Optimal frequency-based weighting for spectral x-ray projection imaging

An experimental framework for assessing the detective quantum efficiency of spectroscopic x-ray detectors

BACKGROUND

Assessing the performance of spectroscopic x-ray detectors (SXDs) requires measurement of the frequency-dependent detective quantum efficiency (DQE). Analytical expressions of the task-based DQE and task-independent DQE of SXDs have been presented in the literature, but standardizable experimental methods for measuring them have not. The task-based DQE quantifies the efficiency with which an SXD uses the x-ray quanta incident upon it to either quantify or detect a basis material (e.g., soft tissue or bone) of interest. The task-independent DQE is akin to the conventional DQE in that it is independent of the basis material to be detected or quantified.

PURPOSE

The purpose of this paper is to develop an experimental framework to present a method for experimental analysis of the DQE of SXDs, including the task-based DQE and task-independent DQE.

METHODS

We develop methods to measure the frequency-dependent DQE for task of quantifying or detecting a perturbation in a known basis material. We also develop methods for measuring a task-independent DQE. We show that the task-based DQEs and the task-independent DQE can be measured using a modest extension of the methods prescribed by International Electrotechnical Commission (IEC). Specifically, measuring the task-independent DQE requires measuring the modulation transfer function (MTF) and noise power spectrum (NPS) of each energy-bin image, in addition to the cross NPS between energy-bin images. Measuring the task-based DQEs requires an additional measurement of the transmission fraction through a thin basis-material absorber. We implemented the developed methods using standardized IEC x-ray spectra, aluminum (Al) and polymethyl methacrylyte (PMMA) basis materials, and a cadmium telluride (CdTe) SXD equipped with two energy bins and analog charge summing (ACS) for charge-sharing suppression. We also performed a regression analysis to determine whether or not the task-independent DQE is predictive of the task-based DQEs.

RESULTS

Experimental results of the task-based DQEs were consistent with simulation results presented in the literature. In general, and as expected, ACS increased the task-based DQEs and task-independent DQE. This effect was most pronounced for quantification tasks, in some instances yielding a five-fold increase in the DQE. For both spectra, with and without ACS for charge sharing correction, the task-based DQEs were linearly related to the task-independent DQE, as demonstrated by R² -values ranging from 0.89 to 1.00.

CONCLUSIONS

We have extended experimental DQE analysis to SXDs that count photons in multiple energy bins in a single x-ray exposure. The developed framework is an extension of existing IEC methods, and provides a standardized approach to assessing the performance of SXDs.

A detective quantum efficiency for spectroscopic X-ray imaging detectors

PURPOSE

Spectroscopic X-ray detectors (SXDs) are under development for X-ray imaging applications. Recent efforts to extend the detective quantum efficiency (DQE) to SXDs impose a barrier to experimentation and/or do not provide a task-independent measure of detector performance. The purpose of this article is to define a task-independent DQE for SXDs that can be measured using a modest extension of established DQE-metrology methods.

METHODS

We defined a task-independent spectroscopic DQE and performed a simulation study to determine the relationship between the zero-frequency DQE and the ideal-observer signal-to-noise ratio (SNR) of low-frequency soft-tissue, bone, iodine, and gadolinium signals. In our simulations, we used calibrated models of the spatioenergetic response of cadmium telluride (CdTe) and cadmium-zinc-telluride (CdZnTe) SXDs. We also measured the zero-frequency DQE of a CdTe detector with two energy bins and of a CdZnTe detector with up to six energy bins for an RQA9 spectrum and compared with model predictions.

RESULTS

The spectroscopic DQE accounts for spectral distortions, energy-bin-dependent spatial resolution, interbin spatial noise correlations, and intrabin spatial noise correlations; it is mathematically equivalent to the squared SNR per unit fluence of the generalized least-squares estimate of the height of an X-ray impulse in a uniform noisy background. The zero-frequency DQE has a strong linear relationship with the ideal-observer SNR of low-frequency soft-tissue, bone, iodine, and gadolinium signals, and can be expressed in terms of the product of the quantum efficiency and a Swank noise factor that accounts for DQE degradation due to, for example, charge sharing (CS) and electronic noise. The spectroscopic Swank noise factor of the CdTe detector was measured to be 0.81 ± 0.04 and 0.83 ± 0.04 with and without anticoincidence logic for CS suppression, respectively. The spectroscopic Swank noise factor of the CdZnTe detector operated with four energy bins was measured to be 0.82 ± 0.02 which is within 5% of the theoretical value.

CONCLUSIONS

The spectroscopic DQE defined here is (1) task-independent, (2) can be measured using a modest extension of existing DQE-metrology methods, and (3) is predictive of the ideal-observer SNR of soft-tissue, bone, iodine, and gadolinium signals. For CT applications, the combination of CS and electronic noise in CdZnTe spectroscopic detectors will degrade the zero-frequency DQE by 10 %-20 % depending on the electronic noise level and pixel size.

