{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:57Z","timestamp":1760242557075,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2017,11,22]],"date-time":"2017-11-22T00:00:00Z","timestamp":1511308800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["26108003","15K16067"],"award-info":[{"award-number":["26108003","15K16067"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>It is known that the process of reconstruction of a Positron Emission Tomography (PET) image from sinogram data is very sensitive to measurement noises; it is still an important research topic to reconstruct PET images with high signal-to-noise ratios. In this paper, we propose a new reconstruction method for a temporal series of PET images from a temporal series of sinogram data. In the proposed method, PET images are reconstructed by minimizing the Kullback\u2013Leibler divergence between the observed sinogram data and sinogram data derived from a parametric model of PET images. The contributions of the proposition include the following: (1) regions of targets in images are explicitly expressed using a set of spatial bases in order to ignore the noises in the background; (2) a parametric time activity model of PET images is explicitly introduced as a constraint; and (3) an algorithm for solving the optimization problem is clearly described. To demonstrate the advantages of the proposed method, quantitative evaluations are performed using both synthetic and clinical data of human brains.<\/jats:p>","DOI":"10.3390\/e19110629","type":"journal-article","created":{"date-parts":[[2017,11,22]],"date-time":"2017-11-22T10:47:38Z","timestamp":1511347658000},"page":"629","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Parametric PET Image Reconstruction via Regional Spatial Bases and Pharmacokinetic Time Activity Model"],"prefix":"10.3390","volume":"19","author":[{"given":"Naoki","family":"Kawamura","sequence":"first","affiliation":[{"name":"Department of Computer Science, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya-shi, Aichi 466-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7368-2060","authenticated-orcid":false,"given":"Tatsuya","family":"Yokota","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya-shi, Aichi 466-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hidekata","family":"Hontani","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya-shi, Aichi 466-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muneyuki","family":"Sakata","sequence":"additional","affiliation":[{"name":"Tokyo Metropolitan Geriatric Hospital, 35-2, Sakae-cho, Itabashi-ku, Tokyo 173-0015, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuichi","family":"Kimura","sequence":"additional","affiliation":[{"name":"Department of Computational Systems Biology, Faculty of Biology-Oriented Science and Technology, Kindai University, 930, Nishimitani, Wakayama 649-6433, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,11,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/BF02984655","article-title":"PET kinetic analysis\u2014Compartmental model","volume":"20","author":"Watabe","year":"2006","journal-title":"Ann. Nucl. Med."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1109\/42.363108","article-title":"Accelerated image reconstruction using ordered subsets of projection data","volume":"13","author":"Hudson","year":"1994","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1109\/83.535846","article-title":"Spatial resolution properties of penalized-likelihood image reconstruction: Space-invariant tomographs","volume":"5","author":"Fessler","year":"1996","journal-title":"IEEE Trans. Image Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1088\/0031-9155\/43\/4\/027","article-title":"High-resolution 3D Bayesian image reconstruction using the microPET small-animal scanner","volume":"43","author":"Qi","year":"1998","journal-title":"Phys. Med. Biol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1717","DOI":"10.1109\/TMI.2009.2021851","article-title":"Generalized algorithms for direct reconstruction of parametric images from dynamic PET data","volume":"28","author":"Wang","year":"2009","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_6","unstructured":"Ross, S.Q. (2014). Clear WhitePaper, GE Healthcare."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1109\/42.363099","article-title":"Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images","volume":"13","author":"Mumcuoglu","year":"1994","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_8","unstructured":"Lee, J.S., Lee, D.D., Choi, S., Park, K.S., and Lee, D.S. (2001, January 4\u201310). Non-negative matrix factorization of dynamic images in nuclear medicine. Proceedings of the IEEE Nuclear Science Symposium Conference Record, San Diego, CA, USA."},{"key":"ref_9","unstructured":"Lee, J.S., Lee, D.D., Choi, S., and Lee, D.S. (2001, January 9\u201313). Application of nonnegative matrix factorization to dynamic positron emission tomography. Proceedings of the 3rd International Conference on Independent Component Analysis and Blind Signal Separation, San Diego, CA, USA."},{"key":"ref_10","unstructured":"Pustelnik, N., Chaux, C., Pesquet, J.C., and Comtat, C. (November, January 30). Parallel algorithm and hybrid regularization for dynamic PET reconstruction. Proceedings of the IEEE Nuclear Science Symposium Conference Record, Knoxville, TN, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1118\/1.3673775","article-title":"Gap compensation during PET image reconstruction by constrained, total variation minimization","volume":"39","author":"Ahn","year":"2012","journal-title":"Med. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"105003","DOI":"10.1088\/0266-5611\/30\/10\/105003","article-title":"Total variation regularization in measurement and image space for PET reconstruction","volume":"30","author":"Burger","year":"2014","journal-title":"Inverse Probl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1288","DOI":"10.1118\/1.2192581","article-title":"Model-based image reconstruction for four-dimensional PET","volume":"33","author":"Li","year":"2006","journal-title":"Med. