{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,15]],"date-time":"2025-01-15T13:40:15Z","timestamp":1736948415820,"version":"3.33.0"},"reference-count":17,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2005,10,20]],"date-time":"2005-10-20T00:00:00Z","timestamp":1129766400000},"content-version":"vor","delay-in-days":3611,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int J Imaging Syst Tech"],"published-print":{"date-parts":[[1995,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The Richardson\u2010Lucy (R\u2010L) algorithm has been widely used to restore degraded astronomical images. This algorithm is nothing more than the expectation\u2010maximization (EM) algorithm applied to Poisson data. The R\u2010L method is iterative in nature and converges to a (possibly local) maximum of the likelihood function. Unfortunately, because of the ill\u2010conditioned nature of the problem, this maximum likelihood estimate may actually be a very poor restoration. One way to prevent degradation of the restoration is to stop the iteration before it reaches convergence. A number of methods have been proposed for determining the optimal stopping point\u2010the point that provides the best trade\u2010off between restoring the image and amplifying the noise. Cross\u2010validation (CV) has recently been proposed as an advantageous method for determining the optimal stopping point. We propose a different form of CV based on generalized cross\u2010validation (GCV) that overcomes some of the difficulties of CV. We derive a GCV\u2010based criterion for the R\u2010L algorithm that can be efficiently evaluated at each iteration. We present examples displaying the power of the stopping rule and discuss the abilities and shortcomings of the method.<\/jats:p>","DOI":"10.1002\/ima.1850060412","type":"journal-article","created":{"date-parts":[[2007,3,5]],"date-time":"2007-03-05T23:30:50Z","timestamp":1173137450000},"page":"387-391","source":"Crossref","is-referenced-by-count":0,"title":["Generalized cross\u2010validation as a stopping rule for the Richardson\u2010Lucy algorithm"],"prefix":"10.1002","volume":"6","author":[{"given":"Stanley J.","family":"Reeves","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,10,20]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm (with discussion)","volume":"39","author":"Dempster A. P.","year":"1977","journal-title":"J. Royal Stat. Soc. 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J.SullivanandH.Chang \u201cA generalized Landweber iteration for ill\u2010conditioned signal restoration \u201d in Proceeding of the 1991 IEEE International Conference on Acoustics Speech and Signal Processing pp.1729\u20131732.","DOI":"10.1109\/ICASSP.1991.150647"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/83.148604"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/83.148606"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1080\/03610918908812806"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1109\/83.287028"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1080\/03610929008830285"}],"container-title":["International Journal of Imaging Systems and Technology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fima.1850060412","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/ima.1850060412","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,14]],"date-time":"2025-01-14T16:27:58Z","timestamp":1736872078000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/ima.1850060412"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,12]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1995,12]]}},"alternative-id":["10.1002\/ima.1850060412"],"URL":"https:\/\/doi.org\/10.1002\/ima.1850060412","archive":["Portico"],"relation":{},"ISSN":["0899-9457","1098-1098"],"issn-type":[{"type":"print","value":"0899-9457"},{"type":"electronic","value":"1098-1098"}],"subject":[],"published":{"date-parts":[[1995,12]]}}}