Photon-counting x-ray detectors for CT

The introduction of photon-counting detectors is expected to be the next major breakthrough in clinical x-ray computed tomography (CT). During the last decade, there has been considerable research activity in the field of photon-counting CT, in terms of both hardware development and theoretical understanding of the factors affecting image quality. In this article, we review the recent progress in this field with the intent of highlighting the relationship between detector design considerations and the resulting image quality. We discuss detector design choices such as converter material, pixel size, and readout electronics design, and then elucidate their impact on detector performance in terms of dose efficiency, spatial resolution, and energy resolution. Furthermore, we give an overview of data processing, reconstruction methods and metrics of imaging performance; outline clinical applications; and discuss potential future developments.

A framework for performance characterization of energy-resolving photon-counting detectors

PURPOSE

Photon-counting, energy-resolving detectors are subject to intense research interest, and there is a need for a general framework for performance assessment of these detectors. The commonly used linear-systems theory framework, which measures detector performance in terms of noise-equivalent quanta (NEQ) and detective quantum efficiency (DQE) is widely used for characterizing conventional x-ray detectors but does not take energy-resolving capabilities into account. The purpose of this work is to extend this framework to encompass energy-resolving photon-counting detectors and elucidate how the imperfect energy response and other imperfections in real-world detectors affect imaging performance, both for feature detection and for material quantification tasks.

METHOD

We generalize NEQ and DQE to matrix-valued quantities as functions of spatial frequency, and show how these matrices can be calculated from simple Monte Carlo simulations. To demonstrate how the new metrics can be interpreted, we compute them for simplified models of fluorescence and Compton scatter in a photon-counting detector and for a Monte Carlo model of a CdTe detector with 0.5 × 0.5 mm 2 pixels.

RESULTS

Our results show that the ideal-linear-observer performance for any detection or material quantification task can be calculated from the proposed generalized NEQ and DQE metrics. We also demonstrate that the proposed NEQ metric is closely related to a generalized version of the Cramér-Rao lower bound commonly used for assessing material quantification performance. Off-diagonal elements in the NEQ and DQE matrices are shown to be related to loss of energy information due to imperfect energy resolution. The Monte Carlo model of the CdTe detector predicts a zero-frequency dose efficiency relative to an ideal detector of 0.86 and 0.65 for detecting water and bone, respectively. When the task instead is to quantify these materials, the corresponding values are 0.34 for water and 0.26 for bone.

CONCLUSIONS

We have developed a framework for assessing the performance of photon-counting energy-resolving detectors and shown that the matrix-valued NEQ and DQE metrics contain sufficient information for calculating the dose efficiency for both detection and quantification tasks, the task having any spatial and energy dependence. This framework will be beneficial for the development and optimization of photon-counting x-ray detectors.

Optimization of beam quality for photon-counting spectral computed tomography in head imaging: simulation study

Head computed tomography (CT) plays an important role in the comprehensive evaluation of acute stroke. Photon-counting spectral detectors, as promising candidates for use in the next generation of x-ray CT systems, allow for assigning more weight to low-energy x-rays that generally contain more contrast information. Most importantly, the spectral information can be utilized to decompose the original set of energy-selective images into several basis function images that are inherently free of beam-hardening artifacts, a potential advantage for further improving the diagnosis accuracy. We are developing a photon-counting spectral detector for CT applications. The purpose of this work is to determine the optimal beam quality for material decomposition in two head imaging cases: nonenhanced imaging and K-edge imaging. A cylindrical brain tissue of 16-cm diameter, coated by a 6-mm-thick bone layer and 2-mm-thick skin layer, was used as a head phantom. The imaging target was a 5-mm-thick blood vessel centered in the head phantom. In K-edge imaging, two contrast agents, iodine and gadolinium, with the same concentration ([Formula: see text]) were studied. Three parameters that affect beam quality were evaluated: kVp settings (50 to 130 kVp), filter materials ([Formula: see text] to 83), and filter thicknesses [0 to 2 half-value layer (HVL)]. The image qualities resulting from the varying x-ray beams were compared in terms of two figures of merit (FOMs): squared signal-difference-to-noise ratio normalized by brain dose ([Formula: see text]) and that normalized by skin dose ([Formula: see text]). For nonenhanced imaging, the results show that the use of the 120-kVp spectrum filtered by 2 HVL copper ([Formula: see text]) provides the best performance in both FOMs. When iodine is used in K-edge imaging, the optimal filter is 2 HVL iodine ([Formula: see text]) and the optimal kVps are 60 kVp in terms of [Formula: see text] and 75 kVp in terms of [Formula: see text]. A tradeoff of 65 kVp was proposed to lower the potential risk of skin injuries if a relatively long exposure time is necessarily performed in the iodinated imaging. In the case of gadolinium imaging, both SD and BD can be minimized at 120 kVp filtered with 2 HVL thulium ([Formula: see text]). The results also indicate that with the same concentration and their respective optimal spectrum, the values of [Formula: see text] and [Formula: see text] in gadolinium imaging are, respectively, around 3 and 10 times larger than those in iodine imaging. However, since gadolinium is used in much lower concentrations than iodine in the clinic, iodine may be a preferable candidate for K-edge imaging.