PET Reconstruction With Non-Negativity Constraint in Projection Space: Optimization Through Hypo-Convergence

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dc.contributor.authorBousse, Alexandre
dc.contributor.authorCourdurier Bettancourt, Matías Alejandro
dc.contributor.authorÉmond, Élise
dc.contributor.authorThielemans, Kris
dc.contributor.authorHutton, Brian F.
dc.contributor.authorIrarrazaval Mena, Pablo
dc.contributor.authorVisvikis, Dimitris
dc.date.accessioned2022-05-18T14:04:53Z
dc.date.available2022-05-18T14:04:53Z
dc.date.issued2020
dc.description.abstractStandard positron emission tomography (PET) reconstruction techniques are based on maximum-likelihood (ML) optimization methods, such as the maximum-likelihood expectation-maximization (MLEM) algorithm and its variations. Most methodologies rely on a positivity constraint on the activity distribution image. Although this constraint is meaningful from a physical point of view, it can be a source of bias for low-count/high-background PET, which can compromise accurate quantification. Existing methods that allow for negative values in the estimated image usually utilize a modified log-likelihood, and therefore break the data statistics. In this paper, we propose to incorporate the positivity constraint on the projections only, by approximating the (penalized) log-likelihood function by an adequate sequence of objective functions that are easily maximized without constraint. This sequence is constructed such that there is hypo-convergence (a type of convergence that allows the convergence of the maximizers under some conditions) to the original log-likelihood, hence allowing us to achieve maximization with positivity constraint on the projections using simple settings. A complete proof of convergence under weak assumptions is given. We provide results of experiments on simulated data where we compare our methodology with the alternative direction method of multipliers (ADMM) method, showing that our algorithm converges to a maximizer, which stays in the desired feasibility set, with faster convergence than ADMM. We also show that this approach reduces the bias, as compared with MLEM images, in necrotic tumors-which are characterized by cold regions surrounded by hot structures-while reconstructing similar activity values in hot regions.
dc.fuente.origenIEEE
dc.identifier.doi10.1109/TMI.2019.2920109
dc.identifier.eissn1558-254X
dc.identifier.issn0278-0062
dc.identifier.urihttps://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8726392
dc.identifier.urihttps://doi.org/10.1109/TMI.2019.2920109
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/64129
dc.information.autorucFacultad de matemáticas ; Courdurier Bettancourt, Matías Alejandro ; S/I ; 1007892
dc.information.autorucEscuela de ingeniería ; Irarrazaval Mena, Pablo ; S/I ; 57376
dc.issue.numero1
dc.language.isoen
dc.nota.accesoContenido parcial
dc.pagina.final86
dc.pagina.inicio75
dc.publisherIEEE
dc.revistaIEEE Transactions on Medical Imaginges_ES
dc.rightsacceso restringido
dc.subjectImage reconstruction
dc.subjectMaximum likelihood estimation
dc.subjectPositron emission tomography
dc.subjectConvergence
dc.subjectLinear programming
dc.subjectOptimization
dc.subjectPhase locked loops
dc.subject.ddc619
dc.subject.deweyMedicina y saludes_ES
dc.subject.otherTomografía computarizada de emisiónes_ES
dc.subject.otherTumoreses_ES
dc.titlePET Reconstruction With Non-Negativity Constraint in Projection Space: Optimization Through Hypo-Convergencees_ES
dc.typeartículo
dc.volumen39
sipa.codpersvinculados1007892
sipa.codpersvinculados57376
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