{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T07:38:11Z","timestamp":1771486691425,"version":"3.50.1"},"publisher-location":"New York, NY","reference-count":100,"publisher":"Springer New York","isbn-type":[{"value":"9781493907892","type":"print"},{"value":"9781493907908","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-1-4939-0790-8_2","type":"book-chapter","created":{"date-parts":[[2015,5,29]],"date-time":"2015-05-29T16:38:04Z","timestamp":1432917484000},"page":"47-90","source":"Crossref","is-referenced-by-count":6,"title":["Large-Scale Inverse Problems in Imaging"],"prefix":"10.1007","author":[{"given":"Julianne","family":"Chung","sequence":"first","affiliation":[]},{"given":"Sarah","family":"Knepper","sequence":"additional","affiliation":[]},{"given":"James G.","family":"Nagy","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"2_CR1","volume-title":"Digital Image Restoration","author":"HC Andrews","year":"1977","unstructured":"Andrews, H.C., Hunt, B.R.: Digital Image Restoration. Prentice-Hall, Englewood Cliffs (1977)"},{"key":"2_CR2","doi-asserted-by":"publisher","first-page":"105004","DOI":"10.1088\/0266-5611\/25\/10\/105004","volume":"25","author":"M Bachmayr","year":"2009","unstructured":"Bachmayr, M., Burger, M.: Iterative total variation schemes for nonlinear inverse problems. Inverse Prob. 25, 105004 (2009)","journal-title":"Inverse Prob."},{"issue":"2","key":"2_CR3","doi-asserted-by":"publisher","first-page":"167","DOI":"10.3934\/ipi.2008.2.167","volume":"2","author":"JM Bardsley","year":"2008","unstructured":"Bardsley, J.M.: An efficient computational method for total variation-penalized Poisson likelihood estimation. Inverse Prob. Imaging 2(2), 167\u2013185 (2008)","journal-title":"Inverse Prob. Imaging"},{"issue":"4","key":"2_CR4","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1007\/s10543-008-0196-6","volume":"48","author":"JM Bardsley","year":"2008","unstructured":"Bardsley, J.M.: Stopping rules for a nonnegatively constrained iterative method for illposed Poisson imaging problems. BIT 48(4), 651\u2013664 (2008)","journal-title":"BIT"},{"issue":"4","key":"2_CR5","doi-asserted-by":"publisher","first-page":"1326","DOI":"10.1137\/S1064827502410451","volume":"25","author":"JM Bardsley","year":"2003","unstructured":"Bardsley, J.M., Vogel, C.R.: A nonnegatively constrained convex programming method for image reconstruction. SIAM J. Sci. Comput. 25(4), 1326\u20131343 (2003)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"2_CR6","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(1), 141\u2013148 (1988)","journal-title":"IMA J. Numer. Anal."},{"issue":"3","key":"2_CR7","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1007\/BF01941141","volume":"28","author":"\u00c5. Bj\u00f6rck","year":"1988","unstructured":"Bj\u00f6rck, \u00c5.: A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations. BIT 28(3), 659\u2013670 (1988)","journal-title":"BIT"},{"key":"2_CR8","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971484","volume-title":"Numerical Methods for Least Squares Problems","author":"\u00c5. Bj\u00f6rck","year":"1996","unstructured":"Bj\u00f6rck, \u00c5.: Numerical Methods for Least Squares Problems. SIAM, Philadelphia (1996)"},{"issue":"4","key":"2_CR9","doi-asserted-by":"publisher","first-page":"510","DOI":"10.1007\/BF01934265","volume":"34","author":"\u00c5. Bj\u00f6rck","year":"1994","unstructured":"Bj\u00f6rck, \u00c5., Grimme, E., van Dooren, P.: An implicit shift bidiagonalization algorithm for ill-posed systems. BIT 34(4), 510\u2013534 (1994)","journal-title":"BIT"},{"key":"2_CR10","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/B978-0-12-239040-1.50014-4","volume-title":"Inverse and Ill-Posed Problems","author":"H Brakhage","year":"1987","unstructured":"Brakhage, H.: On ill-posed problems and the method of conjugate gradients. In: Engl, H.W., Groetsch, C.W. (eds.) Inverse and Ill-Posed Problems, pp.