{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T08:20:56Z","timestamp":1649060456003},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2018,7,19]],"date-time":"2018-07-19T00:00:00Z","timestamp":1531958400000},"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. Appl. Math. Comput."],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s12190-018-1205-9","type":"journal-article","created":{"date-parts":[[2018,7,19]],"date-time":"2018-07-19T12:25:09Z","timestamp":1532003109000},"page":"113-145","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Matrix forms of iterative algorithms to solve large-scale discrete ill-posed problems with an application to image restoration"],"prefix":"10.1007","volume":"60","author":[{"given":"Fernando","family":"Pazos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amit","family":"Bhaya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,7,19]]},"reference":[{"key":"1205_CR1","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1051\/m2an\/2009025","volume":"43","author":"U Ascher","year":"2009","unstructured":"Ascher, U., van den Doel, K., Huang, H., Svaiter, B.: On fast integration to steady state and earlier times. Math. Model. Numer. Anal. 43, 689\u2013708 (2009)","journal-title":"Math. Model. Numer. Anal."},{"key":"1205_CR2","doi-asserted-by":"publisher","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). \n                    https:\/\/doi.org\/10.1093\/imanum\/8.1.141","journal-title":"IMA J. Numer. Anal."},{"key":"1205_CR3","doi-asserted-by":"publisher","first-page":"1795","DOI":"10.1016\/j.matcom.2011.01.016","volume":"81","author":"F Bauer","year":"2011","unstructured":"Bauer, F., Lukas, M.A.: Comparing parameter choice methods for regularization of ill-posed problems. Math. Comput. Simul. 81, 1795\u20131841 (2011). \n                    https:\/\/doi.org\/10.1016\/j.matcom.2011.01.016","journal-title":"Math. Comput. Simul."},{"key":"1205_CR4","doi-asserted-by":"publisher","unstructured":"Bhaya, A., Bliman, P.-A., Pazos, F.: Control-theoretic design of iterative methods for symmetric linear systems of equations. In: Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China (2009). \n                    https:\/\/doi.org\/10.1109\/CDC.2009.5399581","DOI":"10.1109\/CDC.2009.5399581"},{"key":"1205_CR5","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/978-1-4612-0571-5_7","volume-title":"Iterative Solution Methods for Large Linear Discrete Ill-Posed Problems","author":"D Calvetti","year":"1999","unstructured":"Calvetti, D., Reichel, L., Zhang, Q.: Iterative Solution Methods for Large Linear Discrete Ill-Posed Problems, vol. 1, pp. 313\u2013367. Birkh\u00e4user, Boston (1999). \n                    https:\/\/doi.org\/10.1007\/978-1-4612-0571-5_7"},{"key":"1205_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-1740-8","volume-title":"Regularization of Inverse Problems","author":"H Engl","year":"1996","unstructured":"Engl, H., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Kluwer Academic Publishers, London (1996)"},{"key":"1205_CR7","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1088\/0266-5611\/17\/2\/308","volume":"17","author":"Y-F Wang","year":"2001","unstructured":"Wang, Y.-F., Xiao, T.-Y.: Fast realization algorithms for determining regularization parameters in linear inverse problems. Inverse Probl. 17, 281\u2013291 (2001). \n                    https:\/\/doi.org\/10.1088\/0266-5611\/17\/2\/308","journal-title":"Inverse Probl."},{"key":"1205_CR8","doi-asserted-by":"publisher","first-page":"1831","DOI":"10.1137\/S1064827596313310","volume":"20","author":"A Frommer","year":"1999","unstructured":"Frommer, A., Maass, P.: Fast CG-based methods for Tikhonov\u2013Phillips regularization. SIAM J. Sci. Comput. 