{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T01:08:23Z","timestamp":1789088903485,"version":"build-2803163510"},"reference-count":39,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012245","name":"Science and Technology Planning Project of Guangdong Province","doi-asserted-by":"publisher","award":["2024A1515012288"],"award-info":[{"award-number":["2024A1515012288"]}],"id":[{"id":"10.13039\/501100012245","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2025YFE0213502"],"award-info":[{"award-number":["2025YFE0213502"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["12571102"],"award-info":[{"award-number":["12571102"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2024A1515010272"],"award-info":[{"award-number":["2024A1515010272"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2025A1515011544"],"award-info":[{"award-number":["2025A1515011544"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["62172188"],"award-info":[{"award-number":["62172188"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12401120"],"award-info":[{"award-number":["12401120"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2027,2]]},"DOI":"10.1016\/j.cam.2026.117991","type":"journal-article","created":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T00:36:44Z","timestamp":1784853404000},"page":"117991","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A preconditioned proximal gradient algorithm for PET image reconstruction with approximately sparse regularization"],"prefix":"10.1016","volume":"491","author":[{"given":"Yongxin","family":"He","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1400-278X","authenticated-orcid":false,"given":"Yizun","family":"Lin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manchun","family":"Tan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Ye","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yidan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.cam.2026.117991_bib0001","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."},{"issue":"2","key":"10.1016\/j.cam.2026.117991_bib0002","article-title":"Em reconstruction algorithms for emission and transmission tomography","volume":"8","author":"Lange","year":"1984","journal-title":"J. Comput. Assist. Tomogr."},{"issue":"1","key":"10.1016\/j.cam.2026.117991_bib0003","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1109\/42.370409","article-title":"A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography","volume":"14","author":"De Pierro","year":"1995","journal-title":"IEEE Trans. Med. Imag."},{"issue":"2","key":"10.1016\/j.cam.2026.117991_bib0004","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1109\/42.993134","article-title":"Edge-preserving tomographic reconstruction with nonlocal regularization","volume":"21","author":"Yu","year":"2002","journal-title":"IEEE Trans. Med. Imag."},{"issue":"6","key":"10.1016\/j.cam.2026.117991_bib0005","doi-asserted-by":"crossref","first-page":"2202","DOI":"10.1109\/23.819305","article-title":"Total variation regulated EM algorithm","volume":"46","author":"Panin","year":"1999","journal-title":"IEEE Trans. Nucl. Sci."},{"issue":"9","key":"10.1016\/j.cam.2026.117991_bib0006","doi-asserted-by":"crossref","DOI":"10.1088\/0266-5611\/27\/9\/095001","article-title":"An alternating extragradient method for total variation-based image restoration from poisson data","volume":"27","author":"Bonettini","year":"2011","journal-title":"Inverse Probl."},{"issue":"11","key":"10.1016\/j.cam.2026.117991_bib0007","doi-asserted-by":"crossref","DOI":"10.1088\/0266-5611\/28\/11\/115005","article-title":"Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction","volume":"28","author":"Krol","year":"2012","journal-title":"Inverse Probl."},{"issue":"1","key":"10.1016\/j.cam.2026.117991_bib0008","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1111\/j.1365-246X.2007.03409.x","article-title":"Tomographic inversion using \u21131-norm regularization of wavelet coefficients","volume":"170","author":"Loris","year":"2007","journal-title":"Geophys. J. Int."},{"issue":"7","key":"10.1016\/j.cam.2026.117991_bib0009","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1109\/TMI.2008.923698","article-title":"Dynamic PET reconstruction using wavelet regularization with adapted basis functions","volume":"27","author":"Verhaeghe","year":"2008","journal-title":"IEEE Trans. Med. Imag."},{"issue":"1","key":"10.1016\/j.cam.2026.117991_bib0010","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/TNS.2008.2009445","article-title":"Iterative PET image reconstruction using translation invariant wavelet transform","volume":"56","author":"Zhou","year":"2009","journal-title":"IEEE Trans. Nucl. Sci."