Taguchi, Katsuyuki

AbstractBackgroundPhoton counting X‐ray detectors (PCDs) provide better spatial resolution than energy integrating X‐ray detectors, but even higher resolution is desired in some applications. Certain charge sharing compensation techniques such as coincidence counting preferentially detect photons that arrive at the boundary between pixels, and this could be used for subpixel localization of incident photons and enhanced spatial resolution.PurposeTo estimate improvements to spatial resolution and detective quantum efficiency that are possible when using coincidence counting for high‐resolution, non‐spectral imaging.MethodsThe modulation transfer function (MTF), noise power spectrum (NPS), and detective quantum efficiency (DQE) were estimated using numerical simulations of a two‐dimensional parallel‐beam CT system. Coincidence counters were modeled either geometrically or with Monte Carlo simulations. The geometric model consisted of narrow coincidence counters that interlaced with wider ordinary pixels, and showed that using standard filtered backprojection decreases low‐frequency DQE, but that a frequency weighting technique could be used to restore DQE. The Monte Carlo simulations were used to estimate the possible improvements that could be expected from real systems. The pixel pitch was 0.25 mm and the source apertures considered were 0, 0.125, and 0.5 mm. A numerical stent phantom was also used to illustrate possible improvements.ResultsAssuming a 0.125 mm source aperture and the Monte Carlo model, the limiting MTF (at 10%) increased from 20 to 40 lp/cm using coincidence counters. This can be explained by the increased sampling (and higher Nyquist limit) possible from coincidence counters. In the geometric model, coincidence counters are compared to conventional double sampling techniques such as in‐plane flying focal spot, and the MTF at 38 lp/cm increased from 5% to 53%. Without the frequency weighting technique, low‐frequency DQE was reduced by about 20%, but these losses are recovered with frequency weighting. Improvements are much more modest with the 0.25 mm source aperture because the system becomes source‐limited.ConclusionsCoincidence counting could be used to increase spatial resolution in PCDs. The increases in system resolution could be large if a high‐resolution X‐ray source were available.

AbstractBackgroundPhoton counting detectors (PCDs) for x‐ray computed tomography (CT) are the future of CT imaging. At present, semiconductor‐based PCDs such as cadmium telluride (CdTe), cadmium zinc telluride, and silicon have been either used or investigated for clinical PCD CT. Unfortunately, all of them have the same major challenges, namely high cost and limited spectral signal‐to‐noise ratio (SNR). Recent studies showed that some high‐quality scintillators, such as lanthanum bromide doped with cerium (LaBr3:Ce), are less expensive and almost as fast as CdTe.PurposeThe objective of this study is to assess the performance of a LaBr3:Ce PCD for clinical x‐ray CT.MethodsWe performed Monte Carlo simulations and compared the performance of 3 mm thick LaBr3:Ce and 2 mm thick CdTe for PCD CT with x‐rays at 120 kVp and 20–1000 mA. The two PCDs were operated with either a threshold–subtract (TS) counting scheme or a direct energy binning (DB) counting scheme. The performance was assessed in terms of the accuracy of registered spectra, counting capability, and count‐rate‐dependent spectral imaging‐task performance, for conventional CT imaging, water–bone material decomposition, and K‐edge imaging with tungsten as the K‐edge material. The performance for these imaging‐tasks was quantified by nCRLB, that is, the Cramér–Rao lower bound on the variance of basis line‐integral estimation, normalized by the corresponding value of CdTe at 20 mA.ResultsThe spectrum recorded by CdTe was distorted significantly due to charge sharing, whereas the spectra recorded by LaBr3:Ce better matched the incident spectrum. The dead time, estimated by fitting a paralyzable detector model to the count‐rate curves, was 20.7, 15.0, 37.2, and 13.0 ns for CdTe with TS, CdTe with DB, LaBr3:Ce with TS, and LaBr3:Ce with DB, respectively. Conventional CT imaging showed an adverse effect of reduced geometrical efficiency due to optical reflectors in LaBr3:Ce PCD. The nCRLBs (a lower value indicates a better SNR) for CdTe with TS, CdTe with DB, LaBr3:Ce with TS, LaBr3:Ce with DB, and the ideal PCD, were 1.00 ± 0.01, 1.00 ± 0.01, 1.18 ± 0.02, 1.18 ± 0.02, and 0.79 ± 0.01, respectively, at 20 mA. The nCRLBs for water–bone material decomposition, in the same order, were 1.00 ± 0.02, 1.00 ± 0.02, 0.85 ± 0.02, 0.85 ± 0.02, and 0.24 ± 0.02, respectively, at 20 mA; and 0.98 ± 0.02, 0.98 ± 0.02, 1.09 ± 0.02, 0.83 ± 0.02, and 0.24 ± 0.02, respectively, at 1000 mA. Finally, the nCRLBs for K‐edge imaging, the most demanding task among the five, were 1.00 ± 0.02, 1.00 ± 0.02, 0.55 ± 0.02, 0.55 ± 0.02, and 0.13 ± 0.02, respectively, at 20 mA; and 2.45 ± 0.02, 2.29 ± 0.02, 3.12 ± 0.02, 2.11 ± 0.02, and 0.13 ± 0.02, respectively, at 1,000 mA.ConclusionThe Monte Carlo simulations showed that, compared to CdTe with either TS or DB, LaBr3:Ce with DB provided more accurate spectra, comparable or better counting capability, and superior spectral imaging‐task performances, that is, water–bone material decomposition and K‐edge imaging. CdTe had a better performance than LaBr3:Ce for the conventional CT imaging task due to its higher geometrical efficiency. LaBr3:Ce PCD with DB scheme may be an excellent alternative option for CdTe PCD.

