{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T02:02:19Z","timestamp":1768960939896,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T00:00:00Z","timestamp":1768867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"JSPS KAKENHI","award":["24K18832"],"award-info":[{"award-number":["24K18832"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>Emission tomography, including single-photon emission computed tomography (SPECT), requires image reconstruction from noisy and incomplete projection data. The maximum-likelihood expectation maximization (MLEM) algorithm is widely used due to its statistical foundation and non-negativity preservation, but it is highly sensitive to noise, particularly in low-count conditions. Although total variation (TV) regularization can reduce noise, it often oversmooths structural details and requires careful parameter tuning. We propose a Graph-Enhanced Expectation Maximization (GREM) algorithm that incorporates graph-based neighborhood information into an MLEM-type multiplicative reconstruction scheme. The method is motivated by a penalized formulation combining a Kullback\u2013Leibler divergence term with a graph Laplacian regularization term, promoting local structural consistency while preserving edges. The resulting update retains the multiplicative structure of MLEM and preserves the non-negativity of the image estimates. Numerical experiments using synthetic phantoms under multiple noise levels, as well as clinical 99mTc-GSA liver SPECT data, demonstrate that GREM consistently outperforms conventional MLEM and TV-regularized MLEM in terms of PSNR and MS-SSIM. These results indicate that GREM provides an effective and practical approach for edge-preserving noise suppression in emission tomography without relying on external training data.<\/jats:p>","DOI":"10.3390\/jimaging12010048","type":"journal-article","created":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T13:02:07Z","timestamp":1768914127000},"page":"48","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Graph-Enhanced Expectation Maximization for Emission Tomography"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4699-1642","authenticated-orcid":false,"given":"Ryosuke","family":"Kasai","sequence":"first","affiliation":[{"name":"Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7165-6099","authenticated-orcid":false,"given":"Hideki","family":"Otsuka","sequence":"additional","affiliation":[{"name":"Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5629","DOI":"10.1088\/0031-9155\/58\/16\/5629","article-title":"Few-view single photon emission computed tomography (SPECT) reconstruction based on a blurred piecewise constant object model","volume":"58","author":"Wolf","year":"2013","journal-title":"Phys. Med. Biol."},{"key":"ref_2","unstructured":"Luo, S., and Zhou, T. (2012). Superiorization of EM algorithm and its application in single-photon emission computed tomography (SPECT). arXiv."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"R541","DOI":"10.1088\/0031-9155\/51\/15\/R01","article-title":"Iterative reconstruction techniques in emission computed tomography","volume":"51","author":"Qi","year":"2006","journal-title":"Phys. Med. Biol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1097\/MNM.0b013e3282f3a515","article-title":"PET versus SPECT: Strengths, limitations and challenges","volume":"29","author":"Rahmim","year":"2008","journal-title":"Nucl. Med. Commun."},{"key":"ref_5","first-page":"1743","article-title":"Rapidly converging iterative reconstruction algorithms in single-photon emission computed tomography","volume":"34","author":"Wallis","year":"1993","journal-title":"J. Nucl. Med."},{"key":"ref_6","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. Imag."},{"key":"ref_7","first-page":"306","article-title":"EM reconstruction algorithms for emission and transmission tomography","volume":"8","author":"Lange","year":"1984","journal-title":"J. Comput. Assist. Tomogr."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1109\/83.465106","article-title":"Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms","volume":"4","author":"Fessler","year":"1995","journal-title":"IEEE Trans. Image Process."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"050008","DOI":"10.1063\/1.5127700","article-title":"Robust iterative methods: Convergence and applications to proton computed tomography","volume":"2160","author":"Karbasi","year":"2019","journal-title":"AIP Conf. Proc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/42.52985","article-title":"Bayesian reconstructions from emission tomography data using a modified EM algorithm","volume":"9","author":"Green","year":"1990","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"035010","DOI":"10.1088\/0266-5611\/26\/3\/035010","article-title":"Hierarchical regularization for edge-preserving reconstruction of PET images","volume":"26","author":"Bardsley","year":"2010","journal-title":"Inverse Probl."},{"key":"ref_13","unstructured":"Zhou, D., and Sch\u00f6lkopf, B. (2005). A regularization framework for learning from graph data. Proceedings of the 22nd International Conference on Machine Learning (ICML), Association for Computing Machinery."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/0600000020","article-title":"Bilateral filtering: Theory and applications","volume":"4","author":"Paris","year":"2009","journal-title":"Found. Trends Comput. Graph. Vis."},{"key":"ref_15","first-page":"50","article-title":"Image denoising via graph Laplacian regularization","volume":"149","author":"Liu","year":"2018","journal-title":"Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Mahmood, F., Shahid, N., Vandergheynst, P., and Skoglund, U. (2016, January 16\u201320). Graph-based sinogram denoising for tomographic reconstructions. Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Orlando, FL, USA.","DOI":"10.1109\/EMBC.2016.7591594"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2049","DOI":"10.1016\/j.promfg.2015.07.253","article-title":"Graph-based sparse representation for image denoising","volume":"3","author":"Ge","year":"2015","journal-title":"Procedia Manuf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2411","DOI":"10.1109\/TIP.2007.904387","article-title":"An expanded theoretical treatment of iteration-dependent majorize-minimize algorithms","volume":"16","author":"Jacobson","year":"2007","journal-title":"IEEE Trans. Image Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Bertero, M., and Boccacci, P. (1998). Introduction to Inverse Problems in Imaging, IOP Publishing.","DOI":"10.1887\/0750304359"},{"key":"ref_21","unstructured":"Kak, A.C., and Slaney, M. (1988). Principles of Computerized Tomographic Imaging, IEEE Press."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Natterer, H. (2001). The Mathematics of Computerized Tomography, SIAM.","DOI":"10.1137\/1.9780898719284"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1049\/el:20080522","article-title":"Scope of validity of PSNR in image\/video quality assessment","volume":"44","author":"Ghanbari","year":"2008","journal-title":"Electron. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/TBC.2008.2000733","article-title":"The evolution of video quality measurement: From PSNR to hybrid metrics","volume":"54","author":"Winkler","year":"2008","journal-title":"IEEE Trans. Broadcast."},{"key":"ref_25","unstructured":"Wang, Z., Simoncelli, E.P., and Bovik, A.C. (2003, January 1\u20134). Multiscale structural similarity for image quality assessment. Proceedings of the 27th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Mudeng, V., Kim, M., and Choe, S.-w. (2022). Prospects of structural similarity index for medical image analysis. Appl. Sci., 12.","DOI":"10.3390\/app12083754"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."}],"container-title":["Journal of Imaging"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-433X\/12\/1\/48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T13:26:45Z","timestamp":1768915605000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-433X\/12\/1\/48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,20]]},"references-count":27,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["jimaging12010048"],"URL":"https:\/\/doi.org\/10.3390\/jimaging12010048","relation":{},"ISSN":["2313-433X"],"issn-type":[{"value":"2313-433X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,20]]}}}