Projection Angular Sampling Completeness & Probability Density Sensitivity in Self-Collimation SPECT

Self-collimation (SC) is an emerging SPECT architecture in which multi-layer detector arrays serve as both detectors and intrinsic collimators, bypassing the traditional trade-off between spatial resolution and sensitivity imposed by mechanical collimation. This work evaluates Angular Sampling Completeness (ASCI) and Projection Probability Density Function (PPDF) sensitivity as quantitative metrics that characterize the sampling capability and performance of SC-SPECT system designs.

Unlike conventional SPECT, SC configurations generate spatially varying and multiplexed PPDFs, meaning classical sampling or resolution models are insufficient. By analyzing sampling completeness and PPDF-based sensitivity across system configurations, we connect detector layout and operation mode to imaging performance.

System Overview

We evaluate SC-SPECT systems constructed from hexagonal MATRICS detector arrangements, where each panel contains multiple scintillator-filled detector layers.
This architecture naturally introduces multiple projection paths per voxel, enabling improved sampling density without mechanical collimators.

PPDFs are computed analytically via ray tracing, reflecting realistic spatial resolution characteristics of each detector element.
From these PPDFs, we derive ASCI maps to quantify angular coverage at each location in the image space and PPDF-based sensitivity maps to assess detector efficiency.

Methods

Our evaluation framework compares three geometrical SC-SPECT configurations, each differing in detector aperture shape and element spacing.
For each configuration, we compute:

• Projection Probability Density Functions (PPDFs) to model spatial response profiles across the image space
• PPDF-derived strip widths (FWHM) to characterize spatial-resolution behavior
• Angular Sampling Completeness Index (ASCI) to measure directional sampling coverage per pixel
• PPDF Sensitivity to quantify photon detection likelihood
• Reconstructed images from a compressed practical phantom

ASCI and PPDF metrics are assessed under both stationary and rotating gantry operation schemes to study the effect of acquisition motion on sampling quality and reconstruction performance.

Framework Overview

Key Findings

• Rotational SC-SPECT designs produce higher and more uniform ASCI values than stationary configurations
• Increased ASCI correlates with improved reconstruction resolution and artifact suppression
• PPDF-FWHM values modulate effective sampling density and influence regions of weak resolution
• PPDF sensitivity maps provide complementary insight into photon detection efficiency and should be considered jointly with ASCI
• Combined, ASCI and PPDF-FWHM offer a principled basis for predicting SC-SPECT performance prior to full reconstruction

Practical Insights

• Sampling completeness and resolution characteristics depend on detector shape, aperture configuration, and acquisition motion
• Multiplexing effects inherent to SC designs can be leveraged when evaluated with sampling-aware metrics
• ASCI and PPDF-based sensitivity enable data-efficient design iteration without exhaustive simulation

Conclusion

ASCI and PPDF-based metrics demonstrate strong potential as quantitative tools for characterizing and optimizing Self-Collimation SPECT designs.
By linking angular sampling quality and spatial resolution behavior to reconstructed imaging outcomes, these metrics support informed SC-SPECT system development and predictive design assessment.

Acknowledgements

This research is supported by the National Institutes of Biomedical Imaging and Bioengineering (NIBIB) and the National Institute of Health under Grant R21EB032293. Computational work utilized the UB high-performance computing platform.