{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:34:51Z","timestamp":1787326491094,"version":"build-2736575974"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>The tasks of image reconstruction from measured data and the analysis of the resulting images are more or less strictly separated. One group of scientists computes by applying reconstruction algorithms to the images; the other then operates on these images to enhance the analysis. First attempts at combining image reconstruction and image analysis, in a nonsystematic way, are known as Lambda tomography or Tikhonov\u2013Phillips methods with $\\ell_1$-norms or with level-set methods. The aim of this paper is to provide a general tool to combine these two steps; i.e., even in the reconstruction step the future image analysis step is taken into account, leading to a new reconstruction kernel. Here we concentrate on linear methods. As a practical example we consider the image reconstruction problem in computerized tomography followed by an edge detection. We calculate a new reconstruction kernel and present results from simulations.<\/jats:p>","DOI":"10.1137\/070700863","type":"journal-article","created":{"date-parts":[[2008,10,29]],"date-time":"2008-10-29T13:45:01Z","timestamp":1225287901000},"page":"188-208","source":"Crossref","is-referenced-by-count":32,"title":["Combining Image Reconstruction and Image Analysis with an Application to Two-Dimensional Tomography"],"prefix":"10.1137","volume":"1","author":[{"given":"Alfred K.","family":"Louis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,6,11]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1968.tb00216.x"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-87-05547-5"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1109\/83.988951"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1986.4767851"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"M. Cetin and W. C. Karl,\n                      Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization\n                      , IEEE Trans. Image Process., 10 (2001) pp. 623\u2013631.","DOI":"10.1109\/83.913596"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"B. Chalmond,\n                      Modeling and Inverse Problems in Image Analysis\n                      , Springer, Berlin, 2003.","DOI":"10.1007\/978-0-387-21662-1"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160340105"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"U. Eckhardt,\n                      Zur numerischen Behandlung inkorrekt gestellter Aufgaben\n                      , Computing, 17 (1976\/77), pp. 193\u2013206.","DOI":"10.1007\/BF02259645"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"H. W. Engl, M. Hanke, and A. Neubauer,\n                      Regularization of Inverse Problems\n                      , Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.","DOI":"10.1007\/978-94-009-1740-8"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139995286357"},{"key":"R11","unstructured":"B. J\u00e4hne,\n                      Handbook of Digital Image Processing for Scientific and Technical Applications\n                      , 2nd ed., CRC Press, Boca Raton, FL, 2004."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1515\/jiip.2001.9.1.59"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/22\/2\/015"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2007.03409.x"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396494"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1002\/mma.1670050113"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"A. K. Louis,\n                      Inverse und schlecht gestellte Probleme\n                      , Teubner, Stuttgart, Germany, 1989.","DOI":"10.1007\/978-3-322-84808-6"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/12\/2\/005"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/15\/2\/009"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/6\/3\/011"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1109\/42.251129"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"A. K. Louis, P. Maass, and A. Rieder,\n                      Wavelets\n                      , 2nd ed., Teubner, Stuttgart, Germany, 1998 (in German); Wiley, Chichester, UK, 1997 (in English).","DOI":"10.1007\/978-3-322-80136-4"},{"key":"R23","doi-asserted-by":"crossref","unstructured":"D. A. Murio,\n                      The Mollification Method and the Numerical Solution of Ill-Posed Problems\n                      , Wiley, Chichester, UK, 1993.","DOI":"10.1002\/9781118033210"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1080\/00036818408839508"},{"key":"R25","doi-asserted-by":"crossref","unstructured":"F. Natterer,\n                      The Mathematics of Computerized Tomography\n                      , Teubner, Stuttgart, Germany, Wiley, Chichester, UK, 1986.","DOI":"10.1007\/978-3-663-01409-6"},{"key":"R26","unstructured":"S. Oeckl, T. Sch\u00f6n, A. Knauf, and A. K. Louis,\n                      Multiresolution 3D-computerized tomography and its application to NDT\n                      , in Proceedings of the Ninth European Conference on Non-Destructive Testing (ECNDT), Berlin, 2006."},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-005-0655-9"},{"key":"R28","doi-asserted-by":"crossref","unstructured":"E. T. Quinto,\n                      Radon transforms, differential equations, and microlocal analysis\n                      , in Radon Transforms and Tomography, Contemp. Math. 278, AMS, Providence, RI, 2001, pp. 57-68.","DOI":"10.1090\/conm\/278\/04594"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.06.041"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070700863","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:32:03Z","timestamp":1787322723000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070700863"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070700863"],"URL":"https:\/\/doi.org\/10.1137\/070700863","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}