{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:32:27Z","timestamp":1787322747187,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>In this paper we study the inversion of a generalized Radon transform that maps a function in three dimensional space to a family of cylindrical integrals. We derive local backprojection-type inversion formulas for this cylindrical Radon transform. Our inversion formulas can be implemented in a straightforward manner with $\\mathcal{O}(\\mathtt{N}^{4\/3})$ floating point operations, where $\\mathtt{N}$ is the number of spatial reconstruction points. Numerical results are presented which demonstrate the accuracy and validity of the derived algorithms.<\/jats:p>","DOI":"10.1137\/110822505","type":"journal-article","created":{"date-parts":[[2011,8,25]],"date-time":"2011-08-25T18:32:23Z","timestamp":1314297143000},"page":"789-806","source":"Crossref","is-referenced-by-count":5,"title":["Inversion Formulas for a Cylindrical Radon Transform"],"prefix":"10.1137","volume":"4","author":[{"given":"Markus","family":"Haltmeier","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,8,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1996.0090"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/21\/2\/004"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0519016"},{"key":"R4","unstructured":"A. Beltukov,\n                      Inversion of the spherical mean transform with sources on a hyperplane\n                      , http:\/\/arxiv.org\/abs\/0910.1380 http:\/\/arxiv.org\/abs\/0910.1380, 2009."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/23\/6\/S06"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1109\/TUFFC.2005.1516030"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.75.046706"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0145018"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/070682137"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141002417814"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"H. Gr\u00fcn, G. Paltauf, M. Haltmeier, and P. Burgholzer,\n                      Photoacoustic tomography using a fiber based Fabry-Perot interferometer as an integrating line detector and image reconstruction by model-based time reversal method\n                      , in Novel Optical Instrumentation for Biomedical Applications III, C. D. Depeursinge, ed., Proceedings of SPIE 6631, SPIE, 2007, 663107.","DOI":"10.1117\/12.729475"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202509003437"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202507002054"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2009.2022623"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1002\/mma.648"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"S. Helgason,\n                      The Radon Transform\n                      , Progress in Mathematics 5, Birkh\u00e4user Boston, Boston, 1980.","DOI":"10.1007\/978-1-4899-6765-7"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/5\/055006"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"A. C. Kak and M. Slaney,\n                      Principles of Computerized Tomographic Imaging\n                      , Classics Appl. Math. 33, SIAM, Philadelphia, 2001.","DOI":"10.1137\/1.9780898719277"},{"key":"R19","unstructured":"J. Klein,\n                      Inverting the spherical radon transform for physically meaningful functions\n                      , http:\/\/arxiv.org\/abs\/math\/0307348 http:\/\/arxiv.org\/abs\/math\/0307348, 2003."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1364\/AO.42.001899"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792508007353"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/23\/1\/021"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/23\/6\/S02"},{"key":"R24","unstructured":"L. A. Kunyansky,\n                      Fast reconstruction algorithms for the thermoacoustic tomography in certain domains with cylindrical or spherical symmetries\n                      , http:\/\/arxiv.org\/abs\/1102.1413, 2011."},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/27\/2\/025012"},{"key":"R26","doi-asserted-by":"crossref","unstructured":"A. K. Louis and E. T. Quinto,\n                      Local tomographic methods in sonar\n                      , in Surveys on Solution Methods for Inverse Problems, Springer, Vienna, 2000, pp. 147\u2013154.","DOI":"10.1007\/978-3-7091-6296-5_8"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/26\/3\/035014"},{"key":"R28","doi-asserted-by":"crossref","unstructured":"F. 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