Vardi, maximum likelihood reconstruction in positron emission tomography, ieee transactions on medical imaging, vol. Maximum likelihood reconstruction in pet and tofpet. Pdf maximum likelihood algorithms for image reconstruction in. Shepp and yehuda vardi, journalieee transactions on medical imaging, year1982, volume1, pages1122 larry a. Read the texpoint manual before you delete this box aaaaaaaaaaaaa. Suppose each emission in box b is detected in detector unit d with probability pb, d, d 1, d with pb, d a onestep transition matrix, assumed known. The basic problem of image reconstruction in emission tomography et be. Pdf two proposed likelihood models for emission and transmission. Within two years of the initial publication of that emlem algorithm, the method had been extended to listmode acquisitions 16 and to dynamic studies 17. This chapter summarizes maximumlikelihood ml algorithms for. Maximum likelihood reconstruction for emission tomography l.
Abstractprevious models for emission tomography et do not dis. Abstracta new method of reconstruction from spect data is pro posed, which builds on the em approach to maximum likelihood re construction from emission. However, the algorithm is very suited to parallel and vector machines, and on these machine can be made economically feasible even on medically reasonable problems of 16000 variables. Previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography. Vardi, maximum likelihood reconstruction for emission tomography, ieee transactions on medical imaging, vol. Bayesian reconstructions from emission tomography data using a. Expectation maximization for emission tomography camptum. A maximumlikelihood reconstruction algorithm for tomographic.
We give a more accurate general mathematical model for etwhere an unknown emission density x xx, y,z generates, and is to be. We give a more accurate general mathematical model for et where an unknown emission density. Maximum likelihood ml, expectation maximization em pieter abbeel uc berkeley eecs many slides adapted from thrun, burgard and fox, probabilistic robotics texpoint fonts used in emf. Solving emission tomography problems on vector machines. Emission ml image reconstruction electrical engineering. Maximum likelihood reconstruction for emission tomography abstract. Maximum likelihood reconstruction for emission tomography. Maximum likelihood reconstruction in positron emission. Shepp and vardi s maximum likelihood reconstruction algorithm for emission tomography has mostly been ignored by the medical community because of its perceived high computational costs. The maximum likelihood approach in image reconstruc. Vardi abstractprevious models for emission tomography et donotdistinguish the physics ofetfrom that oftransmission tomography. Second, pet data were reconstructed using an intervalvalued extension of the maximum likelihood expectation maximization mlem algorithm shepp et vardi 1982.
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