{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T20:29:54Z","timestamp":1773692994162,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,12,15]],"date-time":"2016-12-15T00:00:00Z","timestamp":1481760000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Engineering and Physical Sciences Research Council (GB)","award":["EP\/M00483X\/1"],"award-info":[{"award-number":["EP\/M00483X\/1"]}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["640156"],"award-info":[{"award-number":["640156"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004299","name":"Senescyt","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004299","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2017,11]]},"DOI":"10.1007\/s10851-016-0692-2","type":"journal-article","created":{"date-parts":[[2016,12,15]],"date-time":"2016-12-15T13:33:45Z","timestamp":1481808825000},"page":"394-414","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Acceleration of the PDHGM on Partially Strongly Convex Functions"],"prefix":"10.1007","volume":"59","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6683-3572","authenticated-orcid":false,"given":"Tuomo","family":"Valkonen","sequence":"first","affiliation":[]},{"given":"Thomas","family":"Pock","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,12,15]]},"reference":[{"key":"692_CR1","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1972","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1972)"},{"key":"692_CR2","doi-asserted-by":"crossref","unstructured":"Ekeland, I., Temam, R.: Convex Analysis and Variational Problems. SIAM (1999)","DOI":"10.1137\/1.9781611971088"},{"key":"692_CR3","doi-asserted-by":"publisher","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\u2013dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120\u2013145 (2011). doi: 10.1007\/s10851-010-0251-1","journal-title":"J. Math. Imaging Vis."},{"issue":"4","key":"692_CR4","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1137\/09076934X","volume":"3","author":"E Esser","year":"2010","unstructured":"Esser, E., Zhang, X., Chan, T.F.: A general framework for a class of first order primal\u2013dual algorithms for convex optimization in imaging science. SIAM J. Imaging Sci. 3(4), 1015\u20131046 (2010). doi: 10.1137\/09076934X","journal-title":"SIAM J. Imaging Sci."},{"issue":"4","key":"692_CR5","doi-asserted-by":"publisher","first-page":"1779","DOI":"10.1137\/130919362","volume":"24","author":"Y Chen","year":"2014","unstructured":"Chen, Y., Lan, G., Ouyang, Y.: Optimal primal\u2013dual methods for a class of saddle point problems. SIAM J. Optim. 24(4), 1779\u20131814 (2014). doi: 10.1137\/130919362","journal-title":"SIAM J. Optim."},{"issue":"1","key":"692_CR6","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s10107-004-0552-5","volume":"103","author":"Y Nesterov","year":"2005","unstructured":"Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program. 103(1), 127\u2013152 (2005). doi: 10.1007\/s10107-004-0552-5","journal-title":"Math. Program."},{"issue":"2","key":"692_CR7","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1137\/100818327","volume":"22","author":"A Beck","year":"2012","unstructured":"Beck, A., Teboulle, M.: Smoothing and first order methods: a unified framework. SIAM J. Optim. 22(2), 557\u2013580 (2012). doi: 10.1137\/100818327","journal-title":"SIAM J. Optim."},{"issue":"3","key":"692_CR8","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1007\/s10208-013-9150-3","volume":"15","author":"B O\u2019Donoghue","year":"2015","unstructured":"O\u2019Donoghue, B., Cand\u00e8s, E.: Adaptive restart for accelerated gradient schemes. Found. Comput. Math. 15(3), 715\u2013732 (2015). doi: 10.1007\/s10208-013-9150-3","journal-title":"Found. Comput. Math."},{"issue":"1","key":"692_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.orl.2013.10.007","volume":"42","author":"A Beck","year":"2014","unstructured":"Beck, A., Teboulle, M.: A fast dual proximal gradient algorithm for convex minimization and applications. Oper. Res. Lett. 42(1), 1\u20136 (2014). doi: 10.1016\/j.orl.2013.10.007","journal-title":"Oper. Res. Lett."},{"issue":"5","key":"692_CR10","doi-asserted-by":"publisher","first-page":"055,012","DOI":"10.1088\/0266-5611\/30\/5\/055012","volume":"30","author":"T Valkonen","year":"2014","unstructured":"Valkonen, T.: A primal\u2013dual hybrid gradient method for non-linear operators with applications to MRI. Inverse Probl. 