Code from the article "3D Activity Reconstruction from Angular Gamma Scanning via Variational Bayes: a proof of concept"

Abstract

This study serves as a proof of concept for a Bayesian variational framework enabling high-resolution 3D activity reconstruction in 220 L waste drums using Angular Segmented Gamma Scanning (ASGS) data and transmission-derived attenuation maps.

Our proposed inference and uncertainty quantification approach is demonstrated using virtual experiments that simulate typical waste characterization scenarios. Computations are made tractable by using stochastic variational inference (SVI) together with a multi-resolution spatial prior to infer the spatial activity distribution.

Results show that the approach can recover the spatial activity distribution within the considered drum, while also providing more accurate total activity estimates than conventional methods, thereby enhancing the accuracy of waste characterization.

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Code Overview

This repository provides the implementation used to generate the results in the paper.
It leverages NumPyro (probabilistic programming on JAX) to perform Bayesian inference on simulated waste drums.

Main features:

• Virtual synthetic drum datasets (Cs-137, Eu-152 and Co-60) available for testing.
• Variational inference (SVI) with an AutoNormal guide.
• Posterior predictive checks and other diagnostic tools included in the flow.
• 2D and (optional) 3D visualization of reconstructed activity distributions.

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Installation

Dependencies (Python 3.10+):

pip install jax jaxlib numpyro matplotlib seaborn pandas scipy SimpleITK

Synthetic Data

The synthetic drum cases (.pkl files) are not included in this repository because of their size.

They can be downloaded from Zenodo:
https://zenodo.org/records/16736172

After downloading, place the files inside:

test/synthetic_cases/voxel_size_1.92/

The folder structure should look like:

test/
└── synthetic_cases/
└── voxel_size_1.92/
├── Cs137_1_1.pkl
├── Cs137_1_2.pkl
├── Eu152_1_2.pkl
└── ...

##Usage

1. Select a case Inside solver_svi_cartesian_HTP.py,

mockup_case = "Cs137_1_2"
isotope = "Cs137"
truth = "point"   # ground truth morphology: "point", "rod", or "homogeneous"

Note: Remember to adjust the parameters of the Beta distribution according to the drum nature:

• Homogeneous drum: α = β = 10
• Hotspot drum: α = 0.1, β > 20

2. Run Inference

python solver_svi_cartesian_HTP.py

3. Outputs

The script will produce outputs in the results/ folder:

• ELBO convergence plot (elbo_values.csv, elbo_plot.svg)
• Posterior predictive checks (post_pred_check_plot.svg)
• Recovered activity histograms (svi_hist_recovered_activity.svg)
• 2D activity heatmaps (heatmap_XZ.svg, heatmap_XY.svg)
• SVI Samples are stored in (f'samples_{mockup_case}.npy')
• (Optional) 3D reconstructed volumes (.mhd, via SimpleITK)

Synthetic Drum Cases

Name	Activity (GBq)	RI	Source Morphology	Matrix	Materials
Cs137_1_1	3	Cs137	Homogeneously distributed	Homogeneous	Sand (1.52 g/cc)
Cs137_1_2	3	Cs137	Voxel @ [23,34,23], voxel_size = 1.92	Homogeneous	Sand (1.52 g/cc)
Cs137_1_4	3	Cs137	Rod: R=1 cm, Rot[38,10,0]°, Pos[-4.0,3.0,-5.0], L=19 cm	Homogeneous	Sand (1.52 g/cc)
Cs137_1_4_2	5	Cs137	Voxel @ [20,34,9], voxel_size = 1.92	Homogeneous	Sand (1.52 g/cc)
EuCo_1_4	9	Co60	Rod: R=1 cm, Rot[38,10,0]°, Pos[-4.0,3.0,-5.0], L=19 cm	Homogeneous	Sand (1.52 g/cc)
	5	Eu152	Voxel @ [20,34,9], voxel_size = 1.92
Eu152_1_1	5	Eu152	Homogeneously distributed	Homogeneous	Sand (1.52 g/cc)
Eu152_1_2	3	Eu152	Voxel @ [23,34,23], voxel_size = 1.92	Homogeneous	Sand (1.52 g/cc)
Eu152_1_4	9	Eu152	Rod: R=1 cm, Rot[38,10,0]°, Pos[-4.0,3.0,-5.0], L=19 cm	Homogeneous	Sand (1.52 g/cc)