Cited by 4,429Medical Imaging Techniques and ApplicationsNumerical methods in inverse problemsImage and Signal Denoising Methods

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Maximum Likelihood Reconstruction for Emission Tomography

Shepp, L. A., Vardi, Y.·1982·IEEE Transactions on Medical Imaging

DOI 10.1109/tmi.1982.4307558

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Abstract

Previous models for emission tomography (ET) do not distinguish the physics of ET from that of transmission tomography. We give a more accurate general mathematical model for ET where an unknown emission density lambda = lambda(x, y, z) generates, and is to be reconstructed from, the number of counts n(*)(d) in each of D detector units d. Within the model, we give an algorithm for determining an estimate lambdainsertion mark of lambda which maximizes the probability p(n(*)|lambda) of observing the actual detector count data n(*) over all possible densities lambda. Let independent Poisson variables n(b) with unknown means lambda(b), b = 1, ..., B represent the number of unobserved emissions in each of B boxes (pixels) partitioning an object containing an emitter. Suppose each emission in box b is detected in detector unit d with probability p(b, d), d = 1, ..., D with p(b,d) a one-step transition matrix, assumed known. We observe the total number n(*) = n(*)(d) of emissions in each detector unit d and want to estimate the unknown lambda = lambda(b), b = 1, ..., B. For each lambda, the observed data n(*) has probability or likelihood p(n(*)|lambda). The EM algorithm of mathematical statistics starts with an initial estimate lambda(0) and gives the following simple iterative procedure for obtaining a new estimate lambdainsertion mark(new), from an old estimate lambdainsertion mark(old), to obtain lambdainsertion mark(k), k = 1, 2, ..., lambdainsertion mark(new)(b)= lambdainsertion mark(old)(b)Sum of (n(*)p(b,d) from d=1 to D/Sum of lambdainsertion mark()old(b('))p(b('),d) from b(')=1 to B), b=1,...B.

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Authors: Shepp, L. A., & Vardi, Y.
Affiliations: AT&T (United States) (US)
Venue: IEEE Transactions on Medical Imaging
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Published: 1982-10
Volume: 1
Issue: 2
Pages: 113-122
ISSN: 0278-0062 (ISSN-L)
1558-254X
DOI: 10.1109/tmi.1982.4307558
OpenAlex: W2069629287
Cited by: 4,429
References: 9
Citations by year: 2026: 74 · 2025: 101 · 2024: 122 · 2023: 101 · 2022: 117 · 2021: 140 · 2020: 154 · 2019: 153 · 2018: 137 · 2017: 142 · 2016: 152 · 2015: 164 · 2014: 167 · 2013: 182 · 2012: 176
FWCI: 10.00
Type: journal article
Language: en
Open access: closed
Licence: ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)
Locations: IEEE Transactions on Medical Imaging (publishedVersion)
PubMed (publishedVersion)
Topics: Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Medical Imaging Techniques and Applications
Physical Sciences › Mathematics › Mathematical Physics › Numerical methods in inverse problems
Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
Keywords: emission tomography, maximum likelihood reconstruction, expectation-maximization algorithm, Poisson likelihood, tomographic reconstruction

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Maximum Likelihood Reconstruction for Emission Tomography

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