EM ALGORITHM IN TOMOGRAPHY : A REVIEW AND A BIBLIOGRAPHY

In many medical imaging problems such as Positron Emission Tomography (PET), Single Photon Emission Computed Tomography (SPECT) and Transmission Computed Tomography, a lot of projection data for different observation aspects on an object are obtained, allowing reconstruction of the three-dimensional structure of the object from its one and two-dimensional projections. This is basically a problem of analysing incomplete data. Conventional methods such as filtered backprojection (FBP) and Fourier-based methods are deterministic and ignore the statistical elements of the data. Maximum likelihood methods based on suitable statistical models have been found to be satisfactory alternatives to these deterministic methods. The Expectation-Maximisation (EM) algorithm synthesised and presented in a generic form by Dempster, Laird and Rubin in 1977, is an effective iterative method of computing maximum likelihood estimates in a variety of situations, especially in incomplete data problems, where Newton-Raphson types of algorithms are far too cumbersome. In this paper, we review applications of the EM algorithm in tomography and present a bibliography of EM algorithm in tomography.