{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T16:49:05Z","timestamp":1774630145555,"version":"3.50.1"},"reference-count":38,"publisher":"Wiley","issue":"12","license":[{"start":{"date-parts":[[2019,12,7]],"date-time":"2019-12-07T00:00:00Z","timestamp":1575676800000},"content-version":"vor","delay-in-days":6,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:sec><jats:title>Purpose<\/jats:title><jats:p>The computational burden associated with model\u2010based iterative reconstruction (<jats:styled-content style=\"fixed-case\">MBIR<\/jats:styled-content>) is still a practical limitation. Iterative coordinate descent (<jats:styled-content style=\"fixed-case\">ICD<\/jats:styled-content>) is an optimization approach for <jats:styled-content style=\"fixed-case\">MBIR<\/jats:styled-content> that has sometimes been thought to be incompatible with modern computing architectures, especially graphics processing units (<jats:styled-content style=\"fixed-case\">GPU<\/jats:styled-content>s). The purpose of this work is to accelerate the previously released open\u2010source Free<jats:styled-content style=\"fixed-case\">CT<\/jats:styled-content>_<jats:styled-content style=\"fixed-case\">ICD<\/jats:styled-content> to include <jats:styled-content style=\"fixed-case\">GPU<\/jats:styled-content> acceleration and to demonstrate computational performance with <jats:styled-content style=\"fixed-case\">ICD<\/jats:styled-content> that is comparable with simultaneous update approaches.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>Free<jats:styled-content style=\"fixed-case\">CT<\/jats:styled-content>_<jats:styled-content style=\"fixed-case\">ICD<\/jats:styled-content> uses a stored system matrix (<jats:styled-content style=\"fixed-case\">SSM<\/jats:styled-content>), which precalculates the forward projector in the form of a sparse matrix and then reconstructs on a rotating coordinate grid to exploit helical symmetry. In our <jats:styled-content style=\"fixed-case\">GPU ICD<\/jats:styled-content> implementation, we shuffle the sinogram memory ordering such that data access in the sinogram coalesce into fewer transactions. We also update <jats:styled-content style=\"fixed-case\">N<jats:sub>S<\/jats:sub><\/jats:styled-content> voxels in the xy\u2010plane simultaneously to improve occupancy. Conventional <jats:styled-content style=\"fixed-case\">ICD<\/jats:styled-content> updates voxels sequentially (<jats:styled-content style=\"fixed-case\">N<jats:sub>S<\/jats:sub><\/jats:styled-content>\u00a0=\u00a01). Using <jats:styled-content style=\"fixed-case\">N<jats:sub>S<\/jats:sub><\/jats:styled-content>\u00a0&gt;\u00a01 eliminates existing convergence guarantees. Convergence behavior in a clinical dataset was therefore studied empirically.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>On a pediatric dataset with sinogram size of 736\u00a0\u00d7\u00a016\u00a0\u00d7\u00a013860 reconstructed to a matrix size of 512\u00a0\u00d7\u00a0512\u00a0\u00d7\u00a0128, our code requires about 20\u00a0s per iteration on a single <jats:styled-content style=\"fixed-case\">GPU<\/jats:styled-content> compared to 2300\u00a0s per iteration for a 6\u2010core <jats:styled-content style=\"fixed-case\">CPU<\/jats:styled-content> using Free<jats:styled-content style=\"fixed-case\">CT<\/jats:styled-content>_<jats:styled-content style=\"fixed-case\">ICD<\/jats:styled-content>. After 400 iterations, the proposed and reference codes converge within 2\u00a0<jats:styled-content style=\"fixed-case\">HU RMS<\/jats:styled-content> difference (<jats:styled-content style=\"fixed-case\">RMSD<\/jats:styled-content>). Using a <jats:styled-content style=\"fixed-case\">wFBP<\/jats:styled-content> initialization, convergence within 10\u00a0<jats:styled-content style=\"fixed-case\">HU RMSD<\/jats:styled-content> is achieved within 4\u00a0min. Convergence is similar with <jats:styled-content style=\"fixed-case\">N<jats:sub>S<\/jats:sub><\/jats:styled-content> values between 1 and 256, and <jats:styled-content style=\"fixed-case\">N<jats:sub>S<\/jats:sub><\/jats:styled-content>\u00a0=\u00a016 was sufficient to achieve maximum performance. Divergence was not observed until <jats:styled-content style=\"fixed-case\">N<jats:sub>S<\/jats:sub><\/jats:styled-content>\u00a0&gt;\u00a01024.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusions<\/jats:title><jats:p>With appropriate modifications, <jats:styled-content style=\"fixed-case\">ICD<\/jats:styled-content> may be able to achieve computational performance competitive with simultaneous update algorithms currently used for <jats:styled-content style=\"fixed-case\">MBIR<\/jats:styled-content>.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.13543","type":"journal-article","created":{"date-parts":[[2019,12,7]],"date-time":"2019-12-07T17:00:06Z","timestamp":1575738006000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Accelerating iterative coordinate descent using a stored system matrix"],"prefix":"10.1002","volume":"46","author":[{"given":"Scott S.","family":"Hsieh","sequence":"first","affiliation":[{"name":"Department of Radiological Sciences UCLA Los Angeles CA 90024 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John M.","family":"Hoffman","sequence":"additional","affiliation":[{"name":"Department of Radiological Sciences UCLA Los Angeles CA 90024 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frederic","family":"Noo","sequence":"additional","affiliation":[{"name":"Department of Radiology and Imaging Sciences University of Utah Salt Lake City UT 84108 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,12,7]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.2789499"},{"key":"e_1_2_6_3_1","volume-title":"Principles of Computerized Tomographic Imaging","author":"Kak A","year":"1988"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/25\/12\/123009"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1148\/radiol.2018180137"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1097\/RCT.0b013e31824e639e"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1067\/j.cpradiol.2005.06.002"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.4881148"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.2214\/AJR.12.9382"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.juro.2014.05.089"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.4941954"},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.1358303"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2018.2832007"},{"key":"e_1_2_6_14_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.4851635"},{"key":"e_1_2_6_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2017.2715284"},{"key":"e_1_2_6_16_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/44\/11\/311"},{"key":"e_1_2_6_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2014.2350962"},{"key":"e_1_2_6_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCI.2015.2479555"},{"key":"e_1_2_6_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/3155284.3018765"},{"key":"e_1_2_6_20_1","doi-asserted-by":"crossref","unstructured":"LiX LiangY ZhangW et\u00a0al. 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