Frequency-dependent signal and noise in spectroscopic x-ray imaging

Contrast and quantum noise in single-exposure dual-energy thoracic imaging with photon-counting x-ray detectors

Objective.Photon-counting x-ray detectors (PCDs) can produce dual-energy (DE) x-ray images of lung cancer in a single x-ray exposure. It is important to understand the factors that affect contrast, noise and the contrast-to-noise ratio (CNR). This study quantifies the dependence of CNR on tube voltage, energy threshold and patient thickness in single exposure, DE, bone-suppressed thoracic imaging with PCDs, and elucidates how the fundamental processes inherent in x-ray detection by PCDs contribute to CNR degradation.Approach.We modeled the DE CNR for five theoretical PCDs, ranging from an ideal PCD that detects every primary photon in the correct energy bin while rejecting all scattered radiation to a non-ideal PCD that suffers from charge-sharing and electronic noise, and detects scatter. CNR was computed as a function of tube voltage and high energy threshold for average and larger-than-average patients. Model predictions were compared with experimental data extracted from images acquired using a cadmium telluride (CdTe) PCD with two energy bins and analog charge summing for charge-sharing suppression. The imaging phantom simulated attenuation, scatter and contrast in lung nodule imaging. We quantified CNR improvements achievable with anti-correlated noise reduction (ACNR) and measured the range of exposure rates over which pulse pile-up is negligible.Main Results.The realistic model predicted overall trends observed in the experimental data. CNR improvements with ACNR were approximately five-fold, and modeled CNR-enhancements were on average within 10% of experiment. CNR increased modestly (i.e.<20%) when increasing the tube voltage from 90 kV to 130 kV. Optimal energy thresholds ranged from 50 keV to 70 keV across all tube voltages and patient thicknesses with and without ACNR. Quantum efficiency, electronic noise, charge sharing and scatter degraded CNR by ~50%. Charge sharing and scatter had the largest effect on CNR, degrading it by ~30% and ~15% respectively. Dead-time losses were less than 5% for patient exposure rates within the range of clinical exposure rates.Significance.In this study, we (1) employed analytical and computational models to assess the impact of different factors on CNR in single-exposure DE imaging with PCDs, (2) evaluated the accuracy of these models in predicting experimental trends, (3) quantified improvements in CNR achievable through ACNR and (4) determined the range of patient exposure rates at which pulse pile-up can be considered negligible. To the best of our knowledge, this study represents the first systematic investigation of single-exposure DE imaging of lung nodules with PCDs.

Can processed images be used to determine the modulation transfer function and detective quantum efficiency?

Purpose

The modulation transfer function (MTF) and detective quantum efficiency (DQE) of x-ray detectors are key Fourier metrics of performance, valid only for linear and shift-invariant (LSI) systems and generally measured following IEC guidelines requiring the use of raw (unprocessed) image data. However, many detectors incorporate processing in the imaging chain that is difficult or impossible to disable, raising questions about the practical relevance of MTF and DQE testing. We investigate the impact of convolution-based embedded processing on MTF and DQE measurements.

Approach

We use an impulse-sampled notation, consistent with a cascaded-systems analysis in spatial and spatial-frequency domains to determine the impact of discrete convolution (DC) on measured MTF and DQE following IEC guidelines.

Results

We show that digital systems remain LSI if we acknowledge both image pixel values and convolution kernels represent scaled Dirac δ -functions with an implied sinc convolution of image data. This enables use of the Fourier transform (FT) to determine impact on presampling MTF and DQE measurements.

Conclusions

It is concluded that: (i) the MTF of DC is always an unbounded cosine series; (ii) the slanted-edge method yields the true presampling MTF, even when using processed images, with processing appearing as an analytic filter with cosine-series MTF applied to raw presampling image data; (iii) the DQE is unaffected by discrete-convolution-based processing with a possible exception near zero-points in the presampling MTF; and (iv) the FT of the impulse-sampled notation is equivalent to the Z transform of image data.

