Hans Bornefalk

Photon-counting spectral computed tomography using silicon strip detectors: a feasibility study

We show how the spectral imaging framework should be modified to account for a high fraction of Compton interactions in low Z detector materials such as silicon. Using this framework, where deposited energies differ from actual photon energies, we compare the performance of a silicon strip detector, including the influence of scatter inside the detector and charge sharing but disregarding signal pileup, with an ideal energy integrating detector. We show that although the detection efficiency for silicon rapidly drops for the acceleration voltages encountered in clinical computed tomography practice, silicon detectors could perform on a par with ideal energy integrating detectors for routine imaging tasks. The use of spectrally sensitive detectors opens up the possibility for decomposition techniques such as k-edge imaging, and we show that the proposed modification of the spectral imaging framework is beneficial for such imaging tasks.

Evaluation of Energy Loss and Charge Sharing in Cadmium Telluride Detectors for Photon-Counting Computed Tomography

We present estimates of energy loss and charge sharing for a pixelated cadmium telluride (CdTe) detector used for photon-counting spectral computed tomography (CT). In a photon-counting pixelated CdTe detector, several physical effects lead to detected events with reduced energies, including Compton scattering, fluorescence emission, charge diffusion, trapping of charge carriers and slow-hole-motion-induced incomplete charge collection. Charge sharing is the result of the lost energy being collected by adjacent pixels. We simulated the photon transport and the charge-collection process with a Monte Carlo-based simulation and evaluated these effects on the detector performance. The trapping effect and poor hole collection have been studied together using an analytical model. We also investigated the detector response under the influence of only the fluorescence effect. We conclude that the charge sharing effects should be taken into account when the pixel is smaller than 1 mm2. A straightforward way to decrease the double counting of X-rays from events with charge sharing is to increase the electronic threshold. However, increasing the threshold comes at the cost of losing low-energy events, which is undesirable, at least in applications such as pediatric imaging.

On the comparison of FROC curves in mammography CAD systems

We present a novel method for assessing the performance of computer-aided detection systems on unseen cases at a given sensitivity level. The sampling error introduced when training the system on a limited data set is captured as the uncertainty in determining the system threshold that would yield a certain predetermined sensitivity on unseen data sets. By estimating the distribution of system thresholds, we construct a confidence interval for the expected number of false positive markings per image at a given sensitivity. We present two alternative procedures for estimating the probability density functions needed for the construction of the confidence interval. The first is based on the common assumption of Poisson distributed number of false positive markings per image. This procedure also relies on the assumption of independence between false positives and sensitivity, an assumption that can be relaxed with the second procedure, which is nonparametric. The second procedure uses the bootstrap applied to the data generated in the leave-one-out construction of the FROC curve, and is a fast and robust way of obtaining the desired confidence interval. Standard FROC curve analysis does not account for the uncertainty in setting the system threshold, so this method should allow for a more fair comparison of different systems. The resulting confidence intervals are surprisingly wide. For our system a conventional FROC curve analysis yields 0.47 false positive markings per image at 90% sensitivity. The 90% confidence interval for the number of false positive markings per image is (0.28, 1.02) with the parametric procedure and (0.27, 1.04) with the nonparametric bootstrap. Due to its computational simplicity and its allowing more fair comparisons between systems, we propose this method as a complement to the traditionally presented FROC curves.

Evaluation of a Second-Generation Ultra-Fast Energy-Resolved ASIC for Photon-Counting Spectral CT

A second-generation ultra-fast energy-resolved application specific integrated circuit (ASIC) has been developed for photon-counting spectral computed tomography (CT). The energy resolution, threshold dispersion and gain of the ASIC were characterized with synchrotron radiation at Diamond Light Source. The standard deviation of threshold offsets at zero keV is 0.89 keV. An RMS energy resolution of 1.09 keV has been demonstrated for 15 keV photon energy at a count rate of 40 kcps, and it deteriorates at a rate of 0.29 keV/Mcps with the increase of output cout rate. The count rate performance of the ASIC has also been evaluated with 120 kV polychromatic x-rays produced by a tungsten anode tube and the results are presented.