30(5), 055,012 (2014). doi: 10.1088\/0266-5611\/30\/5\/055012","journal-title":"Inverse Probl."},{"key":"692_CR11","unstructured":"Benning, M., Knoll, F., Sch\u00f6nlieb, C.B., Valkonen, T.: Preconditioned ADMM with nonlinear operator constraint (2015). arXiv:1511.00425"},{"issue":"2","key":"692_CR12","doi-asserted-by":"publisher","first-page":"827","DOI":"10.1137\/140976601","volume":"8","author":"T M\u00f6llenhoff","year":"2015","unstructured":"M\u00f6llenhoff, T., Strekalovskiy, E., Moeller, M., Cremers, D.: The primal\u2013dual hybrid gradient method for semiconvex splittings. SIAM J. Imaging Sci. 8(2), 827\u2013857 (2015). doi: 10.1137\/140976601","journal-title":"SIAM J. Imaging Sci."},{"issue":"2","key":"692_CR13","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/s10851-014-0523-2","volume":"51","author":"D Lorenz","year":"2015","unstructured":"Lorenz, D., Pock, T.: An inertial forward-backward algorithm for monotone inclusions. J. Math. Imaging Vis. 51(2), 311\u2013325 (2015). doi: 10.1007\/s10851-014-0523-2","journal-title":"J. Math. Imaging Vis."},{"key":"692_CR14","unstructured":"Fercoq, O., Bianchi, P.: A coordinate descent primal\u2013dual algorithm with large step size and possibly non separable functions (2015). arXiv:1508.04625"},{"issue":"1","key":"692_CR15","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183\u2013202 (2009). doi: 10.1137\/080716542","journal-title":"SIAM J. Imaging Sci."},{"issue":"11","key":"692_CR16","doi-asserted-by":"publisher","first-page":"2419","DOI":"10.1109\/TIP.2009.2028250","volume":"18","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process. 18(11), 2419\u20132434 (2009). doi: 10.1109\/TIP.2009.2028250","journal-title":"IEEE Trans. Image Process."},{"issue":"3","key":"692_CR17","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1007\/s11263-010-0357-3","volume":"92","author":"S Setzer","year":"2011","unstructured":"Setzer, S.: Operator splittings, Bregman methods and frame shrinkage in image processing. Int. J. Comput. Vis. 92(3), 265\u2013280 (2011). doi: 10.1007\/s11263-010-0357-3","journal-title":"Int. J. Comput. Vis."},{"key":"692_CR18","doi-asserted-by":"publisher","unstructured":"Valkonen, T.: Optimising big images. In: A.\u00a0Emrouznejad (ed.) Big Data Optimization: Recent Developments and Challenges, Studies in Big Data, pp. 97\u2013131. Springer, Berlin (2016). doi: 10.1007\/978-3-319-30265-2_5","DOI":"10.1007\/978-3-319-30265-2_5"},{"key":"692_CR19","doi-asserted-by":"publisher","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis. Springer, Berlin (1998). doi: 10.1007\/978-3-642-02431-3","DOI":"10.1007\/978-3-642-02431-3"},{"issue":"1","key":"692_CR20","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1137\/100814494","volume":"5","author":"B He","year":"2012","unstructured":"He, B., Yuan, X.: Convergence analysis of primal\u2013dual algorithms for a saddle-point problem: from contraction perspective. SIAM J. Imaging Sci. 5(1), 119\u2013149 (2012). doi: 10.1137\/100814494","journal-title":"SIAM J. Imaging Sci."},{"key":"692_CR21","doi-asserted-by":"publisher","unstructured":"Pock, T., Chambolle, A.: Diagonal preconditioning for first order primal\u2013dual algorithms in convex optimization. In: Computer Vision (ICCV), 2011 IEEE International Conference on, pp. 1762 \u20131769 (2011). doi: 10.1109\/ICCV.2011.6126441","DOI":"10.1109\/ICCV.2011.6126441"},{"key":"692_CR22","unstructured":"Rudin, W.: Functional Analysis. International series in Pure and Applied Mathematics. McGraw-Hill, New York (2006)"},{"key":"692_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9467-7","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics","author":"H Bauschke","year":"2011","unstructured":"Bauschke, H., Combettes, P.