[Paper Review] Improved Gamma-Ray Point Source Quantification in Three Dimensions by Modeling Attenuation in the Scene

Mark S. Bandstra, Daniel Hellfeld+9 more|arXiv (Cornell University)|Nov 1, 2021

Medical Imaging Techniques and Applications40 references16 citations

TL;DR

This paper presents a 3D point source localization and quantification method for gamma-ray sources that models attenuation through intervening materials using LiDAR-derived voxelized scene geometry. By combining maximum likelihood estimation with ray-casting to compute path-length-dependent attenuation, the method jointly estimates source position, activity, and attenuation coefficient, demonstrating accurate reconstruction of source parameters in real-world measurements with complex shielding.

ABSTRACT

Using a series of detector measurements taken at different locations to localize a source of radiation is a well-studied problem. The source of radiation is sometimes constrained to a single point-like source, in which case the location of the point source can be found using techniques such as maximum likelihood. Recent advancements have shown the ability to locate point sources in 2-D and even 3-D but few have studied the effect of intervening material on the problem. In this work, we examine gamma-ray data taken from a freely moving system and develop voxelized 3-D models of the scene using data from its onboard light detection and ranging (LiDAR) unit. Ray casting is used to compute the distance each gamma ray travels through the scene material, which is then used to calculate attenuation assuming a single attenuation coefficient for solids within the geometry. Parameter estimation using maximum likelihood is performed to simultaneously find the attenuation coefficient, source activity, and source position that best match the data. Using a simulation, we validate the ability of this method to reconstruct the true location and activity of a source, along with the true attenuation coefficient of the structure it is inside, and then we apply the method to measured data with sources and find good agreement.

Motivation & Objective

• To address the challenge of inaccurate source quantification and localization in 3D environments due to unmodeled attenuation by intervening materials.
• To develop a method that simultaneously estimates source position, activity, and attenuation coefficient in a 3D scene using freely moving detector data.
• To validate the method’s ability to recover true source parameters and attenuation properties using both simulated and measured data.
• To demonstrate the feasibility of incorporating scene attenuation into point source likelihood (PSL) framework for mobile radiation detection systems.

Proposed method

• The method uses a voxelized 3D scene model generated from onboard LiDAR point cloud data to represent solid materials in the environment.
• Ray casting is performed from each detector position to the candidate source location to compute the total path length through solid materials in the scene.
• Attenuation is modeled using a single, uniform attenuation coefficient (mean free path, λsolid) for all solids, applied along the ray paths to compute expected gamma-ray count rates.
• Maximum likelihood estimation is used to jointly optimize over source position, source activity, and λsolid to best match measured detector counts.
• The optimization is performed on a discrete grid of candidate source positions, with uncertainty quantified via 2σ confidence intervals.
• The method is validated using simulated data and applied to real measurements of 137Cs and 133Ba sources inside steel shipping containers.

Experimental results

Research questions

• RQ1 Can joint estimation of source position, activity, and attenuation coefficient improve 3D gamma-ray source localization accuracy in complex scenes?
• RQ2 How well does the method recover true source parameters when attenuation by intervening materials is present?
• RQ3 To what extent does the LiDAR-derived 3D scene model enable accurate attenuation modeling in the absence of direct material characterization?
• RQ4 What are the limitations of the method when the actual attenuating material is not fully represented by surface geometry alone?

Key findings

• The method successfully reconstructed the true source position and activity for both 137Cs and 133Ba sources in measured data, with results agreeing well with ground truth.
• For the 137Cs source, the best-fit attenuation mean free path (λsolid) was 2.58 m, consistent with the expected value when accounting for voxel size and effective wall thickness (ratio λsolid/∆ ≈ 5.9, within 2σ interval 4.5–9.8).
• For the 133Ba source, the best-fit λsolid/∆ ratio was 9.2–58.7, which excluded the tabulated value but was explained by additional internal materials and thicker attenuating volumes spanning multiple voxels.
• The method performed well when attenuation was dominated by surfaces (e.g., container walls), but performance degraded when internal bulk materials contributed significantly to attenuation and were not resolved by LiDAR.
• Processing time was high (100–210 minutes on a single CPU), but the authors note that GPU acceleration and improved optimization could enable near real-time operation.
• The study highlights the need for additional contextual data (e.g., material classification, segmentation) to model unobserved internal volumes and improve robustness.