Material decomposition with a prototype photon-counting detector CT system: expanding a stoichiometric dual-energy CT method via energy bin optimization and K-edge imaging

Objective.Computed tomography (CT) has advanced since its inception, with breakthroughs such as dual-energy CT (DECT), which extracts additional information by acquiring two sets of data at different energies. As high-flux photon-counting detectors (PCDs) become available, PCD-CT is also becoming a reality. PCD-CT can acquire multi-energy data sets in a single scan by spectrally binning the incident x-ray beam. With this, K-edge imaging becomes possible, allowing high atomic number (high-Z) contrast materials to be distinguished and quantified. In this study, we demonstrated that DECT methods can be converted to PCD-CT systems by extending the method of Bourqueet al(2014). We optimized the energy bins of the PCD for this purpose and expanded the capabilities by employing K-edge subtraction imaging to separate a high-atomic number contrast material.Approach.The method decomposes materials into their effective atomic number (Zeff) and electron density relative to water (ρe). The model was calibrated and evaluated using tissue-equivalent materials from the RMI Gammex electron density phantom with knownρevalues and elemental compositions. TheoreticalZeffvalues were found for the appropriate energy ranges using the elemental composition of the materials.Zeffvaried slightly with energy but was considered a systematic error. Anex vivobovine tissue sample was decomposed to evaluate the model further and was injected with gold chloride to demonstrate the separation of a K-edge contrast agent.Main results.The mean root mean squared percent errors on the extractedZeffandρefor PCD-CT were 0.76% and 0.72%, respectively and 1.77% and 1.98% for DECT. The tissue types in theex vivobovine tissue sample were also correctly identified after decomposition. Additionally, gold chloride was separated from theex vivotissue sample with K-edge imaging.Significance.PCD-CT offers the ability to employ DECT material decomposition methods, along with providing additional capabilities such as K-edge 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.

Theoretical comparison of energy-resolved and digital-subtraction angiography

BACKGROUND

X-ray coronary angiography is a sub-optimal vascular imaging technique because it cannot suppress un-enhanced anatomy that may obscure the visualization of coronary artery disease.

PURPOSE

The purpose of this paper is to evaluate the theoretical image quality of energy-resolved x-ray angiography (ERA) implemented with spectroscopic x-ray detectors (SXDs), which may overcome limitations of x-ray coronary angiography.

METHODS

We modeled the large-area signal-difference-to-noise (SDNR) of contrast-enhanced vasculature in ERA images and compared with that of digital-subtraction angiography (DSA), which served as a gold standard vascular imaging technique. To this end, we used calibrated numerical models of the response of cadmium telluride SXDs including the effects of charge sharing, electronic noise, and energy thresholding. Our models assumed zero scatter, no pulse pile up and small signals such that image contrast is approximately linear in the area density of contrast agents. For DSA, we similarly modeled x-ray detection by cesium iodide energy-integrating detectors using validated numerical models. For ERA, we investigated iodine and gadolinium (Gd) contrast agents, two-material and three-material decompositions, analog charge summing for charge sharing correction, and optimized image quality with respect to the tube voltage and energy thresholds assuming cadmium telluride SXDs with three energy bins.

RESULTS

Our analysis reveals that a three-material decomposition using iodine contrast agents will require x-ray exposures that are approximately 400 times those of DSA to achieve the same SDNR as DSA in coronary applications, and is therefore not feasible in a clinical setting. However, three-material decompositions with Gd contrast agents have the potential to provide SDNR that is ∼45% of that of DSA for matched patient air kerma. For two-material decompositions that suppress soft-tissue, ERA has the potential to produce images with SDNR that is 50%-75% of that of DSA for matched patient air kermas but lower levels of tube loading. Achieving these SDNR levels will require the use of analog charge summing for charge sharing correction, which increased SDNR by up to a factor of 1.7 depending on the contrast agent and whether or not a two-material or three-material decomposition was assumed.

