The mutual information criterion for SPECT aperture evaluation and design

Area of Science:

• Medical Imaging
• Nuclear Medicine
• Information Theory

Background:

• Single-photon-emission computed tomography (SPECT) systems rely on aperture design to balance sensitivity and resolution.
• Optimizing aperture performance is crucial for accurate source estimation in SPECT.
• Existing performance criteria may not fully capture the trade-offs inherent in SPECT imaging.

Purpose of the Study:

• To propose a novel aperture performance criterion for SPECT based on mutual information (MI).
• To derive and evaluate MI-based optimal apertures for various SPECT geometries and source distributions.
• To assess the utility of MI as a metric for SPECT aperture optimization.

Main Methods:

• Developed a mutual information (MI) criterion quantifying the reduction in uncertainty of emitter location given detector data.
• Derived MI expressions for 1D linear and 2D parallel-slice ring geometries under specific assumptions (Poisson emissions, uniform angles, no scatter, known lost-count correction).
• Utilized an iterative maximization procedure to derive MI-optimal apertures and numerically calculated MI for SPRINT II system apertures.

Main Results:

• Established a necessary and sufficient condition for MI-maximizing apertures in 1D geometries.
• Derived MI-optimal apertures for different source distributions.
• Numerically calculated MI for various ring apertures of the SPRINT II system, providing quantitative performance insights.

Conclusions:

• Mutual information offers a robust criterion for SPECT aperture optimization, effectively balancing sensitivity and resolution.
• The derived MI-optimal apertures can lead to improved source estimation accuracy in SPECT.
• This information-theoretic approach provides a valuable framework for designing and evaluating SPECT imaging systems.