Cascaded systems analysis of photon counting detectors

Framework for evaluating photon-counting detectors under pile-up conditions

Purpose

While X-ray photon-counting detectors (PCDs) promise to revolutionize medical imaging, theoretical frameworks to evaluate them are commonly limited to incident fluence rates sufficiently low that the detector response can be considered linear. However, typical clinical operating conditions lead to a significant level of pile-up, invalidating this assumption of a linear response. Here, we present a framework that aims to evaluate PCDs, taking into account their non-linear behavior.

Approach

We employ small-signal analysis to study the behavior of PCDs under pile-up conditions. The response is approximated as linear around a given operating point, determined by the incident spectrum and fluence rate. The detector response is subsequently described by the proposed perturbation point spread function (pPSF). We demonstrate this approach using Monte-Carlo simulations of idealized direct- and indirect-conversion PCDs.

Results

The pPSFs of two PCDs are calculated. It is then shown how the pPSF allows to determine the sensitivity of the detector signal to an arbitrary lesion. This example illustrates the detrimental influence of pile-up, which may cause non-intuitive effects such as contrast/contrast-to-noise ratio inversion or cancellation between/within energy bins.

Conclusions

The proposed framework permits quantifying the spectral and spatial performance of PCDs under clinically realistic conditions at a given operating point. The presented example illustrates why PCDs should not be analyzed assuming that they are linear systems. The framework can, for example, be used to guide the development of PCDs and PCD-based systems. Furthermore, it can be applied to adapt commonly used measures, such as the modulation transfer function, to non-linear PCDs.

Noise power spectrum (NPS) in computed tomography: Enabling local NPS measurement without stationarity and ergodicity assumptions

BACKGROUND

Conventional methods for estimating the noise power spectrum (NPS) often necessitate multiple computed tomography (CT) data acquisitions and are required to satisfy stringent stationarity and ergodicity conditions, which prove challenging in CT imaging systems.

PURPOSE

The aim was to revisit the conventional NPS estimation method, leading to a new framework that estimates local NPS without relying on stationarity or ergodicity, thus facilitating experimental NPS estimations.

METHODS

The scientific foundation of the conventional CT NPS measurement method, based on the Wiener-Khintchine theorem, was reexamined, emphasizing the critical conditions of stationarity and ergodicity. This work proposes an alternative framework, characterized by its independence from stationarity and ergodicity, and its ability to facilitate local NPS estimations. A spatial average of local NPS over a Region of Interest (ROI) yields the conventional NPS for that ROI. The connections and differences between the proposed alternative method and the conventional method are discussed. Experimental studies were conducted to validate the new method.

RESULTS

(1) The NPS estimated using the conventional method was demonstrated to correspond to the spatial average of pointwise NPS from the proposed NPS estimation framework. (2) The NPS estimated over an ROI with the conventional method was shown to be the sum of the NPS estimated from the proposed method and a contribution from measurement uncertainty. (3) Local NPS estimations from the proposed method in this work elucidate the impact of surrounding image content on local NPS variations.

CONCLUSION

The NPS estimation method proposed in this work allows for the estimation of local NPS without relying on stationarity and ergodicity conditions, offering local NPS estimations with significantly improved precision.

Development and validation of a noise insertion algorithm for photon-counting-detector CT

BACKGROUND

Inserting noise into existing patient projection data to simulate lower-radiation-dose exams has been frequently used in traditional energy-integrating-detector (EID)-CT to optimize radiation dose in clinical protocols and to generate paired images for training deep-learning-based reconstruction and noise reduction methods. Recent introduction of photon counting detector CT (PCD-CT) also requires such a method to accomplish these tasks. However, clinical PCD-CT scanners often restrict the users access to the raw count data, exporting only the preprocessed, log-normalized sinogram. Therefore, it remains a challenge to employ projection domain noise insertion algorithms on PCD-CT.

PURPOSE

To develop and validate a projection domain noise insertion algorithm for PCD-CT that does not require access to the raw count data.

MATERIALS AND METHODS

A projection-domain noise model developed originally for EID-CT was adapted for PCD-CT. This model requires, as input, a map of the incident number of photons at each detector pixel when no object is in the beam. To obtain the map of incident number of photons, air scans were acquired on a PCD-CT scanner, then the noise equivalent photon number (NEPN) was calculated from the variance in the log normalized projection data of each scan. Additional air scans were acquired at various mA settings to investigate the impact of pulse pileup on the linearity of NEPN measurement. To validate the noise insertion algorithm, Noise Power Spectra (NPS) were generated from a 30 cm water tank scan and used to compare the noise texture and noise level of measured and simulated half dose and quarter dose images. An anthropomorphic thorax phantom was scanned with automatic exposure control, and noise levels at different slice locations were compared between simulated and measured half dose and quarter dose images. Spectral correlation between energy thresholds T1 and T2, and energy bins, B1 and B2, was compared between simulated and measured data across a wide range of tube current. Additionally, noise insertion was performed on a clinical patient case for qualitative assessment.