\u00a0165\u2013175. Academic, Boston (1987)"},{"issue":"2","key":"2_CR11","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1023\/A:1026083619097","volume":"43","author":"D Calvetti","year":"2003","unstructured":"Calvetti, D., Reichel, L.: Tikhonov regularization of large linear problems. BIT 43(2), 263\u2013283 (2003)","journal-title":"BIT"},{"key":"2_CR12","volume-title":"Introduction to Bayesian Scientific Computing","author":"D Calvetti","year":"2007","unstructured":"Calvetti, D., Somersalo, E.: Introduction to Bayesian Scientific Computing. Springer, New York (2007)"},{"issue":"8","key":"2_CR13","doi-asserted-by":"publisher","first-page":"1207","DOI":"10.1002\/cpa.20124","volume":"59","author":"EJ Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E.J., Romberg, J.K., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207\u20131223 (2006)","journal-title":"Commun. Pure Appl. Math."},{"issue":"6","key":"2_CR14","doi-asserted-by":"publisher","first-page":"1980","DOI":"10.1137\/S0036139999362592","volume":"61","author":"AS Carasso","year":"2001","unstructured":"Carasso, A.S.: Direct blind deconvolution. SIAM J. Appl. Math. 61(6), 1980\u20132007 (2001)","journal-title":"SIAM J. Appl. Math."},{"key":"2_CR15","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719710","volume-title":"An Introduction to Inverse Scattering and Inverse Spectral Problems","author":"K Chadan","year":"1997","unstructured":"Chadan, K., Colton, D., P\u00e4iv\u00e4rinta, L., Rundell, W.: An Introduction to Inverse Scattering and Inverse Spectral Problems. SIAM, Philadelphia (1997)"},{"key":"2_CR16","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717877","volume-title":"Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods","author":"TF Chan","year":"2005","unstructured":"Chan, T.F., Shen, J.: Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. SIAM, Philadelphia (2005)"},{"key":"2_CR17","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719291","volume-title":"Fundamentals of Radar Imaging","author":"M Cheney","year":"2009","unstructured":"Cheney, M., Borden, B.: Fundamentals of Radar Imaging. SIAM, Philadelphia (2009)"},{"issue":"4","key":"2_CR18","doi-asserted-by":"publisher","first-page":"1261","DOI":"10.1088\/0266-5611\/22\/4\/009","volume":"22","author":"J Chung","year":"2006","unstructured":"Chung, J., Haber, E., Nagy, J.: Numerical methods for coupled super-resolution. Inverse Prob. 22(4), 1261\u20131272 (2006)","journal-title":"Inverse Prob."},{"issue":"6","key":"2_CR19","doi-asserted-by":"publisher","first-page":"4654","DOI":"10.1137\/080732213","volume":"31","author":"J Chung","year":"2010","unstructured":"Chung, J., Nagy, J.: An efficient iterative approach for large-scale separable nonlinear inverse problems. SIAM J. Sci. Comput. 31(6), 4654\u20134674 (2010)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"2_CR20","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1137\/090749633","volume":"3","author":"J Chung","year":"2010","unstructured":"Chung, J., Nagy, J., Sechopoulos, I.: Numerical algorithms for polyenergetic digital breast tomosynthesis reconstruction. SIAM J. Imaging Sci. 3(1), 133\u2013152 (2010)","journal-title":"SIAM J. Imaging Sci."},{"key":"2_CR21","first-page":"149","volume":"28","author":"J Chung","year":"2008","unstructured":"Chung, J., Nagy, J.G., O\u2019Leary, D.P.: A weighted GCV method for Lanczos hybrid regularization. Elec. Trans. Numer. Anal. 28, 149\u2013167 (2008)","journal-title":"Elec. Trans. Numer. Anal."},{"issue":"2","key":"2_CR22","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1177\/1094342009106293","volume":"24","author":"J Chung","year":"2010","unstructured":"Chung, J., Sternberg, P., Yang, C.: High performance 3-d image reconstruction for molecular structure determination. Int. J. High Perform. Comput. Appl. 24(2), 117\u2013135 (2010)","journal-title":"Int. J. High Perform. Comput. Appl."},{"issue":"10","key":"2_CR23","doi-asserted-by":"publisher","first-page":"999","DOI":"10.1109\/42.959297","volume":"20","author":"B Man De","year":"2001","unstructured":"De Man, B., Nuyts, J., Dupont, P., Marchal, G., Suetens, P.: An iterative maximumlikelihood polychromatic algorithm for CT. IEEE Trans. Med. Imaging 20(10), 999\u20131008 (2001)","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"5","key":"2_CR24","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1109\/51.790987","volume":"18","author":"A Diaspro","year":"1999","unstructured":"Diaspro, A., Corosu, M., Ramoino, P., Robello, M.: Two-photon excitation imaging based on a compact scanning head. IEEE Eng. Med. Biol. 18(5), 18\u201330 (1999)","journal-title":"IEEE Eng. Med. Biol."