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1109\/TMI.2005.845317","article-title":"Direct reconstruction of kinetic parameter images from dynamic PET data","volume":"24","author":"Kamasak","year":"2005","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_15","unstructured":"Matthews, J.C., Angelis, G.I., Kotasidis, F.A., Markiewicz, P.J., and Reader, A.J. (November, January 30). Direct reconstruction of parametric images using any spatiotemporal 4D image based model and maximum likelihood expectation maximisation. Proceedings of the Nuclear Science Symposium Conference Record, Knoxville, TN, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.cpet.2007.08.001","article-title":"Advances in PET image reconstruction","volume":"2","author":"Reader","year":"2007","journal-title":"PET Clin."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1080\/01621459.1985.10477119","article-title":"A statistical model for positron emission tomography","volume":"80","author":"Vardi","year":"1985","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/42.232252","article-title":"An approximation formula for the variance of PET region-of-interest values","volume":"12","author":"Carson","year":"1993","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1088\/0031-9155\/39\/5\/004","article-title":"Noise properties of the EM algorithm. I. Theory","volume":"39","author":"Barrett","year":"1994","journal-title":"Phys. Med. Biol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1109\/42.293921","article-title":"Penalized weighted least-squares image reconstruction for positron emission tomography","volume":"13","author":"Fessler","year":"1994","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_21","first-page":"709","article-title":"Super-resolution through error energy reduction","volume":"21","author":"Gerchberg","year":"1974","journal-title":"J. Mod. Opt."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1109\/42.764885","article-title":"Fast spatio-temporal image reconstruction for dynamic PET","volume":"18","author":"Wernick","year":"1999","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1006\/nimg.1997.0303","article-title":"Parametric imaging of ligand-receptor binding in PET using a simplified reference region model","volume":"6","author":"Gunn","year":"1997","journal-title":"Neuroimage"},{"key":"ref_24","first-page":"158","article-title":"Reference and target region modeling of [11C]-(R)-PK11195 brain studies","volume":"48","author":"Turkheimer","year":"2007","journal-title":"J. Nucl. Med."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1038\/jcbfm.1990.127","article-title":"Graphical analysis of reversible radioligand binding from time\u2014Activity measurements applied to [N-11C-methyl]-(-)-cocaine PET studies in human subjects","volume":"10","author":"Logan","year":"1990","journal-title":"J. Cereb. Blood Flow Metab."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1006\/nimg.1996.0066","article-title":"Simplified reference tissue model for PET receptor studies","volume":"4","author":"Lammertsma","year":"1996","journal-title":"Neuroimage"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/S0969-8051(00)00137-2","article-title":"Graphical analysis of PET data applied to reversible and irreversible tracers","volume":"27","author":"Logan","year":"2000","journal-title":"Nucl. Med. Biol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1038\/jcbfm.2012.59","article-title":"Optimization of supervised cluster analysis for extracting reference tissue input curves in (R)-[11C] PK11195 brain PET studies","volume":"32","author":"Yaqub","year":"2012","journal-title":"J. Cereb. Blood Flow Metab."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1440","DOI":"10.1097\/01.WCB.0000033967.83623.34","article-title":"Noise reduction in the simplified reference tissue model for neuroreceptor functional imaging","volume":"22","author":"Wu","year":"2002","journal-title":"J. Cereb. Blood Flow Metab."},{"key":"ref_30","unstructured":"Leen, T.K., Dietterich, T.G., and Tresp, V. (2001). Algorithms for non-negative matrix factorization. Advances in Neural Information Processing Systems 13 (NIPS 2000), MIT Press."},{"key":"ref_31","unstructured":"Reader, A.J., Matthews, J.C., Sureau, F.C., Comtat, C., Trebossen, R., and Buvat, I. (November, January 29). Iterative kinetic parameter estimation within fully 4D PET image reconstruction. Proceedings of the IEEE Nuclear Science Symposium Conference Record, San Diego, CA, USA."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1109\/TMI.1982.4307558","article-title":"Maximum likelihood reconstruction for emission tomography","volume":"1","author":"Shepp","year":"1982","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1097\/00004647-199609000-00008","article-title":"Distribution volume ratios without blood sampling from graphical analysis of PET data","volume":"16","author":"Logan","year":"1996","journal-title":"J. Cereb. Blood Flow Metab."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4533","DOI":"10.1088\/0031-9155\/60\/11\/4533","article-title":"Direct 4D PET MLEM reconstruction of parametric images using the simplified reference tissue model with the basis function method for [11C] raclopride","volume":"60","author":"Gravel","year":"2015","journal-title":"Phys. Med. Biol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"802","DOI":"10.7150\/thno.5130","article-title":"Direct estimation of kinetic parametric images for dynamic PET","volume":"3","author":"Wang","year":"2013","journal-title":"Theranostics"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3963","DOI":"10.1118\/1.2966349","article-title":"A survey of approaches for direct parametric image reconstruction in emission tomography","volume":"35","author":"Tsoumpas","year":"2008","journal-title":"Med. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/11\/629\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:50:50Z","timestamp":1760208650000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/11\/629"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,22]]},"references-count":36,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2017,11]]}},"alternative-id":["e19110629"],"URL":"https:\/\/doi.org\/10.3390\/e19110629","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2017,11,22]]}}}