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, Berlin (2011)"},{"key":"692_CR24","unstructured":"Hohage, T., Homann, C.: A generalization of the Chambolle\u2013Pock algorithm to Banach spaces with applications to inverse problems (2014). arXiv:1412.0126"},{"key":"692_CR25","doi-asserted-by":"crossref","unstructured":"Chan, T., Shen, J.: Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. Society for Industrial and Applied Mathematics (SIAM) (2005)","DOI":"10.1137\/1.9780898717877"},{"key":"692_CR26","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.jmr.2013.10.003","volume":"238","author":"M Benning","year":"2014","unstructured":"Benning, M., Gladden, L., Holland, D., Sch\u00f6nlieb, C.B., Valkonen, T.: Phase reconstruction from velocity-encoded MRI measurements\u2014a survey of sparsity-promoting variational approaches. J. Magn. Reson. 238, 26\u201343 (2014). doi: 10.1016\/j.jmr.2013.10.003","journal-title":"J. Magn. Reson."},{"key":"692_CR27","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502456.001.0001","volume-title":"Functions of Bounded Variation and Free Discontinuity Problems","author":"L Ambrosio","year":"2000","unstructured":"Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford (2000)"},{"issue":"1","key":"692_CR28","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1137\/120867172","volume":"6","author":"T Valkonen","year":"2013","unstructured":"Valkonen, T., Bredies, K., Knoll, F.: Total generalised variation in diffusion tensor imaging. SIAM J. Imaging Sci. 6(1), 487\u2013525 (2013). doi: 10.1137\/120867172","journal-title":"SIAM J. Imaging Sci."},{"key":"692_CR29","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1137\/090769521","volume":"3","author":"K Bredies","year":"2011","unstructured":"Bredies, K., Kunisch, K., Pock, T.: Total generalized variation. SIAM J. Imaging Sci. 3, 492\u2013526 (2011). doi: 10.1137\/090769521","journal-title":"SIAM J. Imaging Sci."},{"key":"692_CR30","unstructured":"Bredies, K., Valkonen, T.: Inverse problems with second-order total generalized variation constraints. In: Proceedings of the 9th International Conference on Sampling Theory and Applications (SampTA) 2011, Singapore (2011)"},{"key":"692_CR31","unstructured":"Temam, R.: Mathematical Problems in Plasticity. Gauthier-Villars (1985)"},{"key":"692_CR32","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-015-0957-3","author":"A Chambolle","year":"2015","unstructured":"Chambolle, A., Pock, T.: On the ergodic convergence rates of a first-order primal-dual algorithm. Math. Program. (2015). doi: 10.1007\/s10107-015-0957-3","journal-title":"Math. Program."},{"key":"692_CR33","first-page":"2080","volume":"28","author":"T Goldstein","year":"2015","unstructured":"Goldstein, T., Li, M., Yuan, X.: Adaptive primal\u2013dual splitting methods for statistical learning and image processing. Adv. Neural Inf. Process. Syst. 28, 2080\u20132088 (2015)","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"692_CR34","doi-asserted-by":"publisher","unstructured":"de Los Reyes, J.C., Sch\u00f6nlieb, C.B., Valkonen, T.: Bilevel parameter learning for higher-order total variation regularisation models. J. Math. Imaging Vis. (2016). doi: 10.1007\/s10851-016-0662-8 . Published online","DOI":"10.1007\/s10851-016-0662-8"},{"key":"692_CR35","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1007\/s10851-011-0274-2","volume":"41","author":"K Chen","year":"2011","unstructured":"Chen, K., Lorenz, D.A.: Image sequence interpolation using optimal control. J. Math. Imaging Vis. 41, 222\u2013238 (2011). doi: 10.1007\/s10851-011-0274-2","journal-title":"J. Math. Imaging Vis."},{"issue":"2","key":"692_CR36","doi-asserted-by":"crossref","first-page":"195","DOI":"10.4171\/IFB\/97","volume":"6","author":"A Chambolle","year":"2004","unstructured":"Chambolle, A.: An algorithm for mean curvature motion. Interfaces Free Bound. 6(2), 195 (2004)","journal-title":"Interfaces Free Bound."},{"key":"692_CR37","unstructured":"Suzuki, T.: Stochastic dual coordinate ascent with alternating direction multiplier method (2013). arXiv:1311.0622v1"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-016-0692-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-016-0692-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-016-0692-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T06:35:58Z","timestamp":1718951758000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-016-0692-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,15]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,11]]}},"alternative-id":["692"],"URL":"https:\/\/doi.org\/10.1007\/s10851-016-0692-2","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,12,15]]}}}