Angular Sampling Completeness Index (ASCI) for Self-Collimating SPECT System Design

Read the abstract in Journal of Nuclear Medicine

Self-collimation (SC) in single-photon emission tomography introduces a new imaging paradigm: detector panels arranged in a multi-layer MATRICS configuration allow the front detector layer to simultaneously serve as a collimator for the layer behind it. Unlike traditional mechanical collimation, this architecture breaks the inherent trade-off between spatial resolution and detection sensitivity, opening opportunities for jointly improving both. However, the resulting projection probability density functions (PPDFs) are spatially non-uniform and multiplexed, making existing sampling models—designed for uniform PPDFs—insufficient for SC-SPET evaluation.

To address this gap, we developed an angular sampling completeness index (ASCI) that quantifies how well a system samples the image space while explicitly considering spatial-resolution variability. This metric supports SC-SPET system analysis, design iteration, and optimization by linking sampling completeness to achievable image resolution.

Imaging Geometry & System Configuration

Our research studies a 2-D SC-SPET architecture featuring a hexagonal gantry with six MATRICS detector panels.
Each panel contains four detector blocks positioned tangentially, and each block comprises an 8×8 array of detector elements. Elements are either filled with GAGG(Ce) scintillators or intentionally left vacant, creating controlled detection–collimation configurations.

This design produces non-uniform PPDFs with variable strip width and multiplexing, requiring a metric that captures sampling density as a function of spatial resolution.

Methodology

We compute PPDFs analytically through ray tracing and evaluate system sampling using ASCI, defined as the percentage of angular bins intersected by PPDF strips at a given pixel position over 360°.
The process measures how effectively an imaging point is sampled directionally.

We further analyze the relationship between strip width (FWHM) and sampling completeness, as strip width serves as a spatial sampling index tied to achievable resolution.

Two operational modes were evaluated:

1. Stationary gantry
2. Rotating gantry (24 steps at 2.5° per step)

For both, we generate ASCI maps under varying PPDF widths and compare reconstruction outcomes using parallelized expectation-maximization on a Linux cluster.

Framework Overview

Key Findings

• ASCI magnitude and uniformity increase with gantry rotation, enhancing sampling completeness and reconstruction quality.
• Strip width (FWHM) influences ASCI distribution and correlates with achieved image resolution.
• The relationship between ASCI and reconstruction demonstrates predictive utility for system performance modeling.
• Combined, ASCI + PPDF width provide complementary metrics for evaluating and optimizing SC-SPET designs.

Practical Implications

• Enables sampling-aware system design, guiding detector placement and rotation strategies.
• Supports data-efficient evaluation, reducing simulation and prototyping overhead.
• Offers a unified metric bridging geometry, resolution behavior, and reconstruction outcomes.

Conclusion

This work introduces ASCI as a resolution-dependent sampling completeness metric for SC-SPET systems.
By integrating spatial sampling characteristics with angular coverage assessment, ASCI enables quantitative comparisons across design configurations and operational modes. When analyzed alongside PPDF strip width, ASCI provides a principled way to predict reconstruction quality and guide SC-SPET optimization.