Learning a Nonlinear Solver Optimized to Solve the Problem of Electron Density and Effective Atomic Number Reconstruction

Project Overview

For material identification, characterization, and quantification, it is useful to estimate system-independent material properties that do not depend on the detailed specifications of the X-ray computed tomography (CT) system such as spectral response. System independent rho-e and Z-e (SIRZ) refers to a suite of methods for estimating the system independent material properties of electron density (rho-e) and effective atomic number (Z-e) of an object scanned using dual-energy X-ray CT (DECT). The current state-of-the-art approach, SIRZ-2, makes certain approximations that lead to inaccurate estimates for large atomic numbered (Z-e) materials. We present an extension, SIRZ-3, which iteratively reconstructs the unknown rho-e and Z-e while avoiding the limiting approximations made by SIRZ-2. Unlike SIRZ-2, this allows SIRZ-3 to accurately reconstruct rho-e and Z-e even at large Z-e. SIRZ-3 relies on the use of a new non-linear differentiable forward measurement model that expresses the DECT measurement data as a direct analytical function of rho-e and Z-e. Leveraging this new forward model, we use an iterative optimization algorithm to reconstruct (or solve for) rho-e and Z-e directly from the DECT data. Compared to SIRZ-2, we show that the magnitude of performance improvement using SIRZ-3 increases with increasing values for Z-e. We also achieved promising preliminary results in correcting for model bias, such as due to errors in spectral response estimates, using calibration data and neural networks.

In the original proposal for this LDRD-FS, we proposed to solve SIRZ-3 using neural network solvers (NNS) that are pre-trained using simulated data and then fine-tuned using experimental data. For our chosen datasets, our research determined that neural network solvers (NNS) aren't necessary to solve SIRZ-3. Instead, we used the Limited Memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS) solver for SIRZ-3.

Mission Impact

Our project advances the mission critical areas of Explosive Characterization/Detection and Nuclear Threat Reduction by creating a new technology for non-destructive threat evaluation at border checkpoints using X-ray scanning. Importantly, even though our approach is demonstrated on an inverse problem relevant to national security, it is also directly applicable to solving a variety of non-linear inverse problems in fields such as healthcare, optics, etc. This project also advances the Lab's core competencies in High Performance Computing, Simulation, Data Science, and Non-Destructive Evaluation (NDE) by leveraging LC computing resources to solve complex high-dimensional non-linear inverse problems in NDE. This LDRD FS led to programmatic support for further research and development under the Livermore Explosive Detection Program (LEDP).

Publications, Presentations, and Patents

Mohan, K. A. et al., 2022. "Iterative Reconstruction of the Electron Density and Effective Atomic Number using a Non-Linear Forward Model." Proceedings of SPIE 12104, Anomaly Detection and Imaging with X-Rays (ADIX) VII, 1210403 (June 2022). https://doi.org/10.1117/12.2625136.