},{"issue":"19","key":"2_CR25","doi-asserted-by":"publisher","first-page":"R65","DOI":"10.1088\/0031-9155\/48\/19\/R01","volume":"48","author":"JT Dobbins III","year":"2003","unstructured":"Dobbins, J.T., III, Godfrey, D.J.: Digital X-ray tomosynthesis: current state of the art and clinical potential. Phys. Med. Biol. 48(19), R65\u2013R106 (2003)","journal-title":"Phys. Med. Biol."},{"issue":"1","key":"2_CR26","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1137\/080720796","volume":"2","author":"GR Easley","year":"2009","unstructured":"Easley, G.R., Healy, D.M., Berenstein, C.A.: Image deconvolution using a general ridgelet and curvelet domain. SIAM J. Imaging Sci. 2(1), 253\u2013283 (2009)","journal-title":"SIAM J. Imaging Sci."},{"issue":"12","key":"2_CR27","doi-asserted-by":"publisher","first-page":"1646","DOI":"10.1109\/83.650118","volume":"6","author":"M Elad","year":"1997","unstructured":"Elad, M., Feuer, A.: Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images. IEEE Trans. Image Process. 6(12), 1646\u20131658 (1997)","journal-title":"IEEE Trans. Image Process."},{"key":"2_CR28","volume-title":"Regularization of Inverse Problems","author":"HW Engl","year":"2000","unstructured":"Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Kluwer, Dordrecht (2000)"},{"key":"2_CR29","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/3-540-27167-8_1","volume-title":"Multidisciplinary Methods for Analysis Optimization and Control of Complex Systems","author":"HW Engl","year":"2005","unstructured":"Engl, H.W., K\u00fcgler, P.: Nonlinear inverse problems: theoretical aspects and some industrial applications. In: Capasso, V., P\u00e9riaux, J. (eds.) Multidisciplinary Methods for Analysis Optimization and Control of Complex Systems, pp.\u00a03\u201348. Springer, Berlin (2005)"},{"issue":"4","key":"2_CR30","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1088\/0266-5611\/5\/4\/007","volume":"5","author":"HW Engl","year":"1989","unstructured":"Engl, H.W., Kunisch, K., Neubauer, A.: Convergence rates for Tikhonov regularisation of nonlinear ill-posed problems. Inverse Prob. 5(4), 523\u2013540 (1989)","journal-title":"Inverse Prob."},{"key":"2_CR31","volume-title":"Inverse Problems in Geophysical Applications","year":"1996","unstructured":"Engl, H.W., Louis, A.K., Rundell, W. (eds.): Inverse Problems in Geophysical Applications. SIAM, Philadelphia (1996)"},{"issue":"6","key":"2_CR32","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1080\/10556780410001722471","volume":"19","author":"J Eriksson","year":"2004","unstructured":"Eriksson, J., Wedin, P.: Truncated Gauss-Newton algorithms for ill-conditioned nonlinear least squares problems. Optim. Meth. Softw. 19(6), 721\u2013737 (2004)","journal-title":"Optim. Meth. Softw."},{"issue":"3","key":"2_CR33","first-page":"797","volume":"54","author":"TL Faber","year":"2009","unstructured":"Faber, T.L., Raghunath, N., Tudorascu, D., Votaw, J.R.: Motion correction of PET brain images through deconvolution: I. Theoretical development and analysis in software simulations. Phys. Med. Biol. 54(3), 797\u2013811 (2009)","journal-title":"Theoretical development and analysis in software simulations. Phys. Med. Biol."},{"issue":"4","key":"2_CR34","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1109\/JSTSP.2007.910281","volume":"1","author":"MAT Figueiredo","year":"2007","unstructured":"Figueiredo, M.A.T, Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1(4), 586\u2013597 (2007)","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"2_CR35","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780195182187.001.0001","volume-title":"Three-Dimensional Electron Microscopy of Macromolecular Assemblies","author":"J Frank","year":"2006","unstructured":"Frank, J.: Three-Dimensional Electron Microscopy of Macromolecular Assemblies. Oxford University Press, New York (2006)"},{"issue":"2","key":"2_CR36","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1080\/00401706.1979.10489751","volume":"21","author":"GH Golub","year":"1979","unstructured":"Golub, G.H., Heath, M., Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21(2), 215\u2013223 (1979)","journal-title":"Technometrics"},{"issue":"2","key":"2_CR37","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1145\/355945.355946","volume":"7","author":"GH Golub","year":"1981","unstructured":"Golub, G.H., Luk, F.T., Overton, M.L.: A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix. ACM Trans. Math. Softw. 