20, 1831\u20131850 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"1205_CR9","first-page":"83","volume":"44","author":"S Gazzola","year":"2015","unstructured":"Gazzola, S., Novati, P., Russo, M.R.: On Krylov projection methods and Tikhonov regularization. Electron. Trans. Numer. Anal. 44, 83\u2013123 (2015)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"1205_CR10","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1080\/00401706.1979.10489751","volume":"21","author":"G Golub","year":"1979","unstructured":"Golub, G., Heath, M., Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21, 215\u2013223 (1979). \n                    https:\/\/doi.org\/10.1080\/00401706.1979.10489751","journal-title":"Technometrics"},{"key":"1205_CR11","volume-title":"Matrix Computation","author":"G Golub","year":"1989","unstructured":"Golub, G., Van Loan, C.: Matrix Computation. The Johns Hopkins University Press, Baltimore (1989)"},{"key":"1205_CR12","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1007\/BF01385796","volume":"59","author":"G Golub","year":"1991","unstructured":"Golub, G., von Matt, U.: Quadratically constrained least squares and quadratic problems. Numer. Math. 59, 561\u2013580 (1991). \n                    https:\/\/doi.org\/10.1007\/BF01385796","journal-title":"Numer. Math."},{"key":"1205_CR13","first-page":"3","volume-title":"Workshop on Scientific Computing","author":"G Golub","year":"1997","unstructured":"Golub, G., von Matt, U.: Tikhonov regularization for large scale problems. In: Golub, G.H., Lui, S.H., Luk, F., Plemmons, R. (eds.) Workshop on Scientific Computing, pp. 3\u201326. Springer, New York (1997)"},{"key":"1205_CR14","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970937","volume-title":"Iterative Methods for Solving Linear Systems","author":"A Greenbaum","year":"1997","unstructured":"Greenbaum, A.: Iterative Methods for Solving Linear Systems. SIAM, Philadelphia (1997)"},{"key":"1205_CR15","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-68407-9","volume-title":"Fundations of Optimization","author":"O G\u00fcler","year":"2010","unstructured":"G\u00fcler, O.: Fundations of Optimization. Graduate Texts in Mathematics. Springer, Berlin (2010)"},{"key":"1205_CR16","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/978-3-7091-6296-5_3","volume-title":"Surveys on Solution Methods for Inverse Problems","author":"M Hanke","year":"2000","unstructured":"Hanke, M.: Iterative regularization techniques in image reconstruction. In: Colton, D., Engl, H.W., Louis, A.K., McLaughlin, J.R., Rundell, W. (eds.) Surveys on Solution Methods for Inverse Problems, pp. 35\u201352. Springer, Vienna (2000). \n                    https:\/\/doi.org\/10.1007\/978-3-7091-6296-5_3"},{"key":"1205_CR17","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1088\/0266-5611\/12\/2\/004","volume":"12","author":"M Hanke","year":"1996","unstructured":"Hanke, M., Nagy, J.G.: Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques. Inverse Probl. 12, 157\u2013173 (1996). \n                    https:\/\/doi.org\/10.1088\/0266-5611\/12\/2\/004","journal-title":"Inverse Probl."},{"key":"1205_CR18","unstructured":"Hansen, P.C.: The L-curve and its use in the numerical treatment of inverse problems. In: Johnston, P. (ed.) Computational Inverse Problems in Electrocardiology, Advances in Computational Bioengineering. IMM, Department of Mathematical Modelling, Technical University of Denmark (2000)"},{"key":"1205_CR19","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s11075-007-9136-9","volume":"46","author":"PC Hansen","year":"2007","unstructured":"Hansen, P.C.: Regularization tools: a MATLAB package for analysis and solution of discrete ill-posed problems. Numer. Algorithms 46, 189\u2013194 (2007). \n                    https:\/\/doi.org\/10.1007\/s11075-007-9136-9","journal-title":"Numer. Algorithms"},{"key":"1205_CR20","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718874","volume-title":"Deblurring Images. Matrices, Spectra and Filtering, Fundamentals of Algorithms","author":"PC Hansen","year":"2006","unstructured":"Hansen, P.C., Nagy, J., O\u2019Leary, D.P.: Deblurring Images. Matrices, Spectra and Filtering, Fundamentals of Algorithms. SIAM, Philadelphia (2006)"},{"key":"1205_CR21","doi-asserted-by":"publisher","first-page":"409","DOI":"10.6028\/jres.049.044","volume":"49","author":"MR Hestenes","year":"1952","unstructured":"Hestenes, M.R., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49, 409\u2013436 (1952)","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"1205_CR22","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/j.cam.2014.06.004","volume":"273","author":"ME Hochstenbach","year":"2015","unstructured":"Hochstenbach, M.E., Reichel, L., Rodriguez, G.: Regularization parameter determination for discrete ill-posed problems. J. Comput. Appl. Math. 273, 132\u2013149 (2015). \n                    https:\/\/doi.org\/10.1016\/j.cam.2014.06.004","journal-title":"J. Comput. Appl. Math."