{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:28:26Z","timestamp":1787318906813,"version":"build-2736575974"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","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 local tomography (LT) in the motion contaminated case. It is shown that microlocally, away from some critical directions, LT is equivalent to a pseudodifferential operator of order one. LT also produces nonlocal artifacts that are of the same strength as useful singularities. If motion is not accurately known, singularities inside the object f being scanned spread in different directions. A single edge can become a double edge. In such a case the image of f looks cluttered. Based on this observation we propose an algorithm for motion estimation. We propose an empiric measure of image clutter, which we call edge entropy. By minimizing edge entropy we find the motion model. The algorithm is quite flexible and is also used for solving the misalignment correction problem. The results of numerical experiments on motion estimation and misalignment correction are very encouraging.<\/jats:p>","DOI":"10.1137\/100796728","type":"journal-article","created":{"date-parts":[[2011,3,9]],"date-time":"2011-03-09T18:59:50Z","timestamp":1299697190000},"page":"200-219","source":"Crossref","is-referenced-by-count":29,"title":["Local Tomography and the Motion Estimation Problem"],"prefix":"10.1137","volume":"4","author":[{"given":"A.","family":"Katsevich","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Silver","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Zamyatin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,3,9]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.24.001569"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2006.873224"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/49\/11\/006"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2003.817868"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1118\/1.2219776"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2006.889743"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"Y. V. Egorov and B.W. Schulze,\n                      Pseudo-differential Operators, Singularities, Applications\n                      , Birk-h\u00e4user, Basel, 1997.","DOI":"10.1007\/978-3-0348-8900-1"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"D. Finch, I.R. Lan, and G. Uhlmann,\n                      Microlocal analysis of the x-ray transform with sources on a curve\n                      , in Inside Out: Inverse Problems and Applications, G. Uhlmann, ed., Cambridge University Press, Cambridge, UK, 2003, pp. 193\u2013218.","DOI":"10.1017\/9781009701310.008"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1097\/00004728-200111000-00014"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/47\/15\/304"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/48\/18\/308"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-89-05811-0"},{"key":"R13","unstructured":"L. H\u00f6rmander,\n                      The Analysis of Linear Partial Differential Operators.\n                      IV.\n                      Fourier Integral Operators\n                      , Springer-Verlag, Berlin, 1985."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1118\/1.3301600"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1109\/42.887837"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139998336043"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/22\/2\/015"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/4\/045012"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/51\/14\/011"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/53\/22\/001"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2006.876166"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1109\/42.251129"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/7.4.308"},{"key":"R24","doi-asserted-by":"crossref","unstructured":"J. D. Pack and F. Noo,\n                      Dynamic computed tomography with known motion field\n                      , in Medical Imaging 2004: Image Processing, Proceedings of the SPIE, Vol. 5370, J. M. Fitzpatrick and M. Sonka, eds., 2004, pp. 2097\u20132104.","DOI":"10.1117\/12.536283"},{"key":"R25","unstructured":"E. T. Quinto,\n                      Electron microscope tomography\n                      , Conference talk at workshop on Mathematical Methods in Emerging Modalities of Medical Imaging, Banff International Research Station, Banff, Canada, 2009."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/07068326X"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/52\/12\/016"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2008.2008962"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1002\/rcs.38"},{"key":"R30","doi-asserted-by":"crossref","unstructured":"D. Shen, H. Sundar, Z. Xue, Y. Fan, and H. Litt,\n                      Consistent estimation of cardiac motions by 4D image registration\n                      , in Medical Image Computing and Computer-Assisted Intervention, Lecture Notes in Comput. Sci. 3750, Springer-Verlag, Berlin, Heidelberg, 2005, pp. 902\u2013910.","DOI":"10.1007\/11566489_111"},{"key":"R31","unstructured":"K. Taguchi and H. Kudo,\n                      Motion compensated fan-beam reconstruction for computed tomography using derivative backprojection filtering approach\n                      , in Proceedings of the IXth International Conference on Fully 3D Reconstruction in Radiology and Nuclear Medicine, Lindau, Germany, 2007, pp. 433\u2013436."},{"key":"R32","unstructured":"U. van Stevendaal, C. Lorenz, J. von Berg, and M. Grass,\n                      Motion-compensated reconstruction in helical cardiac CT\n                      , in Proceedings of the IXth International Conference on Fully 3D Reconstruction in Radiology and Nuclear Medicine, Lindau, Germany, 2007, pp. 437\u2013440."},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1118\/1.2731030"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/23\/1\/010"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1118\/1.1879132"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2006.889719"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100796728","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:43:22Z","timestamp":1787316202000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100796728"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1137\/100796728"],"URL":"https:\/\/doi.org\/10.1137\/100796728","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]}}}