7(2), 149\u2013169 (1981)","journal-title":"ACM Trans. Math. Softw."},{"issue":"2","key":"2_CR38","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1137\/0710036","volume":"10","author":"GH Golub","year":"1973","unstructured":"Golub, G.H., Pereyra, V.: The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal. 10(2), 413\u2013432 (1973)","journal-title":"SIAM J. Numer. Anal."},{"key":"2_CR39","doi-asserted-by":"publisher","first-page":"R1","DOI":"10.1088\/0266-5611\/19\/2\/201","volume":"19","author":"GH Golub","year":"2003","unstructured":"Golub, G.H., Pereyra, V.: Separable nonlinear least squares: the variable projection method and its applications. Inverse Prob. 19, R1\u2013R26 (2003)","journal-title":"Inverse Prob."},{"issue":"5","key":"2_CR40","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.1088\/0266-5611\/16\/5\/309","volume":"16","author":"E Haber","year":"2000","unstructured":"Haber, E., Ascher, U.M., Oldenburg, D.: On optimization techniques for solving nonlinear inverse problems. Inverse Prob. 16(5), 1263\u20131280 (2000)","journal-title":"Inverse Prob."},{"issue":"1","key":"2_CR41","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1023\/A:1011599530422","volume":"4","author":"E Haber","year":"2000","unstructured":"Haber, E., Oldenburg, D.: A GCV based method for nonlinear ill-posed problems. Comput. Geosci. 4(1), 41\u201363 (2000)","journal-title":"Comput. Geosci."},{"issue":"2","key":"2_CR42","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1148\/130.2.485","volume":"130","author":"GR Hammerstein","year":"1979","unstructured":"Hammerstein, G.R., Miller, D.W., White, D.R., Masterson, M.E., Woodard, H.Q., Laughlin, J.S.: Absorbed radiation dose in mammography. Radiology 130(2), 485\u2013491 (1979)","journal-title":"Radiology"},{"key":"2_CR43","series-title":"Pitman research notes in mathematics","volume-title":"Conjugate gradient type methods for ill-posed problems","author":"M Hanke","year":"1995","unstructured":"Hanke, M.: Conjugate gradient type methods for ill-posed problems. Pitman research notes in mathematics, Longman Scientific & Technical, Harlow (1995)"},{"issue":"2","key":"2_CR44","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/BF01731984","volume":"36","author":"M Hanke","year":"1996","unstructured":"Hanke, M.: Limitations of the L-curve method in ill-posed problems. BIT 36(2), 287\u2013301 (1996)","journal-title":"BIT"},{"issue":"5","key":"2_CR45","doi-asserted-by":"publisher","first-page":"1008","DOI":"10.1023\/A:1021941328858","volume":"41","author":"M Hanke","year":"2001","unstructured":"Hanke, M.: On Lanczos based methods for the regularization of discrete ill-posed problems. BIT 41(5), 1008\u20131018 (2001)","journal-title":"BIT"},{"issue":"4","key":"2_CR46","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1137\/1034115","volume":"34","author":"PC Hansen","year":"1992","unstructured":"Hansen, P.C.: Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev. 34(4), 561\u2013580 (1992)","journal-title":"SIAM Rev."},{"issue":"6","key":"2_CR47","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1088\/0266-5611\/8\/6\/005","volume":"8","author":"PC Hansen","year":"1992","unstructured":"Hansen, P.C.: Numerical tools for analysis and solution of Fredholm integral equations of the first kind. Inverse Prob. 8(6), 849\u2013872 (1992)","journal-title":"Inverse Prob."},{"issue":"1","key":"2_CR48","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02149761","volume":"6","author":"PC Hansen","year":"1994","unstructured":"Hansen, P.C.: Regularization tools: a MATLAB package for analysis and solution of discrete ill-posed problems. Numer. Algorithms 6(1), 1\u201335 (1994)","journal-title":"Numer. Algorithms"},{"key":"2_CR49","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719697","volume-title":"Rank-Deficient and Discrete Ill-Posed Problems","author":"PC Hansen","year":"1998","unstructured":"Hansen, P.C.: Rank-Deficient and Discrete Ill-Posed Problems. SIAM, Philadelphia (1998)"},{"key":"2_CR50","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718836","volume-title":"Discrete