Mats Persson

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.

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.

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.

Theoretical Comparison of the Iodine Quantification Accuracy of Two Spectral CT Technologies

We compare the theoretical limits of iodine quantification for the photon counting multibin and dual energy technologies. Dual energy systems by necessity have to make prior assumptions in order to quantify iodine. We explicitly allow the multibin system to make the same assumptions and also allow them to be wrong. We isolate the effect of technology from imperfections and implementation issues by assuming both technologies to be ideal, i.e., without scattered radiation, unity detection efficiency and perfect energy response functions, and by applying the Cramér-Rao lower bound methodology to assess the quantification accuracy. When priors are wrong the maximum likelihood estimates will be biased and the mean square error of the quantification error is a more appropriate figure of merit. The evaluation assumes identical X-ray spectra for both methodologies and for that reason a sensitivity analysis is performed with regard to the assumed X-ray spectrum. We show that when iodine is quantified over regions of interest larger than 6 cm2, multibin systems benefit by independent estimation of three basis functions. For smaller regions of interest multibin systems can increase quantification accuracy by making the same prior assumptions as dual energy systems.

Effect of Temperature Variation on the Energy Response of a Photon Counting Silicon CT Detector

The effect of temperature variation on pulse height determination accuracy is determined for a photon counting multibin silicon detector developed for spectral CT. Theoretical predictions of the temperature coefficient of the gain and offset are similar to values derived from synchrotron radiation measurements in a temperature controlled environment. By means of statistical modeling, we conclude that temperature changes affect all channels equally and with separate effects on gain and threshold offset. The combined effect of a 1°C temperature increase is to decrease the detected energy by 0.1 keV for events depositing 30 keV. For the electronic noise, no statistically significant temperature effect was discernible in the data set, although theory predicts a weak dependence. The method is applicable to all x-ray detectors operating in pulse mode.

Optimal Frequency-Based Weighting for Spectral X-Ray Projection Imaging

The purpose of this work is to derive a weighting scheme that maximizes the frequency-dependent ideal observer signal-difference-to-noise ratio, commonly referred to as detectability index or Hotelling-SDNR, for spectral X-ray projection imaging. Starting from basic statistical decision theory, optimal frequency-dependent weights are derived for a multiple-bin system and the Hotelling-SDNR calculated. A 28% increase in detectability index is found for high frequency objects when applying optimal frequency-dependent weights instead of pixel-based weights to a simplified model of a silicon detector, decreasing towards 0% for low frequency objects. Simulation results indicate a potentially large increase in detectability for high-frequency object imaging using silicon detectors, thus meriting further evaluations on a real system.

Spectral response model for a multibin photon-counting spectral computed tomography detector and its applications

Abstract. Variations among detector channels in computed tomography can lead to ring artifacts in the reconstructed images and biased estimates in projection-based material decomposition. Typically, the ring artifacts are corrected by compensation methods based on flat fielding, where transmission measurements are required for a number of material-thickness combinations. Phantoms used in these methods can be rather complex and require an extensive number of transmission measurements. Moreover, material decomposition needs knowledge of the individual response of each detector channel to account for the detector inhomogeneities. For this purpose, we have developed a spectral response model that binwise predicts the response of a multibin photon-counting detector individually for each detector channel. The spectral response model is performed in two steps. The first step employs a forward model to predict the expected numbers of photon counts, taking into account parameters such as the incident x-ray spectrum, absorption efficiency, and energy response of the detector. The second step utilizes a limited number of transmission measurements with a set of flat slabs of two absorber materials to fine-tune the model predictions, resulting in a good correspondence with the physical measurements. To verify the response model, we apply the model in two cases. First, the model is used in combination with a compensation method which requires an extensive number of transmission measurements to determine the necessary parameters. Our spectral response model successfully replaces these measurements by simulations, saving a significant amount of measurement time. Second, the spectral response model is used as the basis of the maximum likelihood approach for projection-based material decomposition. The reconstructed basis images show a good separation between the calcium-like material and the contrast agents, iodine and gadolinium. The contrast agent concentrations are reconstructed with more than 94% accuracy.

Energy Calibration of a Silicon-Strip Detector for Photon-Counting Spectral CT by Direct Usage of the X-ray Tube Spectrum

The variation among energy thresholds in a multibin detector for photon-counting spectral CT can lead to ring artefacts in the reconstructed images. Calibration of the energy thresholds can be used to achieve homogeneous threshold settings or to develop compensation methods to reduce the artefacts. We have developed an energy-calibration method for the different comparator thresholds employed in a photon-counting silicon-strip detector. In our case, this corresponds to specifying the linear relation between the threshold positions in units of mV and the actual deposited photon energies in units of keV. This relation is determined by gain and offset values that differ for different detector channels due to variations in the manufacturing process. Typically, the calibration is accomplished by correlating the peak positions of obtained pulse-height spectra to known photon energies, e.g. with the aid of mono-energetic x rays from synchrotron radiation, radioactive isotopes or fluorescence materials. Instead of mono-energetic x rays, the calibration method presented in this paper makes use of a broad x-ray spectrum provided by commercial x-ray tubes. Gain and offset as the calibration parameters are obtained by a regression analysis that adjusts a simulated spectrum of deposited energies to a measured pulse-height spectrum. Besides the basic photon interactions such as Rayleigh scattering, Compton scattering and photo-electric absorption, the simulation takes into account the effect of pulse pileup, charge sharing and the electronic noise of the detector channels. We verify the method for different detector channels with the aid of a table-top setup, where we find the uncertainty of the keV-value of a calibrated threshold to be between 0.1 and 0.2 keV.

Allowable Forward Model Misspecification for Accurate Basis Decomposition in a Silicon Detector Based Spectral CT

Material basis decomposition in the sinogram domain requires accurate knowledge of the forward model in spectral computed tomography (CT). Misspecifications over a certain limit will result in biased estimates and make quantum limited (where statistical noise dominates) quantitative CT difficult. We present a method whereby users can determine the degree of allowed misspecification error in a spectral CT forward model and still have quantification errors that are limited by the inherent statistical uncertainty. For a particular silicon detector based spectral CT system, we conclude that threshold determination is the most critical factor and that the bin edges need to be known to within 0.15 keV in order to be able to perform quantum limited material basis decomposition. The method as such is general to all multibin systems.

Necessary forward model specification accuracy for basis material decomposition in spectral CT

Material basis decomposition in the sinogram domain requires accurate knowledge of the forward model in spectral CT. Misspecifications over a certain limit will result in biased estimates and make quantum limited quantitative CT difficult. We present a method whereby users can determine the degree of allowed misspecification error in a spectral CT forward model, and still have quantification errors that are quantum limited.