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A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission

E Levitan, G T Herman

IEEE Transactions on Medical Imaging

|January 1, 1987

Summary

This study extends expectation maximization for emission tomography image reconstruction. The new method uses a priori information to prevent noise artifacts, improving image quality over standard maximum likelihood methods.

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Area of Science:

Medical Imaging
Statistical Modeling
Computational Science

Background:

Maximum Likelihood (ML) image reconstruction in emission tomography relies on Poisson distribution assumptions.
Standard ML methods can produce noise artifacts like the 'checkerboard effect' with extensive iterations.

Purpose of the Study:

To extend the expectation maximization (EM) algorithm for maximum a posteriori (MAP) image reconstruction.
To incorporate a multivariate Gaussian prior to enhance image quality and stability.

Main Methods:

The study extends the EM algorithm for maximum likelihood (ML) to maximum a posteriori (MAP) reconstruction.
A multivariate Gaussian prior probability distribution is utilized for the image vector.
A specific penalty function, a weighted sum of squared deviations from prior means, is derived.

Main Results:

The MAP approach is equivalent to penalized ML estimation with a tailored penalty function.
The derived iterative formula effectively maximizes the a posteriori probability.
The method successfully suppresses noise artifacts and the checkerboard effect.

Conclusions:

The proposed MAP reconstruction method offers superior performance compared to pure ML.
Incorporating a priori information via a Gaussian prior significantly improves image reconstruction stability.
This technique is crucial for reducing artifacts in emission tomography.