Performance evaluation of a sub-millimetre spectrally resolved CT system on high- and low-frequency imaging tasks: a simulation

We are developing a photon-counting silicon strip detector with 0.4 × 0.5 mm² detector elements for clinical CT applications. Except for the limited detection efficiency of approximately 0.8 for a spectrum of 80 kVp, the largest discrepancies from ideal spectral behaviour have been shown to be Compton interactions in the detector and electronic noise. Using the framework of cascaded system analysis, we reconstruct the 3D MTF and NPS of a silicon strip detector including the influence of scatter and charge sharing inside the detector. We compare the reconstructed noise and signal characteristics with a reconstructed 3D MTF and NPS of an ideal energy-integrating detector system with unity detection efficiency, no scatter or charge sharing inside the detector, unity presampling MTF and 1 × 1 mm² detector elements. The comparison is done by calculating the dose-normalized detectability index for some clinically relevant imaging tasks and spectra. This work demonstrates that although the detection efficiency of the silicon detector rapidly drops for the acceleration voltages encountered in clinical computed tomography practice, and despite the high fraction of Compton interactions due to the low atomic number, silicon detectors can perform on a par with ideal energy-integrating detectors for routine imaging tasks containing low-frequency components. For imaging tasks containing high-frequency components, the proposed silicon detector system can perform approximately 1.1-1.3 times better than a fully ideal energy-integrating system.

Dose-efficient system for digital mammography

We are developing a dose-efficient system for digital mammography. The system incorporates a refractive x-ray lens combined with a photon counting silicon sensor system. The system matches the digital nature of x-rays and maximum information can be extracted from the transmitted x-ray beam. The photon counting sensor system opens the possibility to weight each photon according to its information content. High- energy photons with little contrast information can be weighted low while low energy photons are weighted high. At the same time, using the refractive x-ray lens, the incident x-ray spectrum can be tuned to the optimum energy for a certain breast thickness. The performance of the system is expected to be close to the theoretical limit in terms of dose efficiency and is entirely limited by quantum noise. Since the standard use of the term DQE does not take into account the incident x-ray energy spectrum, scattered x-rays or the difference in information content from low to high-energy photons an alternative measure of performance is used. We refer to this measure as dose-efficiency and in this case the system is related to an ideal x-ray imaging system.

A Framework for Evaluating Threshold Variation Compensation Methods in Photon Counting Spectral CT

One of the challenges in the development of photon counting spectral computed tomography (CT) detectors is that the location of the energy thresholds tends to vary among detector elements. If not compensated for, this threshold variation leads to ring artifacts in the reconstructed images. In this paper, a framework is presented for the systematic comparison of different methods of compensating for inhomogeneities among detector elements in photon counting CT with multiple energy bins. Furthermore, we propose the use of an affine minimum mean square error estimator, calibrated against transmission measurements on different combinations of two materials, for inhomogeneity compensation. Using the framework developed here, this method is compared to two other compensation schemes, flatfielding using an air scan and signal-to-thickness calibration using a step wedge calibrator, in a simulation study. The results show that for all but the lowest studied level of threshold spread, the proposed method is superior to signal-to-thickness calibration, which in turn is superior to flatfielding. We also demonstrate that the effects of threshold variation can be countered to a large extent by substructuring each detector element into depth segments.

XCOM intrinsic dimensionality for low-Z elements at diagnostic energies.

