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A Basic Positron Emission Tomography System Constructed to Locate a Radioactive Source in a Bi-dimensional Space

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On the relation between the ISRA and the EM algorithm for positron emission tomography.

A R De Pierro¹

¹Inst. de Matematica Estatistica, e Ciencia da Computacao, Univ. Estadual de Campinas, Sao Paulo.

IEEE Transactions on Medical Imaging

|January 1, 1993

Summary

The image space reconstruction algorithm (ISRA) offers a least squares solution for emission computed tomography, differing from the expectation maximization (EM) algorithm. This modification allows for extensions to penalized likelihood estimates in imaging reconstruction.

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Area of Science:

Medical Imaging
Computerized Tomography
Image Reconstruction Algorithms

Background:

The expectation maximization (EM) algorithm is a standard for image reconstruction in emission computed tomography.
Physical considerations are crucial for refining reconstruction algorithms in medical imaging.

Purpose of the Study:

To introduce the image space reconstruction algorithm (ISRA) as a modification of the EM algorithm.
To adapt ISRA for penalized likelihood estimates in emission computed tomography.

Main Methods:

Developed ISRA based on physical principles, modifying the EM algorithm.
Established a common mathematical framework for both ISRA and EM algorithms.
Extended ISRA to incorporate penalized likelihood estimation.

Main Results:

ISRA converges to least squares solutions, unlike the EM algorithm's focus on Poisson likelihoods.
Demonstrated that ISRA and EM algorithms share a unifying mathematical foundation.
Successfully extended ISRA for penalized likelihood estimates, enhancing its applicability.

Conclusions:

ISRA provides a valuable alternative to the EM algorithm for emission computed tomography reconstruction.
The shared mathematical framework facilitates algorithm development and extension.
Penalized likelihood estimation in ISRA offers improved image reconstruction capabilities.