Inverse Problems: Insight and Algorithms","author":"PC Hansen","year":"2010","unstructured":"Hansen, P.C.: Discrete Inverse Problems: Insight and Algorithms. SIAM, Philadelphia (2010)"},{"key":"2_CR51","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718874","volume-title":"Deblurring Images: Matrices, Spectra and Filtering","author":"PC Hansen","year":"2006","unstructured":"Hansen, P.C., Nagy, J.G., O\u2019Leary, D.P.: Deblurring Images: Matrices, Spectra and Filtering. SIAM, Philadelphia (2006)"},{"issue":"6","key":"2_CR52","doi-asserted-by":"publisher","first-page":"1487","DOI":"10.1137\/0914086","volume":"14","author":"PC Hansen","year":"1993","unstructured":"Hansen, P.C., O\u2019Leary, D.P.: The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J Sci Comput 14(6):1487\u20131503 (1993)","journal-title":"SIAM J Sci Comput"},{"issue":"6","key":"2_CR53","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1038\/scientificamerican0694-60","volume":"270","author":"JW Hardy","year":"1994","unstructured":"Hardy, J.W.: Adaptive optics. Sci. Am. 270(6), 60\u201365 (1994)","journal-title":"Sci. Am."},{"key":"2_CR54","volume-title":"Inverse Problems: Principles and Applications in Geophysics, Technology, and Medicine","author":"B Hofmann","year":"1993","unstructured":"Hofmann, B.: Regularization of nonlinear problems and the degree of ill-posedness. In: Anger, G., Gorenflo, R., Jochmann, H., Moritz, H., Webers, W. (eds.) Inverse Problems: Principles and Applications in Geophysics, Technology, and Medicine. Akademie Verlag, Berlin (1993)"},{"issue":"1","key":"2_CR55","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.jsb.2006.07.003","volume":"157","author":"M Hohn","year":"2007","unstructured":"Hohn, M., Tang, G., Goodyear, G., Baldwin, P.R., Huang, Z., Penczek, P.A., Yang, C., Glaeser, R.M., Adams, P.D., Ludtke, S.J.: SPARX, a new environment for Cryo-EM image processing. J. Struct. Biol. 157(1), 47\u201355 (2007)","journal-title":"J. Struct. Biol."},{"key":"2_CR56","volume-title":"Fundamentals of Digital Image Processing","author":"AK Jain","year":"1989","unstructured":"Jain, A.K.: Fundamentals of Digital Image Processing. Prentice-Hall, Englewood Cliffs (1989)"},{"issue":"3","key":"2_CR57","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1109\/MSP.2003.1203206","volume":"20","author":"MG Kang","year":"2003","unstructured":"Kang, M.G., Chaudhuri, S.: Super-resolution image reconstruction. IEEE Signal Process. Mag. 20(3), 19\u201320 (2003)","journal-title":"IEEE Signal Process. Mag."},{"issue":"1","key":"2_CR58","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/BF01932995","volume":"15","author":"L Kaufman","year":"1975","unstructured":"Kaufman, L.: A variable projection method for solving separable nonlinear least squares problems. BIT 15(1), 49\u201357 (1975)","journal-title":"BIT"},{"issue":"1","key":"2_CR59","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1137\/050645592","volume":"29","author":"ME Kilmer","year":"2007","unstructured":"Kilmer, M.E., Hansen, P.C., Espa\u00f1ol, M.I.: A projection-based approach to general-form Tikhonov regularization. SIAM J. Sci. Comput. 29(1), 315\u2013330 (2007)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"2_CR60","doi-asserted-by":"publisher","first-page":"1204","DOI":"10.1137\/S0895479899345960","volume":"22","author":"ME Kilmer","year":"2001","unstructured":"Kilmer, M.E., O\u2019Leary, D.P.: Choosing regularization parameters in iterative methods for ill-posed problems. SIAM J. Matrix. Anal. Appl. 22(4), 1204\u20131221 (2001)","journal-title":"SIAM J. Matrix. Anal. Appl."},{"issue":"3","key":"2_CR61","doi-asserted-by":"publisher","first-page":"615","DOI":"10.2307\/2372313","volume":"73","author":"L Landweber","year":"1951","unstructured":"Landweber, L.: An iteration formula for Fredholm integral equations of the first kind. Am. J. Math. 73(3), 615\u2013624 (1951)","journal-title":"Am. J. Math."