PURPOSE To determine the intrinsic dimensionality of linear attenuation coefficients (LACs) from XCOM for elements with low atomic number (Z = 1-20) at diagnostic x-ray energies (25-120 keV). H(0) (q), the hypothesis that the space of LACs is spanned by q bases, is tested for various q-values. METHODS Principal component analysis is first applied and the LACs are projected onto the first q principal component bases. The residuals of the model values vs XCOM data are determined for all energies and atomic numbers. Heteroscedasticity invalidates the prerequisite of i.i.d. errors necessary for bootstrapping residuals. Instead wild bootstrap is applied, which, by not mixing residuals, allows the effect of the non-i.i.d residuals to be reflected in the result. Credible regions for the eigenvalues of the correlation matrix for the bootstrapped LAC data are determined. If subsequent credible regions for the eigenvalues overlap, the corresponding principal component is not considered to represent true data structure but noise. If this happens for eigenvalues l and l + 1, for any l ≤ q, H(0) (q) is rejected. RESULTS The largest value of q for which H(0) (q) is nonrejectable at the 5%-level is q = 4. This indicates that the statistically significant intrinsic dimensionality of low-Z XCOM data at diagnostic energies is four. CONCLUSIONS The method presented allows determination of the statistically significant dimensionality of any noisy linear subspace. Knowledge of such significant dimensionality is of interest for any method making assumptions on intrinsic dimensionality and evaluating results on noisy reference data. For LACs, knowledge of the low-Z dimensionality might be relevant when parametrization schemes are tuned to XCOM data. For x-ray imaging techniques based on the basis decomposition method (Alvarez and Macovski, Phys. Med. Biol. 21, 733-744, 1976), an underlying dimensionality of two is commonly assigned to the LAC of human tissue at diagnostic energies. The finding of a higher statistically significant dimensionality thus raises the question whether a higher assumed model dimensionality (now feasible with the advent of multibin x-ray systems) might also be practically relevant, i.e., if better tissue characterization results can be obtained.

Performance Characterization of a Silicon Strip Detector for Spectral Computed Tomography Utilizing a Laser Testing System

A new silicon strip detector with sub-millimeter pixel size operated in single photon-counting mode has been developed for use in spectral computed tomography (CT). An ultra fast application specific integrated circuit (ASIC) specially designed for fast photon-counting application is used to process the pulses and sort them into eight energy bins. This report characterizes the ASIC and detector in terms of thermal noise (0.77 keV RMS), energy resolution when electron-hole pairs are generated in the detector diode (1.5 keV RMS) and Poissonian count rate with retained count rate linearity and energy resolution (200 Mcps•mm-2). The performance of the photon-counting detector has been tested using a picosecond pulsed laser system to inject energy into the detector, simulating x-ray interactions. The laser testing results indicate a good energy-discriminating capability of the detector, assigning the pulses to higher and higher energy bins as the intensity of the laser pulses are increased.

A Silicon-Strip Detector for Photon-Counting Spectral CT: Energy Resolution From 40 keV to 120 keV

We are developing a segmented silicon-strip detector for spectral computed tomography. The detector operates in photon-counting mode and allows pulse-height discrimination with 8 adjustable energy bins. In this work, we determine the energy resolution of a detector module using monoenergetic x-rays from 40 keV to 120 keV, provided at the European Synchrotron Radiation Facility, Grenoble. For each incident x-ray energy, pulse height spectra at different input photon fluxes are obtained. We investigate changes of the energy resolution due to charge sharing between pixels and pulse pileup. The different incident energies are used to channel-wise calibrate the pulse-height response in terms of signal gain and offset and to probe the homogeneity of the detector module. The detector shows a linear pulse-height response in the energy range from 40 keV to 120 keV. The gain variation among the channels is below 4%, whereas the variation of the offsets is on the order of 1 keV. We find an absolute energy resolution ( σE) that degrades from 1.5 keV to 1.9 keV with increasing x-ray energy from 40 keV to 100 keV. With increasing input count rate, σE degrades by approximately 4 ·10-3 keV Mcps-1 mm2, which is, within error bars, the same for the different energies. The effect of charge sharing on the width of the response peak is found to be negligible.