},{"issue":"2","key":"10.1016\/j.cam.2026.117991_bib0011","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s10851-007-0042-5","article-title":"Nonlocal prior bayesian tomographic reconstruction","volume":"30","author":"Chen","year":"2008","journal-title":"J. Math. Imag. Vis."},{"issue":"12","key":"10.1016\/j.cam.2026.117991_bib0012","doi-asserted-by":"crossref","first-page":"2194","DOI":"10.1109\/TMI.2012.2211378","article-title":"Penalized likelihood PET image reconstruction using patch-based edge-preserving regularization","volume":"31","author":"Wang","year":"2012","journal-title":"IEEE Trans. Med. Imag."},{"issue":"18","key":"10.1016\/j.cam.2026.117991_bib0013","doi-asserted-by":"crossref","first-page":"6833","DOI":"10.1088\/0031-9155\/61\/18\/6833","article-title":"Patch-based image reconstruction for PET using prior-image derived dictionaries","volume":"61","author":"Tahaei","year":"2016","journal-title":"Phys. Med. Biol."},{"issue":"11","key":"10.1016\/j.cam.2026.117991_bib0014","doi-asserted-by":"crossref","first-page":"3289","DOI":"10.1109\/TMI.2022.3181813","article-title":"A fast convergent ordered-subsets algorithm with subiteration-dependent preconditioners for PET image reconstruction","volume":"41","author":"Guo","year":"2022","journal-title":"IEEE Trans. Med. Imag."},{"issue":"282","key":"10.1016\/j.cam.2026.117991_bib0015","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1090\/S0025-5718-2012-02631-7","article-title":"\u21130 Minimization for wavelet frame based image restoration","volume":"82","author":"Zhang","year":"2013","journal-title":"Math. Comput."},{"issue":"2","key":"10.1016\/j.cam.2026.117991_bib0016","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.acha.2007.10.002","article-title":"A framelet-based image inpainting algorithm","volume":"24","author":"Cai","year":"2008","journal-title":"Appl Comput. Harmon. Anal."},{"issue":"1","key":"10.1016\/j.cam.2026.117991_bib0017","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","article-title":"A fast iterative shrinkage-thresholding algorithm for linear inverse problems","volume":"2","author":"Beck","year":"2009","journal-title":"SIAM J. Imag. Sci."},{"issue":"11","key":"10.1016\/j.cam.2026.117991_bib0018","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6420\/ab23da","article-title":"Sparsity promoting regularization for effective noise suppression in SPECT image reconstruction","volume":"35","author":"Zheng","year":"2019","journal-title":"Inverse Probl."},{"issue":"2","key":"10.1016\/j.cam.2026.117991_bib0019","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1287\/moor.1100.0449","article-title":"Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the kurdyka-\u0141ojasiewicz inequality","volume":"35","author":"Attouch","year":"2010","journal-title":"Math. Oper. Res."},{"issue":"1","key":"10.1016\/j.cam.2026.117991_bib0020","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s10107-013-0701-9","article-title":"Proximal alternating linearized minimization for nonconvex and nonsmooth problems","volume":"146","author":"Bolte","year":"2014","journal-title":"Math. Program."},{"issue":"1","key":"10.1016\/j.cam.2026.117991_bib0021","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s10107-011-0484-9","article-title":"Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward\u2013backward splitting, and regularized gauss\u2013Seidel methods","volume":"137","author":"Attouch","year":"2013","journal-title":"Math. Program."},{"issue":"1","key":"10.1016\/j.cam.2026.117991_bib0022","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.acha.2015.03.001","article-title":"Wavelet inpainting with the \u21130 sparse regularization","volume":"41","author":"Shen","year":"2016","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"9","key":"10.1016\/j.cam.2026.117991_bib0023","doi-asserted-by":"crossref","first-page":"2114","DOI":"10.1109\/TMI.2019.2898271","article-title":"A krasnoselskii-Mann algorithm with an improved EM preconditioner for PET image reconstruction","volume":"38","author":"Lin","year":"2019","journal-title":"IEEE Trans. Med. Imag."