Surrogate distributed radiological sources III: quantitative distributed source reconstructions

In this third part of a multi-paper series, we present quantitative image reconstruction results from aerial measurements of eight different surrogate distributed gamma-ray sources on flat terrain. We show that our quantitative imaging methods can accurately reconstruct the expected shapes, and, after appropriate calibration, the absolute activity of the distributed sources. We conduct several studies of imaging performance versus various measurement and reconstruction parameters, including detector altitude and raster pass spacing, data and modeling fidelity, and regularization type and strength. The imaging quality performance is quantified using various quantitative image quality metrics. Our results confirm the utility of point source arrays as surrogates for truly distributed radiological sources, and advance the quantitative capabilities of Scene Data Fusion gamma-ray imaging methods.

💡 Research Summary

This paper presents a comprehensive evaluation of quantitative gamma‑ray imaging for distributed radiological sources using aerial measurements from unmanned aerial systems (UAS). Building on the first two parts of a series, the authors constructed eight surrogate distributed Cu‑64 source patterns by arranging up to 100 point sources on a 4 m grid to emulate continuous distributions. Measurements were performed in August 2021 at Washington State University using two omnidirectional gamma‑ray imagers, NG‑LAMP and MiniPRISM, which recorded singles events in the 511 keV annihilation line. Each detector was equipped with lidar and an inertial measurement unit, enabling simultaneous localization and mapping (SLAM) to generate high‑resolution 3‑D point clouds of the flight trajectories and ground surface.

The point‑cloud data were meticulously co‑registered to the design coordinate system using a combination of manual least‑squares alignment of a reference square source and iterative closest‑point (ICP) registration for the remaining flights. The resulting alignment error in the horizontal plane averaged 6.2 cm, confirming sub‑decimeter fidelity between the physical source layout and the digital model.

For image reconstruction the authors adopted a linear forward model λ = V w, where w denotes the unknown activity at each voxel, V encodes geometric attenuation, air attenuation, detector effective area, and dwell time, and λ are the expected counts. Poisson statistics were used to formulate a negative log‑likelihood, which was minimized either by maximum‑likelihood expectation‑maximization (ML‑EM) or by a regularized maximum‑a‑posteriori EM (MAP‑EM). Two regularizers were investigated: a sparsity‑promoting L1/2 prior and a total‑variation (TV) prior that preserves edges while smoothing noise. The regularization strength β was swept from 10⁻³ to 10⁻¹, and reconstructions were performed with 30 EM iterations on a GPU‑accelerated implementation (mfdf package with PyOpenCL), completing a 125 m × 80 m scene at 1 m resolution in roughly two seconds.

Performance was quantified with three metrics: (1) the total activity ratio R_tot (reconstructed/true total activity), (2) the normalized root‑mean‑square error (NRMSE) of pixel intensities, and (3) the structure coefficient s (essentially Pearson correlation) computed over the region containing sources. Ground‑truth images were generated by interpolating the designed point‑source arrays to a continuous 1‑m grid.

Results show that under nominal conditions (6 m altitude, 5.2 m raster spacing, β = 10⁻³ L1/2 regularization) the reconstructions accurately reproduced source shapes and, after applying a global calibration factor (≈1.4× to account for source activity uncertainty), yielded R_tot values between 0.90 and 0.96, NRMSE between 0.07 and 0.21, and s between 0.85 and 0.96. Systematic trends were observed: interior regions tended to be slightly over‑estimated, while edges and corners were under‑estimated, leading to rounded boundaries rather than sharp 1‑m transitions. Increasing the separation between high‑activity and zero‑activity zones (e.g., from 8 m to 12 m) improved edge definition, confirming the influence of spatial sampling on resolution.

Parameter sweeps demonstrated that higher flight altitudes or larger raster spacings degraded spatial resolution and activity accuracy, but appropriate adjustment of β could partially recover performance. The TV regularizer excelled at preserving edge sharpness, whereas the L1/2 prior was more effective for sparse source configurations by suppressing background noise.

In conclusion, the study validates that point‑source arrays are effective surrogates for truly distributed radiological sources and that the presented quantitative reconstruction pipeline can deliver reliable absolute activity estimates and detailed spatial maps. The work advances the practical utility of Scene Data Fusion for radiological emergency response, offering a pathway to assess regulatory compliance and to guide dose‑minimization strategies based on aerial gamma‑ray data. Future directions include extending the methodology to multi‑isotope scenarios, irregular terrain, and real‑time adaptive regularization to further enhance field applicability.