{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T23:02:06Z","timestamp":1774047726919,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,12,24]],"date-time":"2014-12-24T00:00:00Z","timestamp":1419379200000},"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 Math Imaging Vis"],"published-print":{"date-parts":[[2015,7]]},"DOI":"10.1007\/s10851-014-0553-9","type":"journal-article","created":{"date-parts":[[2014,12,23]],"date-time":"2014-12-23T16:04:44Z","timestamp":1419350684000},"page":"397-413","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Numerical Methods for Parameter Estimation in Poisson Data Inversion"],"prefix":"10.1007","volume":"52","author":[{"given":"Luca","family":"Zanni","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Benfenati","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mario","family":"Bertero","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valeria","family":"Ruggiero","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,12,24]]},"reference":[{"key":"553_CR1","unstructured":"Arrow, K.J., Hurwicz, L., Uzawa, H.: Studies in Linear and Non-linear Programming. Stanford University Press, Stanford (1958)"},{"key":"553_CR2","doi-asserted-by":"crossref","first-page":"095005","DOI":"10.1088\/0266-5611\/25\/9\/095005","volume":"25","author":"JM Bardsley","year":"2009","unstructured":"Bardsley, J.M., Goldes, J.: Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation. Inverse Problems 25, 095005 (2009)","journal-title":"Inverse Problems"},{"key":"553_CR3","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.: Two point step size gradient methods. IMA J. Numer. Anal. 8, 141\u2013148 (1988)","journal-title":"IMA J. Numer. Anal."},{"key":"553_CR4","doi-asserted-by":"crossref","unstructured":"Ben Hadj, S., Blanc-Feraud, L., Aubert, G., Engler, G.: Blind restoration of confocal microscopy images in presence of a depth-variant blur and poisson noise. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, Canada, pp. 915\u2013919 (2013)","DOI":"10.1109\/ICASSP.2013.6637782"},{"issue":"2","key":"553_CR5","doi-asserted-by":"crossref","first-page":"025004","DOI":"10.1088\/0266-5611\/26\/2\/025004","volume":"26","author":"F Benvenuto","year":"2010","unstructured":"Benvenuto, F., Zanella, R., Zanni, L., Bertero, M.: Nonnegative least-squares image deblurring: improved gradient projection approaches. Inverse Problems 26(2), 025004 (2010)","journal-title":"Inverse Problems"},{"key":"553_CR6","doi-asserted-by":"crossref","first-page":"123006","DOI":"10.1088\/0266-5611\/25\/12\/123006","volume":"25","author":"M Bertero","year":"2009","unstructured":"Bertero, M., Boccacci, P., Desider\u00e1, G., Vicidomini, G.: Image deblurring with Poisson data: from cells to galaxies. Inverse Problems 25, 123006 (2009)","journal-title":"Inverse Problems"},{"key":"553_CR7","doi-asserted-by":"crossref","unstructured":"Bertero, M., Boccacci, P., Talenti, G., Zanella, R., Zanni, L.: A discrepancy principle for Poisson data. Inverse Problems 26, 104004 (2010)","DOI":"10.1088\/0266-5611\/26\/10\/105004"},{"key":"553_CR8","volume-title":"Nonlinear Programming","author":"D Bertsekas","year":"1999","unstructured":"Bertsekas, D.: Nonlinear Programming. Athena Scientific, Belmont (1999)"},{"key":"553_CR9","volume-title":"Parallel and Distributed Computation: Numerical Methods","author":"D Bertsekas","year":"1988","unstructured":"Bertsekas, D., Tsitsiklis, J.: Parallel and Distributed Computation: Numerical Methods. Prentice-Hall, Englewood Cliffs (1988)"},{"key":"553_CR10","doi-asserted-by":"crossref","first-page":"1736","DOI":"10.1137\/120873169","volume":"6","author":"S Bonettini","year":"2013","unstructured":"Bonettini, S., Cornelio, A., Prato, M.: A new semiblind deconvolution approach for Fourier-based image restoration: an application in astronomy. SIAM J. Imaging Sci. 6, 1736\u20131757 (2013)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"553_CR11","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/00207160.2012.716513","volume":"90","author":"S Bonettini","year":"2013","unstructured":"Bonettini, S., Landi, G., Loli Piccolomini, E., Zanni, L.: Scaling techniques for gradient projection-type methods in astronomical image deblurring. Int. J. Comput. Math. 90(1), 9\u201329 (2013)","journal-title":"Int. J. Comput. Math."