Bardsley, Johnathan M.; Goldes, John Techniques for regularization parameter and hyper-parameter selection in PET and SPECT imaging. (English) Zbl 1217.62092 Inverse Probl. Sci. Eng. 19, No. 2, 267-280 (2011). Summary: Penalized maximum likelihood methods are commonly used in positron emission tomography (PET) and single photon emission computed tomography (SPECT). Due to the fact that a Poisson data-noise model is typically assumed, standard regularization parameter choice methods, such as the discrepancy principle or generalized cross validation, cannot be directly applied. In recent work of the authors [see SIAM J. Sci. Comput. 32, No. 1, 171–185 (2010; Zbl 1215.65116); ibid. 25, No. 4, 1326–1343 (2003; Zbl 1061.65047)] , regularization parameter choice methods for penalized negative-log Poisson likelihood problems are introduced. We apply these methods to the applications of PET and SPECT, introducing a modification that improves the performance of the methods. We then demonstrate how these techniques can be used to choose the hyper-parameters in a Bayesian hierarchical regularization approach. Cited in 4 Documents MSC: 62H35 Image analysis in multivariate analysis 92C55 Biomedical imaging and signal processing 65J22 Numerical solution to inverse problems in abstract spaces 65K10 Numerical optimization and variational techniques Keywords:positron emission tomography; single photon emission computed tomography; regularization parameter selection; Bayesian statistical methods; Poisson noise Citations:Zbl 1215.65116; Zbl 1061.65047 PDFBibTeX XMLCite \textit{J. M. Bardsley} and \textit{J. Goldes}, Inverse Probl. Sci. Eng. 19, No. 2, 267--280 (2011; Zbl 1217.62092) Full Text: DOI References: [1] DOI: 10.1109/42.52985 [2] Lange K, J. Comput. Assist. Tomogr. 8 pp 306– (1984) [3] DOI: 10.1109/TMI.1982.4307558 [4] DOI: 10.1109/TMI.2003.812251 [5] DOI: 10.1109/83.465106 [6] DOI: 10.1109/78.324732 [7] DOI: 10.1109/42.476108 [8] DOI: 10.1109/42.363099 [9] DOI: 10.1109/42.993134 [10] DOI: 10.1109/42.24868 [11] DOI: 10.1137/S1064827502410451 · Zbl 1061.65047 [12] DOI: 10.1137/1.9780898719284 · Zbl 0973.92020 [13] DOI: 10.1137/1.9780898718324 · Zbl 0974.92016 [14] Tikhonov AN, Numerical Methods for the Solution of Ill-Posed Problems (1990) [15] DOI: 10.1137/1.9780898717570 · Zbl 1008.65103 [16] DOI: 10.3934/ipi.2010.4.11 · Zbl 1189.65105 [17] DOI: 10.1080/17415970701404235 · Zbl 1258.35206 [18] DOI: 10.1080/17415970802231594 · Zbl 1167.65074 [19] DOI: 10.1007/s10444-008-9081-8 · Zbl 1171.94001 [20] Tikhonov AN, Nonlinear Ill-posed Problems 1 (1998) [21] DOI: 10.1080/10682760290031195 [22] Leonov AS, Moscow Univ. Physics Bull. 50 pp 25– (1984) [23] DOI: 10.1137/0714044 · Zbl 0402.65032 [24] DOI: 10.1088/0266-5611/25/2/025002 · Zbl 1163.65019 [25] DOI: 10.2307/1390722 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.