},{"key":"2_CR62","volume-title":"Lanczos bidiagonalization with partial reorthogonalization. PhD thesis","author":"RM Larsen","year":"1998","unstructured":"Larsen, R.M.: Lanczos bidiagonalization with partial reorthogonalization. PhD thesis, Department of Computer Science, University of Aarhus, Denmark (1998)"},{"key":"2_CR63","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971217","volume-title":"Solving Least Squares Problems","author":"CL Lawson","year":"1995","unstructured":"Lawson, C.L., Hanson, R.J.: Solving Least Squares Problems. SIAM, Philadelphia (1995)"},{"key":"2_CR64","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1117\/12.451791","volume-title":"Image Reconstruction from Incomplete Data II, Seattle","author":"MG L\u00f6fdahl","year":"2002","unstructured":"L\u00f6fdahl, M.G.: Multi-frame blind deconvolution with linear equality constraints. In: Bones, P.J., Fiddy, M.A., Millane, R.P. (eds.) Image Reconstruction from Incomplete Data II, Seattle, vol.\u00a04792\u201321, pp.\u00a0146\u2013155. SPIE (2002)"},{"issue":"8","key":"2_CR65","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1364\/JOSA.55.001007","volume":"55","author":"AW Lohmann","year":"1965","unstructured":"Lohmann, A.W., Paris, D.P.: Space-variant image formation. J. Opt. Soc. Am. 55(8), 1007\u20131013 (1965)","journal-title":"J. Opt. Soc. Am."},{"issue":"1\u20132","key":"2_CR66","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/S0304-3991(97)00127-7","volume":"72","author":"R Marabini","year":"1998","unstructured":"Marabini, R., Herman, G.T., Carazo, J.M.: 3D reconstruction in electron microscopy using ART with smooth spherically symmetric volume elements (blobs). Ultramicroscopy 72(1\u20132), 53\u201365 (1998)","journal-title":"Ultramicroscopy"},{"issue":"1","key":"2_CR67","doi-asserted-by":"publisher","first-page":"A75","DOI":"10.1364\/AO.48.000A75","volume":"48","author":"CL Matson","year":"2009","unstructured":"Matson, C.L., Borelli, K., Jefferies, S., Beckner, C.C., Jr., Hege, E.K., Lloyd-Hart, M.: Fast and optimal multiframe blind deconvolution algorithm for high-resolution groundbased imaging of space objects. Appl. Opt. 48(1), A75\u2013A92 (2009)","journal-title":"Appl. Opt."},{"key":"2_CR68","first-page":"181","volume-title":"The Restoration of HST Images and Spectra II","author":"SR McNown","year":"1994","unstructured":"McNown, S.R., Hunt, B.R.: Approximate shift-invariance by warping shift-variant systems. In: Hanisch, R.J., White, R.L. (eds.) The Restoration of HST Images and Spectra II, pp.\u00a0181\u2013187. Space Telescope Science Institute, Baltimore (1994)"},{"issue":"1","key":"2_CR69","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1137\/0501006","volume":"1","author":"K Miller","year":"1970","unstructured":"Miller, K.: Least squares methods for ill-posed problems with a prescribed bound. SIAM J. Math. Anal. 1(1), 52\u201374 (1970)","journal-title":"SIAM J. Math. Anal."},{"key":"2_CR70","volume-title":"Numerical Methods for Image Registration","author":"J Modersitzki","year":"2004","unstructured":"Modersitzki, J.: Numerical Methods for Image Registration. Oxford University Press, Oxford (2004)"},{"key":"2_CR71","first-page":"414","volume":"7","author":"VA Morozov","year":"1966","unstructured":"Morozov, V.A.: On the solution of functional equations by the method of regularization. Sov. Math. Dokl. 7, 414\u2013417 (1966)","journal-title":"Sov. Math. Dokl."},{"key":"2_CR72","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1117\/12.279513","volume-title":"Advanced Signal Processing: Algorithms, Architectures, and Implementations VII","author":"JG Nagy","year":"1997","unstructured":"Nagy, J.G., O\u2019Leary, D.P.: Fast iterative image restoration with a spatially varying PSF. In: Luk, F.T. (ed.) Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, San Diego, vol.\u00a03162, pp.\u00a0388\u2013399. SPIE (1997)"},{"issue":"4","key":"2_CR73","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(4), 1063\u20131082 (1998)","journal-title":"SIAM J. Sci. Comput."},{"key":"2_CR74","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719284","volume-title":"The Mathematics of Computerized Tomography","author":"F Natterer","year":"2001","unstructured":"Natterer, F.: The Mathematics of Computerized Tomography. SIAM, Philadelphia (2001)"},{"key":"2_CR75","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718324","volume-title":"Mathematical Methods in Image Reconstruction","author":"F Natterer","year":"2001","unstructured":"Natterer, F., W\u00fcbbeling, F.: Mathematical Methods in Image Reconstruction. SIAM, Philadelphia (2001)"},{"issue":"9","key":"2_CR76","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1109\/83.941854","volume":"10","author":"N Nguyen","year":"2001","unstructured":"Nguyen, N., Milanfar, P., Golub, G.: Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement. IEEE Trans. Image Process. 