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Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by exploiting spherical symmetries, although computation time is still slower compared to non-overlapping basis functions. In this work, we have implemented the reconstruction algorithm using Graphical Processing Unit (GPU) technology for speed and a precomputed Monte-Carlo-calculated SRM for accuracy. The reconstruction time achieved using spherical basis functions on a GPU was 4.3 times faster than the Central Processing Unit (CPU) and 2.5 times faster than a CPU-multi-core parallel implementation using eight cores. Overwriting hazards are minimized by combining a random line of response ordering and constrained atomic writing. Small differences in image quality were observed between implementations.<\/jats:p>","DOI":"10.1155\/2012\/452910","type":"journal-article","created":{"date-parts":[[2012,4,2]],"date-time":"2012-04-02T17:00:56Z","timestamp":1333386056000},"page":"1-11","source":"Crossref","is-referenced-by-count":6,"title":["High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid"],"prefix":"10.1155","volume":"2012","author":[{"given":"J.","family":"Cabello","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica Corpuscular, Universitat de Val\u00e8ncia\/CSIC, Edificio Institutos de Investigaci\u00f3n, 22085 Valencia, Spain"}]},{"given":"J. E.","family":"Gillam","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica Corpuscular, Universitat de Val\u00e8ncia\/CSIC, Edificio Institutos de Investigaci\u00f3n, 22085 Valencia, Spain"}]},{"given":"M.","family":"Rafecas","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica Corpuscular, Universitat de Val\u00e8ncia\/CSIC, Edificio Institutos de Investigaci\u00f3n, 22085 Valencia, Spain"},{"name":"Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universitat de Val\u00e8ncia, 46100 Valencia, Spain"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/41\/9\/015"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/51\/15\/R01"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.nima.2004.03.113"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2006.876171"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2010.2040188"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/56\/10\/003"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/53\/23\/018"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1118\/1.3501884"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/TNS.2004.834827"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/51\/18\/007"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1118\/1.3455287"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2011.2109732"},{"issue":"7","key":"15","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1088\/0031-9155\/57\/7\/1759","volume":"57","year":"2012","journal-title":"Physics in Medicine and Biology"},{"issue":"10","key":"17","doi-asserted-by":"crossref","first-page":"1834","DOI":"10.1364\/JOSAA.7.001834","volume":"7","year":"1990","journal-title":"Journal of the Optical Society of America A"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1109\/23.910827"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/49\/11\/003"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1109\/TNS.2006.878004"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1109\/TNS.2011.2158113"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/56\/20\/015"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1118\/1.3661998"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/56\/13\/018"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1109\/TNS.2004.843114"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/49\/19\/007"},{"issue":"1","key":"28","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/42.481442","volume":"15","year":"1996","journal-title":"IEEE Transactions on Medical Imaging"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/49\/20\/005"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1118\/1.3490711"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/j.mibio.2004.03.002"},{"issue":"5","key":"32","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1364\/AO.43.001053","volume":"43","year":"2004","journal-title":"Applied Optics"}],"container-title":["International Journal of Biomedical Imaging"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijbi\/2012\/452910.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijbi\/2012\/452910.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijbi\/2012\/452910.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,20]],"date-time":"2017-06-20T12:31:25Z","timestamp":1497961885000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijbi\/2012\/452910\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":28,"alternative-id":["452910","452910"],"URL":"https:\/\/doi.org\/10.1155\/2012\/452910","relation":{},"ISSN":["1687-4188","1687-4196"],"issn-type":[{"type":"print","value":"1687-4188"},{"type":"electronic","value":"1687-4196"}],"subject":[],"published":{"date-parts":[[2012]]}}}