RESULTS

The NPS generated from simulated low dose water tank images showed similar shape and amplitude to that generated from the measured low dose images, differing by a maximum of 5.0% for half dose (HD) T1 images, 6.3% for HD T2 images, 4.1% for quarter dose (QD) T1 images, and 6.1% for QD T2 images. Noise versus slice measurements of the lung phantom showed comparable results between measured and simulated low dose images, with root mean square percent errors of 5.9%, 5.4%, 5.0%, and 4.6% for QD T1, HD T1, QD T2, and HD T2, respectively. NEPN measurements in air were linear up until 112 mA, after which pulse pileup effects significantly distort the air scan NEPN profile. Spectral correlation between T1 and T2 in simulation agreed well with that in the measured data in typical dose ranges.

CONCLUSIONS

A projection-domain noise insertion algorithm was developed and validated for PCD-CT to synthesize low-dose images from existing scans. It can be used for optimizing scanning protocols and generating paired images for training deep-learning-based methods.

Image quality models for 2D and 3D x-ray imaging systems: A perspective vignette

Image quality models based on cascaded systems analysis and task-based imaging performance were an important aspect of the emergence of 2D and 3D digital x-ray systems over the last 25 years. This perspective vignette offers cursory review of such developments and personal insights that may not be obvious within previously published scientific literature. The vignette traces such models to the mid-1990s, when flat-panel x-ray detectors were emerging as a new base technology for digital radiography and benefited from the rigorous, objective characterization of imaging performance gained from such models. The connection of models for spatial resolution and noise to spatial-frequency-dependent descriptors of imaging task provided a useful framework for system optimization that helped to accelerate the development of new technologies to first clinical use. Extension of the models to new technologies and applications is also described, including dual-energy imaging, photon-counting detectors, phase contrast imaging, tomosynthesis, cone-beam CT, 3D image reconstruction, and image registration.

Method of determining technique from weight and height to achieve targeted detector exposures in portable chest and abdominal digital radiography

This study presents a methodology to develop an X-ray technique chart for portable chest and abdomen imaging which utilizes patient data available in the modality worklist (MWL) to reliably achieve a predetermined exposure index (EI) at the detector for any patient size. The method assumes a correlation between the patients' tissue equivalent thickness and the square root of the ratio of the patient's weight to height. To assess variability in detector exposures, the EI statistics for 75 chest examinations and 99 abdominal portable X-ray images acquired with the new technique chart were compared to those from a single portable unit (chest: 3877 images; abdomen: 200 images) using a conventional technique chart with three patient sizes, and to a stationary radiography room utilizing automatic exposure control (AEC) (chest: 360 images; abdomen: 112 images). The results showed that when using the new technique chart on a group of portable units, the variability in EI was significantly reduced (p < 0.01) for both AP chest and AP abdomen images compared to the single portable using a standard technique chart with three patient sizes. The variability in EI for the images acquired with the new chart was comparable to the stationary X-ray room with an AEC system (p > 0.05). This method could be used to streamline the entire imaging chain by automatically selecting an X-ray technique based on patient demographic information contained in the MWL to provide higher quality examinations to clinicians by eliminating outliers. In addition, patient height and weight can be used to estimate the patients' tissue equivalent thickness.

Spectral Photon Counting CT: Imaging Algorithms and Performance Assessment

Photon counting x-ray detectors (PCDs) with spectral capabilities have the potential to revolutionize computed tomography (CT) for medical imaging. The ideal PCD provides accurate energy information for each incident x-ray, and at high spatial resolution. This information enables material-specific imaging, enhanced radiation dose efficiency, and improved spatial resolution in CT images. In practice, PCDs are affected by non-idealities, including limited energy resolution, pulse pileup, and cross talk due to charge sharing, K-fluorescence, and Compton scattering. In order to maximize their performance, PCDs must be carefully designed to reduce these effects and then later account for them during correction and post-acquisition steps. This review article examines algorithms for using PCDs in spectral CT applications, including how non-idealities impact image quality. Performance assessment metrics that account for spatial resolution and noise such as the detective quantum efficiency (DQE) can be used to compare different PCD designs, as well as compare PCDs with conventional energy integrating detectors (EIDs). These methods play an important role in enhancing spectral CT images and assessing the overall performance of PCDs.

An x-ray crosstalk correction method using FCNN for a novel energy resolving scheme in spectral CT

Spectral computed tomography has great potential for multi-energy imaging and anti-artifacts. The complete absorption-based energy resolving scheme of x-rays has been used for the integrity of detected information. However, this scheme is limited by the fact that the detector pixel thickness is high and fixed. Here, an energy resolving scheme is proposed using the crosstalk correction method for the incomplete absorption detection of x-rays. A fully connected neural network (FCNN)-based method was used to correct the difference caused by internal x-ray crosstalk of the edge-on detector. The energy and spatial features of the data which is collected in layers were combined to establish the mapping between the ideal data and the data with crosstalk at the pre-processing stage. Thereafter, to reconstruct the stable and highly accurate energy-resolving equations, the layers with low relative energy difference were selected and grouped together to reduce the accumulation difference. The experiment results demonstrate the feasibility of this energy resolving scheme. The differences caused by crosstalk can be suppressed through the proposed FCNN-based method. The resolving accuracy can be further improved by grouping more layers at forward positions in the pixel. Moreover, this improvement can be observed in the reconstructed images with reduced artifacts and improved quality.

