{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T22:51:32Z","timestamp":1768431092388,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,3,21]],"date-time":"2012-03-21T00:00:00Z","timestamp":1332288000000},"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":[[2013,3]]},"DOI":"10.1007\/s10589-012-9475-x","type":"journal-article","created":{"date-parts":[[2012,3,20]],"date-time":"2012-03-20T14:38:47Z","timestamp":1332254327000},"page":"441-459","source":"Crossref","is-referenced-by-count":41,"title":["Primal and dual alternating direction algorithms for \u2113 1-\u2113 1-norm minimization problems in compressive sensing"],"prefix":"10.1007","volume":"54","author":[{"given":"Yunhai","family":"Xiao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Soon-Yi","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,3,21]]},"reference":[{"key":"9475_CR1","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A. Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: A\u00a0fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183\u2013202 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"9475_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."},{"key":"9475_CR3","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S. Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)"},{"key":"9475_CR4","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1137\/080714488","volume":"31","author":"E. Berg van\u00a0den","year":"2008","unstructured":"van\u00a0den Berg, E., Friedlander, M.P.: Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31, 890\u2013912 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"9475_CR5","volume-title":"Parallel and Distributed Computation: Numerical Methods","author":"D.P. Bertsekas","year":"1989","unstructured":"Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods. Prentice Hall, Englewood Cliffs (1989)"},{"key":"9475_CR6","doi-asserted-by":"crossref","first-page":"2992","DOI":"10.1109\/TIP.2007.909319","volume":"16","author":"J.M. Bioucas-Dias","year":"2007","unstructured":"Bioucas-Dias, J.M., Figueiredo, M.: A\u00a0new TwIST: Two-step iterative shrinkage\/thresholding algorithms for image restoration. IEEE Trans. Image Process. 16, 2992\u20133004 (2007)","journal-title":"IEEE Trans. Image Process."},{"key":"9475_CR7","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s10208-004-0162-x","volume":"6","author":"E. Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E., Romberg, J.: Quantitative robust uncertainty principles and optimally sparse decompositions. Found. Comput. Math. 6, 227\u2013254 (2006)","journal-title":"Found. Comput. Math."},{"key":"9475_CR8","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/cpa.20124","volume":"59","author":"E. Cand\u00e8s","year":"2005","unstructured":"Cand\u00e8s, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate information. Commun. Pure Appl. Math. 59, 1207\u20131233 (2005)","journal-title":"Commun. Pure Appl. Math."},{"key":"9475_CR9","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 frequence information. IEEE Trans. Inf. Theory 52, 489\u2013509 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9475_CR10","doi-asserted-by":"crossref","first-page":"5406","DOI":"10.1109\/TIT.2006.885507","volume":"52","author":"E. Cand\u00e8s","year":"2004","unstructured":"Cand\u00e8s, E., Tao, T.: Near optimal signal recovery from random projections: universal encoding strategies. IEEE Trans. Inf. Theory 52, 5406\u20135425 (2004)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9475_CR11","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1007\/s10851-010-0251-1","volume":"40","author":"A. Chambolle","year":"2010","unstructured":"Chambolle, A., Pock, T.: A\u00a0first-order primal-dual algorithm for convex problems with applications to imaging. J.\u00a0Math. Imaging Vis. 40, 120\u2013145 (2010)","journal-title":"J.\u00a0Math. Imaging Vis."},{"key":"9475_CR12","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1137\/S003614450037906X","volume":"43","author":"S.S. Chen","year":"2001","unstructured":"Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43, 129\u2013159 (2001)","journal-title":"SIAM Rev."},{"key":"9475_CR13","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"E.D. Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"9475_CR14","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"D.L. Donoho","year":"2006","unstructured":"Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52, 1289\u20131306 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9475_CR15","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1002\/cpa.20131","volume":"59","author":"D.L. Donoho","year":"2006","unstructured":"Donoho, D.L.: For most large underdetemind systems of linear equations, the minimal \u2113 1-norm solution is also the sparsest solution. Commun. Pure Appl. Math. 59, 907\u2013934 (2006)","journal-title":"Commun. Pure Appl. Math."},{"key":"9475_CR16","unstructured":"Esser, E.: Applications of Lagrangian-based alternating direction methods and connections to split Bregman. TR. 09-31, CAM, UCLA (2009). Available at ftp:\/\/ftp.math.ucla.edu\/pub\/camreport\/cam09-31.pdf"},{"key":"9475_CR17","first-page":"586","volume-title":"IEEE J. Selected Topics in Signal Process.","author":"M. Figueiredo","year":"2007","unstructured":"Figueiredo, M., Nowak, R., Wright, S.J.: Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. In: IEEE J. Selected Topics in Signal Process., pp.