Normalization of the task-dependent detective quantum efficiency of spectroscopic x-ray imaging detectors

TL;DR

This paper develops mathematical models and tabulated data for ideal spectroscopic x-ray detectors to normalize their performance metrics, enabling better evaluation of their efficiency in medical imaging tasks.

Contribution

It introduces a comprehensive framework for normalizing the detective quantum efficiency of spectroscopic x-ray detectors using ideal detector models and standardized spectra.

Findings

Derived analytic expressions for the noise power spectrum of ideal SXDs.

Tabulated NPS values for RQA spectra for various materials.

Identified a single matrix governing the noise power in detection and quantification tasks.

Abstract

Spectroscopic x-ray detectors (SXDs) are poised to play a substantial role in the next generation of medical x-ray imaging. Evaluating their performance in terms of the detective quantum efficiency (DQE) requires normalization of the frequency-dependent signal-to-noise ratio (SNR) by that of an ideal SXD. We provide mathematical expressions of the SNR of ideal SXDs for quantification and detection tasks and tabulate their numeric values for standardized tasks. We propose using standardized RQA-series x-ray spectra. We define ideal SXDs as those that (1) have an infinite number of infinitesimal energy bins, (2) do not distort the incident distribution of x-ray photons in the spatial or energy domains, and (3) do not decrease the frequency-dependent SNR of the incident distribution of x-ray quanta. We derive analytic expressions for the noise power spectrum (NPS) of such ideal detectors for detection and quantification tasks. We tabulate the NPS of ideal SXDs for RQA x-ray spectra for detection and quantification of aluminum, PMMA, iodine, and gadolinium basis materials. Our analysis shows that a single matrix determines the noise power of ideal SXDs in detection and quantification tasks, including basis material decomposition and line-integral estimation for pseudo-mono-energetic imaging. This NPS matrix is determined by the x-ray spectrum incident on the detector and the mass-attenuation coefficients of the set of basis materials. Combining existing tabulated values of the mass-attenuation coefficients of basis materials with standardized RQA x-ray spectra enabled tabulating numeric values of the NPS matrix for selected spectra and tasks. The numeric values and mathematical expressions of the NPS of ideal SXDs reported here can be used to normalize measurements of the frequency-dependent SNR of SXDs for experimental study of the task-dependent DQE.