Task-Based Information-Theoretic Design of X-Ray Computed Tomography Systems: Detection and Estimation Tasks

Abstract

X-ray Computed Tomography (CT) is an established imaging and anomaly detection modality that is employed widely across multiple applications such as medical imaging, security screening and non-destructive testing. In security screening applications, traditional X-ray threat detection systems employ image reconstruction and segmentation as pre-processing steps before making threat/non-threat decision. In this work, we consider image reconstruction and threat detection as separate tasks. For the threat detection task, we consider detection directly on the raw CT sinogram data without any post-measurement data processing steps like image reconstruction and segmentation. We also explore methods that improve the X-ray CT threat detection and image reconstruction performance using non-traditional measurement designs. In the first part of this work, we consider multiplexed measurement design by optimizing a metric on the threat detection error rate (Bhattacharyya Bound), given a fixed photon budget. We also consider an adaptive measurement design for X-ray threat detection, where the next measurement design is based on the information retrieved from previous measurements. We observe that while multiplexed and conventional systems have comparable threat detection performance, the adaptive system outperforms both systems in terms of detection error rate. We also study the effect of material variation on the threat detection performance of X-ray CT systems. Traditionally, X-ray measurements are modeled by Poisson distribution (shot-noise) based on a fixed photon-absorption model. The fixed photon absorption model ignores the inherent material variations due to environmental and manufacturing factors that are encountered in applications. Here we incorporate material variability in the X-ray measurement by employing a Negative Binomial (NB) distribution. Based on this measurement model, we derive an information-theoretic metric (Cauchy-Schwarz Mutual Information) as a measure of threat detection performance. We observe that material variation in high Signal to Noise Ratio (SNR) region becomes a limiting factor for threat detection performance of X-ray systems. However, in low SNR region the measurement is dominated by shot-noise and the effect of material variation on threat detection performance is negligible. In the second part of this work, we consider multiplexed measurement design for the image reconstruction task using the Bayesian Cramer-Rao Lower Bound (BCRLB) on Mean Squared Error (MSE) metric subject to a fixed photon budget. We observed that the multiplexed system with 5 exposures outperforms the conventional system in terms of MSE.