{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:53:08Z","timestamp":1776847988401,"version":"3.51.2"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2007,9,12]],"date-time":"2007-09-12T00:00:00Z","timestamp":1189555200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2007,10,23]]},"DOI":"10.1007\/s00211-007-0109-7","type":"journal-article","created":{"date-parts":[[2007,9,11]],"date-time":"2007-09-11T09:32:54Z","timestamp":1189503174000},"page":"151-175","source":"Crossref","is-referenced-by-count":9,"title":["Optimality of the fully discrete filtered backprojection algorithm for tomographic inversion"],"prefix":"10.1007","volume":"108","author":[{"given":"Andreas","family":"Rieder","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arne","family":"Schneck","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,9,12]]},"reference":[{"key":"109_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/9781118032725","volume-title":"Applied Functional Analysis, Pure & Applied Mathematics","author":"J.-P. Aubin","year":"2000","unstructured":"Aubin J.-P. (2000). Applied Functional Analysis, Pure & Applied Mathematics. Wiley, New York","edition":"2"},{"key":"109_CR2","doi-asserted-by":"crossref","unstructured":"Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods, vol. 15 of Texts in Applied Mathematics. Springer, New York (1994)","DOI":"10.1007\/978-1-4757-4338-8"},{"key":"109_CR3","doi-asserted-by":"crossref","first-page":"896","DOI":"10.1118\/1.598606","volume":"26","author":"R.R. Galigekere","year":"1999","unstructured":"Galigekere R.R., Wiesent K. and Holdsworth D.W. (1999). Techniques to alleviate the effects of view aliasing artifacts in computed tomography. Med. Phys. 26: 896\u2013904","journal-title":"Med. Phys."},{"key":"109_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9486-0","volume-title":"Minimal Surfaces and Functions of Bounded Variation","author":"E. Giusti","year":"1984","unstructured":"Giusti E. (1984). Minimal Surfaces and Functions of Bounded Variation. Birkh\u00e4user, Basel"},{"key":"109_CR5","doi-asserted-by":"crossref","unstructured":"Kress, R.: Numerical Analysis, vol. 181 of Graduate Texts in Mathematics. Springer, New York (1998)","DOI":"10.1007\/978-1-4612-0599-9"},{"key":"109_CR6","first-page":"85","volume":"50","author":"R.M. Lewitt","year":"1978","unstructured":"Lewitt R.M., Bates R.H.T. and Peters T.M. (1978). Image reconstruction from projections II: Modified backprojection methods. Optik 50: 85\u2013109","journal-title":"Optik"},{"key":"109_CR7","volume-title":"Non-Homogeneous Boundary Value Problems and Applications, Vol. 1","author":"J.L. Lions","year":"1972","unstructured":"Lions J.L. and Magenes E. (1972). Non-Homogeneous Boundary Value Problems and Applications, Vol. 1. Springer, New York"},{"key":"109_CR8","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1109\/PROC.1983.12596","volume":"71","author":"A.K. Louis","year":"1983","unstructured":"Louis A.K. and Natterer F. (1983). Mathematical problems in computerized tomography. Proc. IEEE 71: 379\u2013389","journal-title":"Proc. IEEE"},{"key":"109_CR9","doi-asserted-by":"crossref","unstructured":"Natterer, F.: Genauigkeitsfragen bei der numerischen Rekonstruktion von Bildern, vol. 49 of International series of numerical mathematics (ISNM), Birkh\u00e4user Verlag, Basel, Switzerland, pp. 131\u2013146 (1979)","DOI":"10.1007\/978-3-0348-6285-1_10"},{"key":"109_CR10","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1137\/0139034","volume":"39","author":"F. Natterer","year":"1980","unstructured":"Natterer F. (1980). A Sobolev space analysis of picture reconstruction. SIAM J. Appl. Math. 39: 402\u2013411","journal-title":"SIAM J. Appl. Math."},{"key":"109_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-663-01409-6","volume-title":"The Mathematics of Computerized Tomography","author":"F. Natterer","year":"1986","unstructured":"Natterer F. (1986). The Mathematics of Computerized Tomography. Wiley, Chichester"},{"key":"109_CR12","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1137\/S0036142902405643","volume":"41","author":"A. Rieder","year":"2003","unstructured":"Rieder A. and Faridani A. (2003). The semi-discrete filtered backprojection algorithm is optimal for tomographic inversion. SIAM J. Numer. Anal. 41: 869\u2013892","journal-title":"SIAM J. Numer. Anal."},{"key":"109_CR13","doi-asserted-by":"crossref","first-page":"1909","DOI":"10.1137\/S0036142998347619","volume":"37","author":"A. Rieder","year":"2000","unstructured":"Rieder A. and Schuster Th. (2000). The approximate inverse in action with an application to computerized tomography. SIAM J. Numer. Anal. 37: 1909\u20131929","journal-title":"SIAM J. Numer. Anal."},{"key":"109_CR14","unstructured":"Schneck, A.: Konvergenz von Rekonstruktionsalgorithmen in der 2D-Tomographie: Der voll-diskrete Fall (Convergence of reconstruction algorithms in 2D-tomography: The fully discrete case). Diploma thesis, Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Karlsruhe, D-76128 Karlsruhe, Germany (2006)"},{"key":"109_CR15","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TNS.1974.6499235","volume":"21","author":"L.A. Shepp","year":"1974","unstructured":"Shepp L.A. and Logan B.F. (1974). The Fourier reconstruction of a head section. IEEE Trans. Nucl. Sci. 21: 21\u201343","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"109_CR16","doi-asserted-by":"crossref","first-page":"1244","DOI":"10.1103\/PhysRevLett.70.1244","volume":"70","author":"D.T. Smithey","year":"1993","unstructured":"Smithey D.T., Beck M., Raymer M.G. and Faridani A. (1993). Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum. Phys. Rev. Lett. 70: 1244\u20131247","journal-title":"Phys. Rev. Lett."},{"key":"109_CR17","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1088\/0031-9155\/27\/9\/005","volume":"27","author":"G.H. Weiss","year":"1982","unstructured":"Weiss G.H., Talbert A.J. and Brooks R.A. (1982). The use of phantom views to reduce CT streaks due to insufficient sampling. Phys. Med. Biol. 27: 1151\u20131162","journal-title":"Phys. Med. Biol."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0109-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-007-0109-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0109-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T06:56:58Z","timestamp":1629701818000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-007-0109-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9,12]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,10,23]]}},"alternative-id":["109"],"URL":"https:\/\/doi.org\/10.1007\/s00211-007-0109-7","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,9,12]]}}}