},{"key":"553_CR12","doi-asserted-by":"crossref","first-page":"095001","DOI":"10.1088\/0266-5611\/26\/9\/095001","volume":"26","author":"S Bonettini","year":"2010","unstructured":"Bonettini, S., Prato, M.: Nonnegative image reconstruction from sparse Fourier data: a new deconvolution algorithm. Inverse Problems 26, 095001 (2010)","journal-title":"Inverse Problems"},{"key":"553_CR13","unstructured":"Bonettini, S., Prato, M.: A new general framework for gradient projection methods. Submitted arXiv:1406.6601v1 (2014)"},{"key":"553_CR14","doi-asserted-by":"crossref","unstructured":"Bonettini, S., Ruggiero, V.: On the uniqueness of the solution of image reconstruction problems with Poisson data, vol. 1281. In: Simos, T.E. et al. (ed.) Proceedings of ICNAAM 2010, AIP Conference Proceedings, pp. 1803\u20131806, AIP (2010)","DOI":"10.1063\/1.3498239"},{"key":"553_CR15","doi-asserted-by":"crossref","first-page":"015002","DOI":"10.1088\/0266-5611\/25\/1\/015002","volume":"25","author":"S Bonettini","year":"2009","unstructured":"Bonettini, S., Zanella, R., Zanni, L.: A scaled gradient projection method for constrained image deblurring. Inverse Problems 25, 015002 (2009)","journal-title":"Inverse Problems"},{"issue":"1","key":"553_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2011","unstructured":"Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends R Mach. Learn. 3(1), 1\u2013122 (2011)","journal-title":"Found. Trends R Mach. Learn."},{"key":"553_CR17","doi-asserted-by":"crossref","unstructured":"Carlavan, M., Blanc-F\u00e9raud, L.: Two constrained formulations for deblurring Poisson noisy images. In: Proceedings of IEEE International Conference on Image Processing (ICIP), Brussels, Belgium (2011)","DOI":"10.1109\/ICIP.2011.6116646"},{"issue":"4","key":"553_CR18","doi-asserted-by":"crossref","first-page":"1834","DOI":"10.1109\/TIP.2011.2175934","volume":"21","author":"M Carlavan","year":"2012","unstructured":"Carlavan, M., Blanc-F\u00e9raud, L.: Sparse Poisson noisy image deblurring. IEEE Trans. Image Process. 21(4), 1834\u20131846 (2012)","journal-title":"IEEE Trans. Image Process."},{"key":"553_CR19","doi-asserted-by":"crossref","unstructured":"Cavicchioli, R., Chaux, C., Blanc-Feraud, L., Zanni, L.: ML estimation of wavelet regularization hyperparameters in inverse problems. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, Canada, pp. 1553\u20131557 (2013)","DOI":"10.1109\/ICASSP.2013.6637912"},{"key":"553_CR20","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\u2013dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120\u2013145 (2011)","journal-title":"J. Math. Imaging Vis."},{"issue":"3","key":"553_CR21","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1007\/s10851-012-0392-5","volume":"47","author":"R Ciak","year":"2012","unstructured":"Ciak, R., Shafei, B., Steidl, G.: Homogeneous penalizers and constraints in convex image restoration. J. Math. Imaging Vis. 47(3), 210\u2013230 (2012)","journal-title":"J. Math. Imaging Vis."},{"key":"553_CR22","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s10107-005-0595-2","volume":"106","author":"YH Dai","year":"2006","unstructured":"Dai, Y.H., Fletcher, R.: New algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds. Math. Program. Ser. A 106, 403\u2013421 (2006)","journal-title":"Math. Program. Ser. A"},{"issue":"2","key":"553_CR23","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1109\/TMI.1986.4307748","volume":"5","author":"ME Daube Witherspoon","year":"1986","unstructured":"Daube Witherspoon, M.E., Muehllener, G.: An iterative image space reconstruction algorithm suitable for volume ECT. IEEE Trans. Med. Imaging 5(2), 61\u201366 (1986)","journal-title":"IEEE Trans. Med. Imaging"},{"key":"553_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-1740-8","volume-title":"Regularization of Inverse Problems","author":"HW Engl","year":"1996","unstructured":"Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Kluwer Academic Publishers, Dordrecht (1996)"},{"key":"553_CR25","doi-asserted-by":"crossref","first-page":"3133","DOI":"10.1109\/TIP.2010.2053941","volume":"19","author":"MAT Figueiredo","year":"2010","unstructured":"Figueiredo, M.A.T., Bioucas-Dias, J.M.: Restoration of Poissonian images using alternating direction optimization. IEEE Trans. Image Process. 