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EM reconstruction algorithms for emission and transmission tomography.
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1984
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Image ReconstructionEngineeringImage AnalysisSignal ReconstructionPhoton-counting Computed TomographyRadiologyHealth SciencesActual ReconstructionsReconstruction TechniqueMedical ImagingMaximum Likelihood ApproachInverse ProblemsMedical Image ComputingSignal ProcessingTransmission Image ReconstructionBiomedical ImagingImage RestorationTransmission TomographyTomography
The paper introduces two likelihood models for emission and transmission tomography that accurately incorporate Poisson photon‑counting noise and other physical features, and notes that reconstruction regions are partitioned into pixels with concentration or attenuation coefficients estimated via iterative EM algorithms. The study aims to discuss the general principles of EM algorithms and derive detailed algorithms for emission and transmission tomography. The authors employ a maximum‑likelihood framework, iteratively maximizing the likelihood of photon counts while specifying physical features such as source and detector geometries, to derive EM algorithms for emission and transmission tomography. The EM algorithms accurately incorporate a physical model, enforce non‑negativity constraints, provide an excellent reconstruction quality metric, and converge globally to a unique parameter vector. Actual reconstructions are deferred to a later time.
Two proposed likelihood models for emission and transmission image reconstruction accurately incorporate the Poisson nature of photon counting noise and a number of other relevant physical features. As in most algebraic schemes, the region to be reconstructed is divided into small pixels. For each pixel a concentration or attenuation coefficient must be estimated. In the maximum likelihood approach these parameters are estimated by maximizing the likelihood (probability of the observations). EM algorithms are iterative techniques for finding maximum likelihood estimates. In this paper we discuss the general principles behind all EM algorithms and derive in detail the specific algorithms for emission and transmission tomography. The virtues of the EM algorithms include (a) accurate incorporation of a good physical model, (b) automatic inclusion of non-negativity constraints on all parameters, (c) an excellent measure of the quality of a reconstruction, and (d) global convergence to a single vector of parameter estimates. We discuss the specification of necessary physical features such as source and detector geometries. Actual reconstructions are deferred to a later time.