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High-Resolution Cardiac Positron Emission Tomography/Computed Tomography for Small Animals

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Negative binomial maximum likelihood expectation maximization (NB-MLEM) algorithm for reconstruction of pre-corrected

Michele Scipioni¹, Maria Filomena Santarelli², Assuero Giorgetti³

¹Dipartimento di Ingegneria dell'Informazione, University of Pisa, Pisa, Italy; CNR Institute of Clinical Physiology, Via Moruzzi,1, 56124, Pisa, Italy.

Computers in Biology and Medicine

|October 19, 2019

Summary

A new Negative Binomial Maximum Likelihood Expectation-Maximization (NB-MLEM) algorithm improves Positron Emission Tomography (PET) image reconstruction. This method accurately handles over-dispersed data from pre-corrected counts, outperforming standard Poisson methods.

Keywords:

Image reconstruction Maximum likelihood expectation maximization Negative binomial PET Pre-corrected PET data

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Area of Science:

Medical Imaging
Nuclear Medicine
Statistical Modeling

Background:

Positron Emission Tomography (PET) image reconstruction typically relies on Maximum Likelihood (ML) iterative methods assuming Poisson-distributed data.
Pre-correction of raw PET data can introduce over-dispersion, violating the Poisson assumption and potentially reducing image accuracy.

Purpose of the Study:

To develop and evaluate a novel PET image reconstruction algorithm based on the Negative Binomial (NB) distribution.
To address the limitations of Poisson-based methods when dealing with over-dispersed PET data resulting from pre-correction.

Main Methods:

Mathematical derivation of the Negative Binomial Maximum Likelihood Expectation-Maximization (NB-MLEM) algorithm.
Comparative performance analysis using simulated PET data, comparing NB-MLEM against the conventional Poisson-based MLEM (P-MLEM).
Validation of the NB-MLEM algorithm on real phantom and human brain PET data.

Main Results:

The NB-MLEM algorithm generalizes the conventional P-MLEM, performing similarly for non-over-dispersed data.
For over-dispersed PET data, NB-MLEM incorporates a dispersion parameter, leading to more accurate image reconstruction compared to P-MLEM.
The NB-MLEM algorithm demonstrates superior performance in reconstructing PET images from pre-corrected data.

Conclusions:

A novel NB-MLEM approach for PET image reconstruction from pre-corrected data has been successfully developed.
The NB-MLEM algorithm effectively accounts for the over-dispersion inherent in pre-corrected PET data, outperforming methods that assume no over-dispersion.
This method offers improved accuracy for PET image reconstruction when the Poisson assumption is invalidated by data pre-processing.