CONCLUSIONS

We conclude that three-material ERA implemented with Gd contrast agents and two-material ERA implemented with either iodine or Gd contrast agents, should be investigated as alternatives to DSA in situations where motion artifacts preclude the use of DSA, such as in coronary imaging.

The detective quantum efficiency of cadmium telluride photon-counting x-ray detectors in breast imaging applications

PURPOSE

In breast imaging applications, cadmium telluride (CdTe) photon counting x-ray detectors (PCDs) may reduce radiation dose and enable single-shot multi-energy x-ray imaging. The purpose of this work is to determine the upper limits of the detective quantum efficiency (DQE) of CdTe PCDs for x-ray mammography and to compare them with the published DQEs of energy-integrating detectors (EIDs) and other PCDs.

METHODS

We calibrated and validated a Monte Carlo (MC) model of the DQE of CdTe PCDs using an XCounter CdTe PCD. Our model accounted for charge sharing, electronic noise, and charge summation logic. We used a 28 kVp Mo/Mo spectrum hardened by 3.9 cm of Lucite to optimize the detector thickness and energy threshold for pixel sizes of 50, 85, and 100 μ m with and without inter-pixel charge summation logic. The figure of merit used for optimization was the integral of the DQE, which is equivalent to the detectability index for a delta function task function, which represents a high-frequency task.

RESULTS

For an electronic noise level equal to that of the XCounter, the optimal DQE(0) without charge summing was 0.74. Charge summing for charge-sharing correction reduced DQE(0) by 14% due to an increase in electronic noise. Reducing the electronic noise to ∼0.5 keV per pixel in combination with charge summing resulted in DQE(0) ≈ 0.78 for 85  μ m pixels, which is approximately equal to that of a-Se and slot-scanning silicon-strip PCDs. At higher spatial frequencies, and for matched pixel sizes, the DQE was inferior to that of a-Se EIDs and superior to that of slot-scanning silicon-strip PCDs in the scan direction but inferior in the slit direction.

CONCLUSIONS

(1) CdTe PCDs have the potential to provide a zero-frequency DQE equal to that of a-Se EIDs and slot-scanning silicon-strip PCDs, but this will require electronic noise levels ∼0.5 keV per pixel. (2) At mid-to-high spatial frequencies the DQE of CdTe PCDs may be (a) inferior to that of a-Se EIDs and slot-scanning silicon-strip PCDs in the slit direction, and (b) superior to slot-scanning silicon-strip PCDs in the scan direction.

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.

Anomalous edge response of cadmium telluride-based photon counting detectors jointly caused by high-flux radiation and inter-pixel communication

This work reports an edge enhancing effect experimentally observed in cadmium telluride (CdTe)-based photon counting detector (PCD) systems operated under the charge summing (CS) mode and irradiated by high-flux x-rays. Experimental measurements of the edge spread functions (ESFs) of a PCD system (100μm pixel size, 88 ns deadtime) were performed at different input flux levels from 4.5 × 105count per second (cps) mm-2to 1.5 × 109cps mm-2for the single pixel mode (SP) and the CS mode. A theoretical model that incorporates the impacts of inter-pixel communications and the arbitration process involved in the CS mode was developed to help explain the physical origin of the observed edge enhancing effect. Compared with the monotonically increasing ESF of the SP mode, the ESF of the CS mode measured at high-flux levels shows a peak at an intermediate location (50μm from the edge). The peak became more pronounced with increasing flux levels. The theoretically calculated ESFs agreed well with experimental results with relative errors less than 5% at all flux levels and tested. These results indicate that the anomalous edge enhancing effect is jointly caused by the pileup effect and the CS circuit that introduces negative correlations between adjacent pixels. When the input flux is high enough to deliver photons to multiple adjacent pixels within the same deadtime period, the CS mode may treat the coincident x-rays as shared charges and thus introduce count losses in addition to the well-known pileup count loss. When a high contrast object partially blocks certain pixels from x-rays, the adjacent unblocked pixels have an increased probability of registering counts as a result of the negative correlation. This leads to a peak on the ESF at a pixel-to-edge distance half of the pixel pitch.