author":"E. Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E., Tao, T.: Near optimal signal recovery from random projections: universal encoding strategies. IEEE Trans. Inf. Theory 52(12), 5406\u20135425 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9576_CR8","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":"3","key":"9576_CR9","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1109\/83.661187","volume":"7","author":"T. Chan","year":"1998","unstructured":"Chan, T., Wong, C.K.: Total variation blind deconvolution. IEEE Trans. Image Process. 7(3), 370\u2013375 (1998)","journal-title":"IEEE Trans. Image Process."},{"key":"9576_CR10","volume-title":"ISMRM","author":"T. Chang","year":"2006","unstructured":"Chang, T., He, L., Fang, T.: MR image reconstruction from sparse radial samples using Bregman iteration. In: ISMRM (2006)"},{"issue":"4","key":"9576_CR11","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"D. Donoho","year":"2006","unstructured":"Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289\u20131306 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9576_CR12","doi-asserted-by":"crossref","unstructured":"Donoho, D.: Neighborly polytopes and sparse solution of underdetermined linear equations. IEEE Trans. Inf. Theory (2006)","DOI":"10.1109\/ISIT.2006.261816"},{"key":"9576_CR13","first-page":"1537","volume-title":"39th Asilomar Conference on Signals, Systems and Computers","author":"M.F. Duarte","year":"2005","unstructured":"Duarte, M.F., Sarvotham, S., Baron, D., Wakin, M.B., Baraniuk, R.G.: Distributed compressed sensing of jointly sparse signals. In: 39th Asilomar Conference on Signals, Systems and Computers, pp. 1537\u20131541 (2005)"},{"key":"9576_CR14","series-title":"Application \u00e0 la R\u00e9solution Num\u00e9rique de Probl\u00e8mes aux Limites","volume-title":"M\u00e9thodes de Lagrangien Augment\u00e9","author":"M. Fortin","year":"1982","unstructured":"Fortin, M., Glowinski, R.: M\u00e9thodes de Lagrangien Augment\u00e9. Application \u00e0 la R\u00e9solution Num\u00e9rique de Probl\u00e8mes aux Limites. Dunod-Bordas, Paris (1982) (in French)"},{"key":"9576_CR15","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0898-1221(76)90003-1","volume":"2","author":"D. Gabay","year":"1976","unstructured":"Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximations. Comput. Appl. Math. 2, 17\u201340 (1976)","journal-title":"Comput. Appl. Math."},{"key":"9576_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12613-4","volume-title":"Numerical Methods for Nonlinear Variational Problems","author":"R. Glowinski","year":"1984","unstructured":"Glowinski, R.: Numerical Methods for Nonlinear Variational Problems. Springer, Berlin (1984)"},{"key":"9576_CR17","first-page":"1649","volume":"278A","author":"R. Glowinski","year":"1974","unstructured":"Glowinski, R., Marrocco, A.: Sur l\u2019approximation par \u00e9l\u00e9ments finis d\u2019ordre un et la r\u00e9solution par p\u00e9nalisation-dualit\u00e9 d\u2019une classe de probl\u00e8mes de Dirichlet nonlin\u00e9aires. C. R. Math. Acad. Sci. Paris 278A, 1649\u20131652 (1974) (in French)","journal-title":"C. R. Math. Acad. Sci. Paris"},{"issue":"2","key":"9576_CR18","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":"9576_CR19","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1137\/0723046","volume":"23","author":"L. Grippo","year":"1986","unstructured":"Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton\u2019s method. SIAM J. Numer. Anal. 23, 707\u2013716 (1986)","journal-title":"SIAM J. Numer. Anal."},{"key":"9576_CR20","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1137\/090775063","volume":"4","author":"W.W. Hager","year":"2011","unstructured":"Hager, W.W., Phan, D.T., Zhang, H.: Gradient-based methods for sparse recovery. SIAM J. Imaging Sci. 4, 146\u2013165 (2011)","journal-title":"SIAM J. Imaging Sci."},{"key":"9576_CR21","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF00927673","volume":"4","author":"M.R. Hestenes","year":"1969","unstructured":"Hestenes, M.R.: Multiplier and gradient methods. J. Optim. Theory Appl. 4, 303\u2013320 (1969)","journal-title":"J. Optim. Theory Appl."},{"key":"9576_CR22","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1002\/bltj.20539","volume":"16","author":"H. Jiang","year":"2012","unstructured":"Jiang, H., Li, C., Haimi-Cohen, R., Wilford, P., Zhang, Y.: Scalable video coding using compressive sensing. Bell Labs Tech. J. 16, 149\u2013169 (2012)","journal-title":"Bell Labs Tech. J."},{"key":"9576_CR23","volume-title":"Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS)","author":"J. Laska","year":"2007","unstructured":"Laska, J., Kirolos, S., Duarte, M., Ragheb, T., Baraniuk, R., Massoud, Y.: Theory and implementation of an analog-to-information converter using random demodulation. In: Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS), New Orleans, Louisiana (2007)"},{"key":"9576_CR24","first-page":"2077","volume-title":"IEEE Wireless Communications and Networking Conference (WCNC)","author":"C. Li","year":"2011","unstructured":"Li, C., Jiang, H., Wilford, P., Zhang, Y.: Video coding using compressive sensing for wireless communications. In: IEEE Wireless Communications and Networking Conference (WCNC), pp. 2077\u20132082 (2011). doi: 10.1109\/WCNC.2011.5779474"},{"key":"9576_CR25","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1109\/TIP.2011.2167626","volume":"21","author":"C. Li","year":"2012","unstructured":"Li, C., Sun, T., Kelly, K., Zhang, Y.: A compressive sensing and unmixing scheme for hyperspectral data processing. IEEE Trans. Image Process. 