},{"issue":"2","key":"10.1016\/j.cam.2026.117991_bib0024","doi-asserted-by":"crossref","first-page":"273","DOI":"10.24033\/bsmf.1625","article-title":"Proximit\u00e9 et dualit\u00e9 dans un espace hilbertien","volume":"93","author":"Moreau","year":"1965","journal-title":"Bull. Soc. Math. France"},{"key":"10.1016\/j.cam.2026.117991_bib0025","series-title":"Variational Analysis","volume":"317","author":"Rockafellar","year":"2009"},{"key":"10.1016\/j.cam.2026.117991_bib0026","series-title":"Nonlinear Programming","author":"Bertsekas","year":"1999"},{"key":"10.1016\/j.cam.2026.117991_bib0027","series-title":"Convex Analysis and Monotone Operator Theory in Hilbert Space","author":"Bauschke","year":"2017"},{"issue":"1","key":"10.1016\/j.cam.2026.117991_bib0028","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.jmaa.2014.11.044","article-title":"Compositions and convex combinations of averaged nonexpansive operators","volume":"425","author":"Combettes","year":"2015","journal-title":"J. Math. Anal. Appl."},{"issue":"2","key":"10.1016\/j.cam.2026.117991_bib0029","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF03007664","article-title":"Quelques propri\u00e9t\u00e9s des op\u00e9rateurs angle-born\u00e9s etn-cycliquement monotones","volume":"26","author":"Baillon","year":"1977","journal-title":"Isr. J. Math."},{"issue":"1","key":"10.1016\/j.cam.2026.117991_bib0030","first-page":"123","article-title":"Two remarks on the method of successive approximations","volume":"10","author":"Krasnosel\u2019skii","year":"1955","journal-title":"Uspekhi Mat. Nauk"},{"issue":"3","key":"10.1016\/j.cam.2026.117991_bib0031","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1090\/S0002-9939-1953-0054846-3","article-title":"Mean value methods in iteration","volume":"4","author":"Mann","year":"1953","journal-title":"Proc. Am. Math. Soc."},{"issue":"4","key":"10.1016\/j.cam.2026.117991_bib0032","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1137\/050626090","article-title":"Signal recovery by proximal forward-backward splitting","volume":"4","author":"Combettes","year":"2005","journal-title":"Multiscale Model. Sim."},{"issue":"2","key":"10.1016\/j.cam.2026.117991_bib0033","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/s10444-014-9363-2","article-title":"Multi-step fixed-point proximity algorithms for solving a class of optimization problems arising from image processing","volume":"41","author":"Li","year":"2015","journal-title":"Adv. Comput. Math."},{"issue":"8","key":"10.1016\/j.cam.2026.117991_bib0034","doi-asserted-by":"crossref","first-page":"4083","DOI":"10.1002\/mp.12292","article-title":"Relaxed ordered subset preconditioned alternating projection algorithm for PET reconstruction with automated penalty weight selection","volume":"44","author":"Schmidtlein","year":"2017","journal-title":"Med. Phys."},{"key":"10.1016\/j.cam.2026.117991_bib0035","doi-asserted-by":"crossref","first-page":"S236","DOI":"10.1016\/j.nima.2010.11.092","article-title":"Fundamental limits of spatial resolution in PET","volume":"648","author":"Moses","year":"2011","journal-title":"Nucl. Instrum. Methods Phys. Res. A."},{"issue":"8","key":"10.1016\/j.cam.2026.117991_bib0036","first-page":"969","article-title":"PETSTEP: Generation of synthetic PET lesions for fast evaluation of segmentation methods","volume":"31","author":"Berthon","year":"2015","journal-title":"Phys. Med. Biol."},{"key":"10.1016\/j.cam.2026.117991_bib0037","series-title":"Orthogonal Transforms for Digital Signal Processing","author":"Ahmed","year":"2012"},{"issue":"4","key":"10.1016\/j.cam.2026.117991_bib0038","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0165-1684(90)90158-U","article-title":"Fast fourier transforms: a tutorial review and a state of the art","volume":"19","author":"Duhamel","year":"1990","journal-title":"Signal Proc."},{"issue":"3","key":"10.1016\/j.cam.2026.117991_bib0039","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1561\/0100000006","article-title":"Toeplitz and circulant matrices: a review","volume":"2","author":"Gray","year":"2006","journal-title":"Found. Trends. Commun."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726006333?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726006333?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T00:18:53Z","timestamp":1789085933000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726006333"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,2]]},"references-count":39,"alternative-id":["S0377042726006333"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117991","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2027,2]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A preconditioned proximal gradient algorithm for PET image reconstruction with approximately sparse regularization","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117991","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117991"}}