Abstract Background Silicon (Si) is a possible sensor material for photon counting detectors (PCDs). A major drawback of Si is that roughly two‐thirds of x‐ray interactions in the diagnostic energy range are Compton scattering. Because Compton scattering is an energy‐insensitive process, it is commonly assumed that Compton events retain little spectral information. Purpose To quantify how much information can be recovered from Compton scattering events in models of Si PCDs. Methods We built a simplified model of Si interactions including two interaction mechanisms: photoelectric effect and Compton scattering. We considered three different binning options that represent strategies for handling Compton events: in Compton censoring, all events under 38 keV (the maximum energy possible from Compton scattering for a 120 keV incident photon) were discarded; in Compton counting, all events between 1 and 38 keV were placed into a single bin; in Compton binning, all events were placed into energy bins of uniform width. These were compared to the ideal detector, which always recorded the correct energy (i.e., 100% photoelectric effect). Every photon was assumed to interact once and only once with Si, and the energy bin width was 5 keV. In the primary analysis, the Si detector was irradiated with a 120 kV spectrum filtered by 30 cm of water, with 99.5% of the arriving spectrum above 38 keV so that there was good separation between photoelectric effect and Compton scattering, and the figures of merit were the Cramér – Rao lower bound (CRLB) of the variance of iodine and water basis material decomposition images, as well as the CRLB of virtual monoenergetic images (i.e., linear combinations of material images) that maximize iodine CNR or water CNR. We also constructed a local linear estimator that attains the CRLB. In secondary analyses, we applied other sources of spectral distortion: (1) a nonzero minimum energy threshold; (2) coarser, 10 keV energy bins; and (3) a model of charge sharing. Results With our chosen spectrum, 67% of the interactions were Compton scattering. Consistent with this, the material decomposition variance for the Compton censoring model, averaged over both basis materials, was 258% greater than the ideal detector. If Compton events carried no spectral information, the Compton counting model would show similar variance. Instead, its basis material variance was 103% greater than the ideal detector, implying that Compton counts indeed carry significant spectral information. The Compton binning model had a basis material variance 60% greater than the ideal detector. The Compton binning model was not affected by a 5 keV minimum energy threshold, but the variance increased from 60% to 107% when charge sharing was included and to 78% with coarser energy bins. For optimized CNR images, the average variance was 149%, 12%, and 10% higher than the ideal detector for the Compton censoring, counting, and binning models, reinforcing the hypothesis that Compton counts are useful for detection tasks and that precise energy assignments are not necessary. Conclusions Substantial spectral information remains after Compton scattering events in silicon PCDs.

AbstractBackgroundPhoton counting detectors (PCDs) for x‐ray computed tomography (CT) face spectral distortion from pulse pileup and charge sharing. The photon counting scheme used by many PCDs is threshold–subtract (TS) with pulse height analysis (PHA), where each counter counts up‐crossing events when pulses exceed an energy threshold. PCD data are not Poisson‐distributed due to charge sharing and pulse pileup, but the counting statistics have never been studied yet.PurposeThe objectives of this study were (1) to propose a modified photon counting scheme, direct energy binning (DB), that is expected to be robust against pulse pileup; (2) to assess the performance of DB compared to TS; and (3) to evaluate its counting statistics.MethodsWith DB scheme, counter k starts a timer upon an up‐crossing event of energy threshold k, and adds a count only if the next higher energy threshold (k+1) was not crossed within a short time window (hence, the pulse peak belongs to the energy bin k). We used Monte Carlo (MC) simulation and assessed count‐rate curves and count‐rate‐dependent spectral imaging task performance for conventional CT imaging as well as water thickness estimation, water–bone material decomposition, and K‐edge imaging with tungsten as the K‐edge material. We also assessed count‐rate‐dependent measurement statistics such as expectation, variance, and covariance of total counts as well as energy bin outputs. The agreement with counting statistics models was also evaluated.ResultsThe DB scheme improved the count‐rate curve, that is, mean measured counts as a function of input count‐rate, and peaked with 59% higher count‐rate capability than the TS scheme (3.5 × 108 counts per second (cps)/mm2 versus 2.3 × 108 cps/mm2). The Cramér–Rao lower bounds (CRLB) of the variance of basis line integrals estimation for DB was better than those for TS by 2% for the conventional CT imaging, 30% for water–bone material decomposition, and 32% for K‐edge imaging at 1000 mA (at 7.3 × 107 cps/sub‐pixel after charge sharing). When count‐rates were lower, PCD data statistics were dominated by charge sharing: the variance of total counts and lower energy bins was larger than the mean counts; the covariance of bin data was positive and non‐zero. When count‐rates were higher, PCD data statistics were dominated by pulse pileup: the variance of data was lower than the mean; the covariance of bin data was negative. The transition between the two regimes occurred smoothly, and pulse pileup dominated the statistics ≥400 mA (when the count‐rate after charge sharing was 2.9 × 107 cps/sub‐pixel and the probability of count‐loss for DB was 37%). Both DB and TS had good agreement with Yu–Fessler's models of total counts; however, DB had a better agreement with Wang's variance and covariance models for energy bin data than TS did.ConclusionsThe proposed DB scheme had several advantages over TS. At low to moderate flux, DB could improve the resilience of PCDs to pulse pileup. Counting statistics deviated from the Poisson distribution due to charge sharing for lower count‐rate conditions and pulse pileup for higher count‐rate conditions.