21, 1200\u20131210 (2012)","journal-title":"IEEE Trans. Image Process."},{"key":"9576_CR26","unstructured":"Li, C., Zhang, Y., Yin, W.: http:\/\/www.caam.rice.edu\/~optimization\/L1\/TVAL3\/"},{"key":"9576_CR27","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1137\/0716071","volume":"16","author":"P.L. Lions","year":"1979","unstructured":"Lions, P.L., Mercier, B.: Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16, 964\u2013979 (1979)","journal-title":"SIAM J. Numer. Anal."},{"key":"9576_CR28","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1137\/S0097539792240406","volume":"24","author":"B.K. Natarajan","year":"1995","unstructured":"Natarajan, B.K.: Sparse approximate solutions to linear systems. SIAM J. Comput. 24, 227\u2013234 (1995)","journal-title":"SIAM J. Comput."},{"key":"9576_CR29","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10107-004-0552-5","volume":"103","author":"Yu. Nesterov","year":"2005","unstructured":"Nesterov, Yu.: Smooth minimization of non-smooth functions. Math. Program., Ser. A 103, 127\u2013152 (2005)","journal-title":"Math. Program., Ser. A"},{"key":"9576_CR30","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1137\/040605412","volume":"4","author":"S. Osher","year":"2005","unstructured":"Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An iterated regularization method for total variation based image restoration. Multiscale Model. Simul. 4, 460\u2013489 (2005)","journal-title":"Multiscale Model. Simul."},{"key":"9576_CR31","first-page":"283","volume-title":"Optimization","author":"M.J.D. Powell","year":"1969","unstructured":"Powell, M.J.D.: A method for nonlinear constraints in minimization problems. In: Fletcher, R. (ed.) Optimization, pp. 283\u2013298. Academic Press, London (1969)"},{"issue":"6","key":"9576_CR32","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/BF00934777","volume":"12","author":"R.T. Rockafellar","year":"1973","unstructured":"Rockafellar, R.T.: The multiplier method of Hestenes and Powell applied to convex programming. J.\u00a0Optim. Theory Appl. 12(6), 555\u2013562 (1973)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9576_CR33","doi-asserted-by":"crossref","unstructured":"Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 259\u2013268 (1992)","DOI":"10.1016\/0167-2789(92)90242-F"},{"key":"9576_CR34","volume-title":"Proceedings of the 35th International Symposium for Testing and Failure Analysis","author":"T. Sun","year":"2009","unstructured":"Sun, T., Woods, G.L., Duarte, M.F., Kelly, K.F., Li, C., Zhang, Y.: OBIC measurements without lasers or raster-scanning based on compressive sensing. In: Proceedings of the 35th International Symposium for Testing and Failure Analysis (2009)"},{"key":"9576_CR35","first-page":"43","volume-title":"Computational Imaging IV","author":"D. Takhar","year":"2006","unstructured":"Takhar, D., Laska, J.N., Wakin, M.B., Duarte, M.F., Baron, D., Sarvotham, S., Kelly, K.F., Baraniuk, R.G.: A new compressive imaging camera architecture using optical-domain compression. In: Computational Imaging IV, vol. 6065, pp. 43\u201352 (2006)"},{"issue":"4","key":"9576_CR36","doi-asserted-by":"crossref","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(4), 248\u2013272 (2008)","journal-title":"SIAM J. Imaging Sci."},{"key":"9576_CR37","unstructured":"Yang, J., Yin, W., Zhang, Y.: A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data. Technical Report, TR08-27, CAAM, Rice University (2008)"},{"key":"9576_CR38","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1137\/070703983","volume":"1","author":"W. Yin","year":"2008","unstructured":"Yin, W., Osher, S., Goldfarb, D., Darbon, J.: Bregman iterative algorithms for \u2113 1-minimization with applications to compressed sensing. SIAM J. Imaging Sci. 1, 143\u2013168 (2008)","journal-title":"SIAM J. Imaging Sci."},{"key":"9576_CR39","volume-title":"Proceedings of Visual Communications and Image Processing (VCIP)","author":"W. Yin","year":"2010","unstructured":"Yin, W., Morgan, S., Yang, J., Zhang, Y.: Practical compressive sensing with Toeplitz and circulant matrices. In: Proceedings of Visual Communications and Image Processing (VCIP) (2010)"},{"key":"9576_CR40","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1137\/S1052623403428208","volume":"14","author":"H. Zhang","year":"2004","unstructured":"Zhang, H., Hager, W.W.: A nonmonotone line search technique and its application to unconstrained optimization. SIAM J. Optim. 14, 1043\u20131056 (2004)","journal-title":"SIAM J. Optim."},{"key":"9576_CR41","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1007\/s10851-011-0314-y","volume":"44","author":"Y. Xiao","year":"2012","unstructured":"Xiao, Y., Song, H.: An inexact alternating directions algorithm for constrained total variation regularized compressive sensing problems. J. Math. Imaging Vis. 44, 114\u2013127 (2012)","journal-title":"J. Math. Imaging Vis."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9576-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-013-9576-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9576-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,16]],"date-time":"2019-07-16T19:24:33Z","timestamp":1563305073000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-013-9576-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,3]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["9576"],"URL":"https:\/\/doi.org\/10.1007\/s10589-013-9576-1","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7,3]]}}}