10(9), 1299\u20131308 (2001)","journal-title":"IEEE Trans. Image Process."},{"key":"2_CR77","doi-asserted-by":"publisher","DOI":"10.1007\/b98874","volume-title":"Numerical Optimization","author":"J Nocedal","year":"1999","unstructured":"Nocedal, J., Wright, S.: Numerical Optimization. Springer, New York (1999)"},{"issue":"4","key":"2_CR78","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1137\/0902037","volume":"2","author":"DP O\u2019Leary","year":"1981","unstructured":"O\u2019Leary, D.P., Simmons, J.A.: A bidiagonali-zation-regularization procedure for large scale discretizations of ill-posed problems. SIAM J. Sci. Stat. Comput. 2(4), 474\u2013489 (1981)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"2_CR79","first-page":"1","volume":"28","author":"MR Osborne","year":"2007","unstructured":"Osborne, M.R.: Separable least squares, variable projection, and the Gauss-Newton algorithm. Elec. Trans. Numer. Anal. 28, 1\u201315 (2007)","journal-title":"Elec. Trans. Numer. Anal."},{"issue":"2","key":"2_CR80","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.: Algorithm 583 LSQR: sparse linear equations and least squares problems. ACM Trans. Math. Softw. 8(2), 195\u2013209 (1982)","journal-title":"ACM Trans. Math. Softw."},{"issue":"1","key":"2_CR81","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1145\/355984.355989","volume":"8","author":"CC Paige","year":"1982","unstructured":"Paige, C.C., Saunders, M.A.: LSQR: an algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Softw. 8(1), 43\u201371 (1982)","journal-title":"ACM Trans. Math. Softw."},{"issue":"1","key":"2_CR82","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/0304-3991(92)90233-A","volume":"40","author":"PA Penczek","year":"1992","unstructured":"Penczek, P.A., Radermacher, M., Frank, J.: Three-dimensional reconstruction of single particles embedded in ice. Ultramicroscopy 40(1), 33\u201353 (1992)","journal-title":"Ultramicroscopy"},{"issue":"1","key":"2_CR83","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1145\/321105.321114","volume":"9","author":"DL Phillips","year":"1962","unstructured":"Phillips, D.L.: A technique for the numerical solution of certain integral equations of the first kind. J. Assoc. Comput. Mach. 9(1), 84\u201397 (1962)","journal-title":"J. Assoc. Comput. Mach."},{"issue":"3","key":"2_CR84","first-page":"813","volume":"54","author":"N Raghunath","year":"2009","unstructured":"Raghunath, N., Faber, T.L., Suryanarayanan, S., Votaw, J.R.: Motion correction of PET brain images through deconvolution: II. Practical implementation and algorithm optimization. Phys. Med. Biol. 54(3), 813\u2013829 (2009)","journal-title":"Practical implementation and algorithm optimization. Phys. Med. Biol."},{"key":"2_CR85","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"LI Rudin","year":"1992","unstructured":"Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259\u2013268 (1992)","journal-title":"Physica D"},{"issue":"3","key":"2_CR86","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1137\/1022057","volume":"22","author":"A Ruhe","year":"1980","unstructured":"Ruhe, A., Wedin, P.: Algorithms for separable nonlinear least squares problems. SIAM Rev. 22(3), 318\u2013337 (1980)","journal-title":"SIAM Rev."},{"issue":"5","key":"2_CR87","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1137\/0717059","volume":"17","author":"Y Saad","year":"1980","unstructured":"Saad, Y.: On the rates of convergence of the Lanczos and the block-Lanczos methods. SIAM J. Numer. Anal. 17(5), 687\u2013706 (1980)","journal-title":"SIAM J. Numer. Anal."},{"issue":"24","key":"2_CR88","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1128\/JVI.01652-06","volume":"80","author":"SD Saban","year":"2006","unstructured":"Saban, S.D., Silvestry, M., Nemerow, G.R., Stewart, P.L.: Visualization of \u03b1-helices in a 6-\u00c5ngstrom resolution cryoelectron microscopy structure of adenovirus allows refinement of capsid protein assignments. J. Virol. 