},{"key":"1205_CR23","volume-title":"Fundamentals of Digital Image Processing","author":"A Jain","year":"1989","unstructured":"Jain, A.: Fundamentals of Digital Image Processing. Prentice-Hall, Englewood Cliffs, NJ (1989)"},{"key":"1205_CR24","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/s10543-006-0109-5","volume":"47","author":"TK Jensen","year":"2007","unstructured":"Jensen, T.K., Hansen, P.C.: Iterative regularization with minimum-residual methods. BIT Numer. Math. 47, 103\u2013120 (2007). \n                    https:\/\/doi.org\/10.1007\/s10543-006-0109-5","journal-title":"BIT Numer. Math."},{"key":"1205_CR25","doi-asserted-by":"publisher","first-page":"1204","DOI":"10.1137\/S0895479899345960","volume":"22","author":"M Kilmer","year":"2001","unstructured":"Kilmer, M., O\u2019Leary, D.P.: Choosing regularization parameters in iterative methods for ill-posed problems. SIAM J. Matrix Anal. Appl. 22, 1204\u20131221 (2001). \n                    https:\/\/doi.org\/10.1137\/S0895479899345960","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1205_CR26","doi-asserted-by":"publisher","first-page":"1247","DOI":"10.1088\/0266-5611\/14\/5\/010","volume":"14","author":"K Kunisch","year":"1998","unstructured":"Kunisch, K., Zou, J.: Iterative choices of regularization parameters in linear inverse problems. Inverse Probl. 14, 1247\u20131264 (1998). \n                    https:\/\/doi.org\/10.1088\/0266-5611\/14\/5\/010","journal-title":"Inverse Probl."},{"key":"1205_CR27","volume-title":"Regularization Methods for Ill-Posed Problems","author":"VA Morozov","year":"1993","unstructured":"Morozov, V.A.: Regularization Methods for Ill-Posed Problems. CRC Press, Albany, NY (1993)"},{"key":"1205_CR28","doi-asserted-by":"publisher","first-page":"1003","DOI":"10.1023\/B:BITN.0000014546.51341.53","volume":"43","author":"JG Nagy","year":"2003","unstructured":"Nagy, J.G., Palmer, K.M.: Steepest descent, CG and iterative regularization of ill posed problems. BIT Numer. Math. 43, 1003\u20131017 (2003). \n                    https:\/\/doi.org\/10.1023\/B:BITN.0000014546.51341.53","journal-title":"BIT Numer. Math."},{"key":"1205_CR29","doi-asserted-by":"publisher","unstructured":"Nagy, J.G., Palmer, K.M.: Quasi-Newton methods for image restoration. In: Proceedings of SPIE\u2014The International Society for Optical Engineering, vol. 5559, pp. 412\u2013422 (2004). \n                    https:\/\/doi.org\/10.1117\/12.561060","DOI":"10.1117\/12.561060"},{"key":"1205_CR30","doi-asserted-by":"publisher","unstructured":"Nagy, J.G., O\u2019Leary, D.P.: Fast iterative image restoration with a spatially-varying PSF. In: Luk, F.T. (ed.) Proceedings of SPIE\u2014The International Society for Optical Engineering, vol. 3162, pp. 388\u2013399. San Diego, CA, USA (1997). \n                    https:\/\/doi.org\/10.1117\/12.279513","DOI":"10.1117\/12.279513"},{"key":"1205_CR31","doi-asserted-by":"publisher","first-page":"1063","DOI":"10.1137\/S106482759528507X","volume":"19","author":"JG Nagy","year":"1998","unstructured":"Nagy, J.G., O\u2019Leary, D.P.: Restoring images degraded by spatially variant blur. SIAM J. Sci. Comput. 19, 1063\u20131082 (1998). \n                    https:\/\/doi.org\/10.1137\/S106482759528507X","journal-title":"SIAM J. Sci. Comput."},{"key":"1205_CR32","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1007\/s11075-013-9712-0","volume":"65","author":"P Novati","year":"2014","unstructured":"Novati, P., Russo, M.R.: Adaptive Arnoldi\u2013Tikhonov regularization for image restoration. Numer. Algorithms 65, 745\u2013757 (2014). \n                    https:\/\/doi.org\/10.1007\/s11075-013-9712-0","journal-title":"Numer. Algorithms"},{"key":"1205_CR33","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1145\/355993.356000","volume":"8","author":"CC Paige","year":"1982","unstructured":"Paige, C.C., Saunders, M.A.: LSQR: sparse linear equations and least squares problems. ACM Trans. Math. Softw. 8, 195\u2013209 (1982). \n                    https:\/\/doi.org\/10.1145\/355993.356000","journal-title":"ACM Trans. Math. Softw."