19, 3133\u20133145 (2010)","journal-title":"IEEE Trans. Image Process."},{"issue":"1\u20132","key":"553_CR26","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/s10107-011-0479-6","volume":"135","author":"R Fletcher","year":"2012","unstructured":"Fletcher, R.: A limited memory steepest descent method. Math. Program. 135(1\u20132), 413\u2013436 (2012)","journal-title":"Math. Program."},{"issue":"2","key":"553_CR27","doi-asserted-by":"crossref","first-page":"299","DOI":"10.3934\/jimo.2008.4.299","volume":"4","author":"G Frassoldati","year":"2008","unstructured":"Frassoldati, G., Zanni, L., Zanghirati, G.: New adaptive stepsize selections in gradient methods. J. Ind. Manag. Optim. 4(2), 299\u2013312 (2008)","journal-title":"J. Ind. Manag. Optim."},{"key":"553_CR28","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 elements approximations. Comput. Math. Appl. 2, 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"issue":"6","key":"553_CR29","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","volume":"6","author":"S Geman","year":"1984","unstructured":"Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6(6), 721\u2013741 (1984)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"553_CR30","doi-asserted-by":"crossref","unstructured":"Glowinski, R., Marrocco, A.: Sur l\u2019approximation, par elements finis d\u2019ordre un, et la resolution, par penalisation-dualit\u00e9, d\u2019une classe de problems de dirichlet non lineares. Revue Fran\u00e7aise d\u2019Automatique, Infomatique, et Recherche Op\u00e9rationelle (1975)","DOI":"10.1051\/m2an\/197509R200411"},{"key":"553_CR31","volume-title":"Matrix Computations","author":"G Golub","year":"1996","unstructured":"Golub, G., Van Loan, C.: Matrix Computations, 3rd edn. The Johns Hopkins Press, Baltimore (1996)","edition":"3"},{"issue":"2","key":"553_CR32","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1023\/A:1004603514434","volume":"106","author":"BS He","year":"2000","unstructured":"He, B.S., Yang, Y., Wang, S.L.: Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities. J. Optim. Theory Appl. 106(2), 337\u2013356 (2000)","journal-title":"J. Optim. Theory Appl."},{"key":"553_CR33","doi-asserted-by":"crossref","unstructured":"Hiriart, J.B., Lemarechal, C.: Convex Analysis and Minimization Algorithms, vol. 1. Springer, Berlin (1993)","DOI":"10.1007\/978-3-662-02796-7"},{"issue":"5","key":"553_CR34","doi-asserted-by":"crossref","first-page":"1397","DOI":"10.1088\/0266-5611\/18\/5\/313","volume":"18","author":"H Lant\u00e9ri","year":"2002","unstructured":"Lant\u00e9ri, H., Roche, M., Aime, C.: Penalized maximum likelihood image restoration with positivity constraints: multiplicative algorithms. Inverse Problems 18(5), 1397\u20131419 (2002)","journal-title":"Inverse Problems"},{"key":"553_CR35","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.: A variational approach to reconstructing images corrupted by Poisson noise. J. Math. Imaging Vis. 27, 257\u2013263 (2007)","journal-title":"J. Math. Imaging Vis."},{"key":"553_CR36","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1086\/111605","volume":"79","author":"LB Lucy","year":"1974","unstructured":"Lucy, L.B.: An iterative technique for the rectification of observed distributions. Astron. J. 79, 745\u2013754 (1974)","journal-title":"Astron. J."},{"key":"553_CR37","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.cnsns.2014.08.035","volume":"21","author":"F Porta","year":"2015","unstructured":"Porta, F., Zanella, R., Zanghirati, G., Zanni, L.: Limited-memory scaled gradient projection methods for real-time image deconvolution in microscopy. Commun. Nonlinear Sci. Numer. Simul. 