80(24), 49\u201359 (2006)","journal-title":"J. Virol."},{"key":"2_CR89","first-page":"1624","volume":"4","author":"AN Tikhonov","year":"1963","unstructured":"Tikhonov, A.N.: Regularization of incorrectly posed problems. Sov. Math. Dokl. 4, 1624\u20131627 (1963)","journal-title":"Sov. Math. Dokl."},{"key":"2_CR90","first-page":"1035","volume":"4","author":"AN Tikhonov","year":"1963","unstructured":"Tikhonov, A.N.: Solution of incorrectly formulated problems and the regularization method. Sov. Math. Dokl. 4, 1035\u20131038 (1963)","journal-title":"Sov. Math. Dokl."},{"key":"2_CR91","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, Washington (1977)"},{"key":"2_CR92","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-5167-4","volume-title":"Nonlinear Ill-Posed Problems","author":"AN Tikhonov","year":"1998","unstructured":"Tikhonov, A.N., Leonov, A.S., Yagola, A.G.: Nonlinear Ill-Posed Problems, vol.\u00a01\u20132. Chapman and Hall, London (1998)"},{"issue":"1","key":"2_CR93","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1109\/83.128039","volume":"1","author":"HJ Trussell","year":"1992","unstructured":"Trussell, H.J., Fogel, S.: Identification and restoration of spatially variant motion blurs in sequential images. IEEE Trans. Image Process. 1(1), 123\u2013126 (1992)","journal-title":"IEEE Trans. Image Process."},{"issue":"3","key":"2_CR94","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1016\/j.sigpro.2005.05.029","volume":"86","author":"Y Tsaig","year":"2006","unstructured":"Tsaig, Y., Donoho, D.L.: Extensions of compressed sensing. Signal Process. 86(3), 549\u2013571 (2006)","journal-title":"Signal Process."},{"issue":"2","key":"2_CR95","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1137\/0904012","volume":"4","author":"JM Varah","year":"1983","unstructured":"Varah, J.M.: Pitfalls in the numerical solution of linear ill-posed problems. SIAM J. Sci. Stat. Comput. 4(2), 164\u2013176 (1983)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"1","key":"2_CR96","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1137\/0723007","volume":"23","author":"CR Vogel","year":"1986","unstructured":"Vogel, C.R.: Optimal choice of a truncation level for the truncated SVD solution of linear first kind integral equations when data are noisy. SIAM J. Numer. Anal. 23(1), 109\u2013117 (1986)","journal-title":"SIAM J. Numer. Anal."},{"key":"2_CR97","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/B978-0-12-239040-1.50019-3","volume-title":"Inverse and Ill-Posed Problems","author":"CR Vogel","year":"1987","unstructured":"Vogel, C.R.: An overview of numerical methods for nonlinear ill-posed problems. In: Engl, H.W., Groetsch, C.W. (eds.) Inverse and Ill-Posed Problems, pp.\u00a0231\u2013245. Academic, Boston (1987)"},{"issue":"4","key":"2_CR98","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1088\/0266-5611\/12\/4\/013","volume":"12","author":"CR Vogel","year":"1996","unstructured":"Vogel, C.R.: Non-convergence of the L-curve regularization parameter selection method. Inverse Prob. 12(4), 535\u2013547 (1996)","journal-title":"Inverse Prob."},{"key":"2_CR99","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717570","volume-title":"Computational Methods for Inverse Problems","author":"CR Vogel","year":"2002","unstructured":"Vogel, C.R.: Computational Methods for Inverse Problems. SIAM, Philadelphia (2002)"},{"issue":"4","key":"2_CR100","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1109\/42.14517","volume":"7","author":"FC Wagner","year":"1988","unstructured":"Wagner, F.C., Macovski, A., Nishimura, D.G.: A characterization of the scatter pointspread-function in terms of air gaps. IEEE Trans. Med. Imaging 7(4), 337\u2013344 (1988)","journal-title":"IEEE Trans. Med. Imaging"}],"container-title":["Handbook of Mathematical Methods in Imaging"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4939-0790-8_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T03:27:21Z","timestamp":1559186841000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-1-4939-0790-8_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9781493907892","9781493907908"],"references-count":100,"URL":"https:\/\/doi.org\/10.1007\/978-1-4939-0790-8_2","relation":{},"subject":[],"published":{"date-parts":[[2015]]}}}