{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,10]],"date-time":"2024-02-10T07:10:17Z","timestamp":1707549017928},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Image Grap."],"published-print":{"date-parts":[[2007,1]]},"abstract":"<jats:p>This work presents an inversion algorithm for the exponential Radon transform (ERT) over 180\u00b0 range of view angles. The algorithm can be applied to two-dimensional parallel beam geometry in single photon emission computed tomography. First the differentiation of the ERT over \u03c0 is backprojected. A convolutional relation between this backprojected differentiation and the original image is then established. In order to invert the convolution relation, the least-squares method is utilized to obtain a numerically generated filtering kernel, which readily restores the original image. The advantages of the proposed algorithm are, first, it only requires half the view angles of the conventional inversion algorithm, second, it deals with truncation in ERT data in certain situations, and third, the numerically generated filtering kernel can be pre-calculated and stored for later applications. The algorithm is an analytical approach except for the pre-calculated inverse kernel.<\/jats:p>","DOI":"10.1142\/s0219467807002544","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T11:30:57Z","timestamp":1169033457000},"page":"71-85","source":"Crossref","is-referenced-by-count":4,"title":["AN ANALYTICAL INVERSION OF THE 180\u00b0 EXPONENTIAL RADON TRANSFORM WITH A NUMERICALLY GENERATED KERNEL"],"prefix":"10.1142","volume":"07","author":[{"given":"QIU","family":"HUANG","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, UT 84112, USA"}]},{"given":"GENGSHENG L.","family":"ZENG","sequence":"additional","affiliation":[{"name":"Utah Center for Advanced Imaging Research, Department of Radiology, University of Utah, Salt Lake City, UT 84108, USA"}]},{"given":"GRANT T.","family":"GULLBERG","sequence":"additional","affiliation":[{"name":"E. O. Lawrence Berkeley National Laboratory, One Cyclotron Road, Mail Stop 55R0121, Berkeley, CA 94720, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-663-01409-6","volume-title":"The Mathematics of Computerized Tomography","author":"Natterer F.","year":"1986"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8749-5_9"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/0139029"},{"key":"rf4","volume-title":"Principles of Computerized Tomography","author":"Kak A. C.","year":"1987"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(89)90209-6"},{"key":"rf6","first-page":"221","volume":"53","author":"Kuchment P.","journal-title":"Appl. Anal."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/12\/5\/013"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/17\/5\/308"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/18\/3\/319"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02385485"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/20\/2\/006"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02384507"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/20\/4\/009"},{"key":"rf14","first-page":"3903","volume":"47","author":"Noo F.","journal-title":"Phys. Med. Bio."},{"key":"rf15","volume-title":"Numerical Recipes in C++","author":"Press W. H.","year":"2002"},{"key":"rf16","volume-title":"Integral Equations and Their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology","author":"Mikhlin S. G.","year":"1957"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2004.840899"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/50\/1\/002"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/22\/3\/L01"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/22\/3\/019"},{"key":"rf22","volume-title":"Linear Integral Equations Theory and Technique","author":"Kanwal R. P.","year":"1971"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8199-9"},{"key":"rf24","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198504207.001.0001","volume-title":"Iterative Methods for Toeplitz Systems","author":"Ng M. K.","year":"2004"}],"container-title":["International Journal of Image and Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219467807002544","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,10]],"date-time":"2024-02-10T06:56:12Z","timestamp":1707548172000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219467807002544"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1]]},"references-count":23,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,1]]}},"alternative-id":["10.1142\/S0219467807002544"],"URL":"https:\/\/doi.org\/10.1142\/s0219467807002544","relation":{},"ISSN":["0219-4678","1793-6756"],"issn-type":[{"value":"0219-4678","type":"print"},{"value":"1793-6756","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1]]}}}