21, 112\u2013127 (2015)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"553_CR38","doi-asserted-by":"crossref","first-page":"A133","DOI":"10.1051\/0004-6361\/201118681","volume":"539","author":"M Prato","year":"2012","unstructured":"Prato, M., Cavicchioli, R., Zanni, L., Boccacci, P., Bertero, M.: Efficient deconvolution methods for astronomical imaging: algorithms and IDL-GPU codes. Astron. Astrophys. 539, A133 (2012)","journal-title":"Astron. Astrophys."},{"issue":"1","key":"553_CR39","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1364\/JOSA.62.000055","volume":"62","author":"WH Richardson","year":"1972","unstructured":"Richardson, W.H.: Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. A 62(1), 55\u201359 (1972)","journal-title":"J. Opt. Soc. Am. A"},{"key":"553_CR40","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"key":"553_CR41","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.: Deblurring Poissonian images by split Bregman techniques. J. Vis. Commun. Image R. 21, 193\u2013199 (2010)","journal-title":"J. Vis. Commun. Image R."},{"issue":"2","key":"553_CR42","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1109\/TMI.1982.4307558","volume":"1","author":"LA Shepp","year":"1982","unstructured":"Shepp, L.A., Vardi, Y.: Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imaging 1(2), 113\u2013122 (1982)","journal-title":"IEEE Trans. Med. Imaging"},{"key":"553_CR43","doi-asserted-by":"crossref","first-page":"125003","DOI":"10.1088\/0266-5611\/27\/12\/125003","volume":"27","author":"A Staglian\u00f2","year":"2011","unstructured":"Staglian\u00f2, A., Boccacci, P., Bertero, M.: Analysis of an approximate model for Poisson data reconstruction and a related discrepancy principle. Inverse Problems 27, 125003 (2011)","journal-title":"Inverse Problems"},{"key":"553_CR44","doi-asserted-by":"crossref","first-page":"035007","DOI":"10.1088\/0266-5611\/29\/3\/035007","volume":"29","author":"T Teuber","year":"2013","unstructured":"Teuber, T., Steidl, G., Chan, R.H.: Minimization and parameter estimation for seminorm regularization models with I-divergence constraints. Inverse Problems 29, 035007 (2013)","journal-title":"Inverse Problems"},{"issue":"2","key":"553_CR45","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1023\/A:1017522623963","volume":"109","author":"SL Wang","year":"2001","unstructured":"Wang, S.L., Liao, L.Z.: Decomposition method with a variable parameter for a class of monotone variational inequality problems. J. Optim. Theory Appl. 109(2), 415\u2013429 (2001)","journal-title":"J. Optim. Theory Appl."},{"key":"553_CR46","doi-asserted-by":"crossref","first-page":"045010","DOI":"10.1088\/0266-5611\/25\/4\/045010","volume":"25","author":"R Zanella","year":"2009","unstructured":"Zanella, R., Boccacci, P., Zanni, L., Bertero, M.: Efficient gradient projection methods for edge-preserving removal of Poisson noise. Inverse Problems 25, 045010 (2009)","journal-title":"Inverse Problems"},{"key":"553_CR47","doi-asserted-by":"crossref","first-page":"119501","DOI":"10.1088\/0266-5611\/29\/11\/119501","volume":"29","author":"R Zanella","year":"2013","unstructured":"Zanella, R., Boccacci, P., Zanni, L., Bertero, M.: Corrigendum: efficient gradient projection methods for edge-preserving removal of Poisson noise. Inverse Problems 29, 119501 (2013)","journal-title":"Inverse Problems"},{"key":"553_CR48","doi-asserted-by":"crossref","unstructured":"Zanella, R., Zanghirati, G., Cavicchioli, R., Zanni, L., Boccacci, P., Bertero, M., Vicidomini, G.: Towards real-time image deconvolution: application to confocal and sted microscopy. Scientific Reports 3 (2013)","DOI":"10.1038\/srep02523"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-014-0553-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-014-0553-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-014-0553-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,18]],"date-time":"2019-08-18T19:24:07Z","timestamp":1566156247000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-014-0553-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,24]]},"references-count":48,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,7]]}},"alternative-id":["553"],"URL":"https:\/\/doi.org\/10.1007\/s10851-014-0553-9","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,24]]}}}