\u00a0586\u2013597. IEEE Press, Piscataway (2007)"},{"key":"9475_CR18","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\u00a0dual algorithm for the solution of nonlinear variational problems via finite-element approximations. Comput. Math. Appl. 2, 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"key":"9475_CR19","first-page":"41","volume":"2","author":"R. Glowinski","year":"1975","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, Revue Francaise d\u2019automatique, informatique, recherche op\u00e9retionnelle. Anal. Num\u00e9r. 2, 41\u201376 (1975)","journal-title":"Anal. Num\u00e9r."},{"key":"9475_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 \u2113 1-regularized problems. SIAM J. Imaging Sci. 2, 323\u2013343 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"9475_CR21","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1137\/070698920","volume":"19","author":"E.T. Hale","year":"2008","unstructured":"Hale, E.T., Yin, W., Zhang, Y.: Fixed-point continuation for \u2113 1-minimization: Methodology and convergence. SIAM J. Optim. 19, 1107\u20131130 (2008)","journal-title":"SIAM J. Optim."},{"key":"9475_CR22","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s101070100280","volume":"92","author":"B.S. He","year":"2002","unstructured":"He, B.S., Liao, L.Z., Han, D., Yang, H.: A\u00a0new inexact alternating directions method for monotone variational inequalities. Math. Program. 92, 103\u2013118 (2002)","journal-title":"Math. Program."},{"key":"9475_CR23","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S0167-6377(98)00044-3","volume":"23","author":"B.S. He","year":"1998","unstructured":"He, B.S., Yang, H.: Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities. Oper. Res. Lett. 23, 151\u2013161 (1998)","journal-title":"Oper. Res. Lett."},{"key":"9475_CR24","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1023\/A:1004603514434","volume":"106","author":"B.S. He","year":"2000","unstructured":"He, B.S., Yang, H., Wang, S.L.: Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities. J.\u00a0Optim. Theory Appl. 106, 337\u2013356 (2000)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9475_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/b98874","volume-title":"Numerical Optimization","author":"J. Nocedal","year":"1999","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, Berlin (1999)"},{"key":"9475_CR26","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s11263-010-0357-3","volume":"92","author":"S. Setzer","year":"2011","unstructured":"Setzer, S.: Operator splitting, Bregman methods and frame shrinkage in image processing. Int. J. Comput. Vis. 92, 265\u2013280 (2011)","journal-title":"Int. J. Comput. Vis."},{"key":"9475_CR27","unstructured":"Shen, Y., Wen, Z., Zhang, Y.: Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization. TR11-02, Rice University (2011). Available at http:\/\/www.caam.rice.edu\/~zhang\/reports\/tr1102.pdf"},{"key":"9475_CR28","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, 168\u2013184 (2010)","journal-title":"J. Math. Imaging Vis."},{"key":"9475_CR29","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1137\/100781894","volume":"21","author":"M. Tao","year":"2011","unstructured":"Tao, M., Yuan, X.M.: Recovering low-rank and sparse components of matrices from incomplete and noisy observations. SIAM J. Optim. 21, 57\u201381 (2011)","journal-title":"SIAM J. Optim."},{"key":"9475_CR30","unstructured":"Wright, J., Ma, Y.: Dense error correction via \u2113 1-minimization. Available online at http:\/\/www.dsp.ece.rice.edu\/cs\/"},{"key":"9475_CR31","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.1109\/TSP.2009.2016892","volume":"57","author":"S.J. Wright","year":"2009","unstructured":"Wright, S.J., Nowak, R., Figueiredo, M.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57, 2479\u20132493 (2009)","journal-title":"IEEE Trans. Signal Process."},{"key":"9475_CR32","author":"Y. Xiao","year":"2011","unstructured":"Xiao, Y., Jin, Z.: An alternating direction method for linear-constrained matrix nuclear norm minimization. Numer. Linear Algebra Appl. (2011). doi: 10.1002\/nla.783","journal-title":"Numer. Linear Algebra Appl."},{"key":"9475_CR33","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 \u2113 1-problems in compressive sensing. SIAM J. Sci. Comput. 33, 250\u2013278 (2011)","journal-title":"SIAM J. Sci. Comput."},{"key":"9475_CR34","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1080\/10556780600552693","volume":"22","author":"C.H. Ye","year":"2007","unstructured":"Ye, C.H., Yuan, X.M.: A\u00a0descent method for structured monotone variational inequalities. Optim. Methods Softw. 22, 329\u2013338 (2007)","journal-title":"Optim. Methods Softw."},{"key":"9475_CR35","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s10589-009-9251-8","volume":"48","author":"S. Yun","year":"2011","unstructured":"Yun, S., Toh, K.C.: A\u00a0coordinate gradient descent method for \u2113 1-regularized convex minimization. Comput. Optim. Appl. 48, 273\u2013307 (2011)","journal-title":"Comput. Optim. Appl."},{"key":"9475_CR36","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/s10915-010-9408-8","volume":"46","author":"X. Zhang","year":"2011","unstructured":"Zhang, X., Burger, M., Osher, S.: A\u00a0unified primal-dual framework based on Bregman iteration. J.\u00a0Sci. Comput. 46, 20\u201346 (2011)","journal-title":"J.\u00a0Sci. Comput."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-012-9475-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-012-9475-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-012-9475-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:42Z","timestamp":1559302602000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-012-9475-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,21]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,3]]}},"alternative-id":["9475"],"URL":"https:\/\/doi.org\/10.1007\/s10589-012-9475-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,21]]}}}