},{"key":"1205_CR34","doi-asserted-by":"publisher","first-page":"17","DOI":"10.14257\/ijsip.2014.7.6.02","volume":"7","author":"F Pazos","year":"2014","unstructured":"Pazos, F., Bhaya, A.: Matrix forms of gradient descent algorithms applied to restoration of blurred images. Int. J. Signal Process. Image Process. Pattern Recognit. 7, 17\u201328 (2014). \n                    https:\/\/doi.org\/10.14257\/ijsip.2014.7.6.02","journal-title":"Int. J. Signal Process. Image Process. Pattern Recognit."},{"key":"1205_CR35","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.cam.2014.10.022","volume":"279","author":"F Pazos","year":"2015","unstructured":"Pazos, F., Bhaya, A.: Adaptive choice of the Tikhonov regularization parameter to solve ill-posed linear algebraic equations via Liapunov optimizing control. J. Comput. Appl. Math. 279, 123\u2013132 (2015). \n                    https:\/\/doi.org\/10.1016\/j.cam.2014.10.022","journal-title":"J. Comput. Appl. Math."},{"key":"1205_CR36","doi-asserted-by":"publisher","first-page":"740","DOI":"10.1137\/S1064827593252672","volume":"17","author":"T Regi\u0144ska","year":"1996","unstructured":"Regi\u0144ska, T.: A regularization parameter in discrete ill-posed problems. SIAM J. Sci. Comput. 17, 740\u2013749 (1996). \n                    https:\/\/doi.org\/10.1137\/S1064827593252672","journal-title":"SIAM J. Sci. Comput."},{"key":"1205_CR37","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s11075-012-9612-8","volume":"63","author":"L Reichel","year":"2013","unstructured":"Reichel, L., Rodriguez, G.: Old and new parameter choice rules for discrete ill-posed problems. Numer. Algorithms 63, 65\u201387 (2013). \n                    https:\/\/doi.org\/10.1007\/s11075-012-9612-8","journal-title":"Numer. Algorithms"},{"key":"1205_CR38","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1007\/s10543-008-0179-7","volume":"48","author":"L Reichel","year":"2008","unstructured":"Reichel, L., Shyshkov, A.: A new zero-finder for Tikhonov regularization. BIT Numer. Math. 48, 627\u2013643 (2008). \n                    https:\/\/doi.org\/10.1007\/s10543-008-0179-7","journal-title":"BIT Numer. Math."},{"key":"1205_CR39","volume-title":"Solutions of Ill-Posed Problems","author":"AN Tikhonov","year":"1977","unstructured":"Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-Posed Problems. Winston & Sons, Washignton, DC (1977)"},{"key":"1205_CR40","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1088\/0266-5611\/18\/3\/307","volume":"18","author":"J Xie","year":"2002","unstructured":"Xie, J., Zou, J.: An improved model function method for choosing regularization parameters in linear inverse problems. Inverse Probl. 18, 631\u2013643 (2002). \n                    https:\/\/doi.org\/10.1088\/0266-5611\/18\/3\/307","journal-title":"Inverse Probl."},{"key":"1205_CR41","doi-asserted-by":"publisher","unstructured":"You, Y.-L., Kaveh, M.: Regularization and image restoration using differential equations. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), vol. 5, pp. 285\u2013288 (1993). \n                    https:\/\/doi.org\/10.1109\/ICASSP.1993.319803","DOI":"10.1109\/ICASSP.1993.319803"},{"key":"1205_CR42","first-page":"1317","volume":"15","author":"D Zhang","year":"2013","unstructured":"Zhang, D., Huang, T.-Z.: Generalized Tikhonov regularization method for large-scale linear inverse problems. J. Comput. Anal. Appl. 15, 1317\u20131331 (2013)","journal-title":"J. Comput. Anal. Appl."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-018-1205-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12190-018-1205-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-018-1205-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,18]],"date-time":"2019-07-18T19:19:52Z","timestamp":1563477592000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12190-018-1205-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,19]]},"references-count":42,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["1205"],"URL":"https:\/\/doi.org\/10.1007\/s12190-018-1205-9","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,19]]},"assertion":[{"value":"3 March 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 July 2018","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}