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.

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.

Detective quantum efficiency of photon-counting CdTe and Si detectors for computed tomography: a simulation study

Purpose: Developing photon-counting CT detectors requires understanding the impact of parameters, such as converter material, thickness, and pixel size. We apply a linear-systems framework, incorporating spatial and energy resolution, to study realistic silicon (Si) and cadmium telluride (CdTe) detectors at a low count rate. Approach: We compared CdTe detector designs with 0.5 × 0.5    mm 2 and 0.225 × 0.225    mm 2 pixels and Si detector designs with 0.5 × 0.5    mm 2 pixels of 30 and 60 mm active thickness, with and without tungsten scatter blockers. Monte-Carlo simulations of photon transport were used together with Gaussian charge sharing models fitted to published data. Results: For detection in a 300-mm-thick object at 120 kVp, the 0.5- and 0.225-mm pixel CdTe systems have 28% to 41% and 5% to 29% higher detective quantum efficiency (DQE), respectively, than the 60-mm Si system with tungsten, whereas the corresponding numbers for two-material decomposition are 2% lower to 11% higher DQE and 31% to 54% lower DQE compared to Si. We also show that combining these detectors with dual-spectrum acquisition is beneficial. Conclusions: In the low-count-rate regime, CdTe detector systems outperform the Si systems for detection tasks, whereas silicon outperforms one or both of the CdTe systems for material decomposition.

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

Purpose

We present a new framework for theoretical analysis of the noise power spectrum (NPS) of photon‐counting x‐ray detectors, including simple photon‐counting detectors (SPCDs) and spectroscopic x‐ray detectors (SXDs), the latter of which use multiple energy thresholds to discriminate photon energies.

Methods

We show that the NPS of SPCDs and SXDs, including spatio‐energetic noise correlations, is determined by the joint probability density function (PDF) of deposited photon energies, which describes the probability of recording two photons of two different energies in two different elements following a single‐photon interaction. We present an analytic expression for this joint PDF and calculate the presampling and digital NPS of CdTe SPCDs and SXDs. We calibrate our charge sharing model using the energy response of a cadmium zinc telluride (CZT) spectroscopic x‐ray detector and compare theoretical results with Monte Carlo simulations.

Results

Our analysis shows that charge sharing increases pixel signal‐to‐noise ratio (SNR), but degrades the zero‐frequency signal‐to‐noise performance of SPCDs and SXDs. In all cases considered, this degradation was greater than 10%. Comparing the presampling NPS with the sampled NPS showed that degradation in zero‐frequency performance is due to zero‐frequency noise aliasing induced by charge sharing.

Conclusions

Noise performance, including spatial and energy correlations between elements and energy bins, are described by the joint PDF of deposited energies which provides a method of determining the photon‐counting NPS, including noise‐aliasing effects and spatio‐energetic effects in spectral imaging. Our approach enables separating noise due to x‐ray interactions from that associated with sampling, consistent with cascaded systems analysis of energy‐integrating systems. Our methods can be incorporated into task‐based assessment of image quality for the design and optimization of spectroscopic x‐ray detectors.

An On-Board Spectral-CT/CBCT/SPECT Imaging Configuration for Small-Animal Radiation Therapy Platform: A Monte Carlo Study

This study investigated the feasibility of a highly specific multiplexed image-guided small animal radiation therapy (SART) platform based on triple imaging from on-board single-photon emission computed tomography (SPECT), spectral-CT, and cone-beam CT (CBCT) guidance in radiotherapy treatment. As a proof-of-concept, the SART system was built with the capability of triple on-board image guidance by utilizing an x-ray tube and a single cadmium zinc telluride (CZT) semiconductor photon-counting imager via a Monte Carlo simulation study. The x-ray tube can be set at a low tube current for imaging mode and a high tube current for radiation therapy mode, respectively. In the imaging mode, both x-ray and gamma-ray projection data were collected by the imager to reconstruct CBCT, SPECT and spectral CT images of small animals being treated. The modulation transfer function (MTF) of the pixelated CZT imager measured was 8.6 lp/mm. The overall performances of the CBCT and SPECT imaging of the system were evaluated with sufficient spatial resolution and imaging quality to be fitted into the SART platform. The material differentiation and decomposition capacities of spectral CT within the system were verified using K-edge imaging, image-based optimal energy weighted imaging, and image-based linear material decomposition methods. The triple imaging capability of the system was demonstrated using a PMMA phantom containing gadolinium, iodine and radioisotope ^99mTc inserts. All the probes were clearly identified in the registered image. The results demonstrated that a novel SART platform with high-quality on-board CBCT, spectral-CT, SPECT image guidance is technically feasible by using a single semiconductor imager, thus affording comprehensive image guidance from anatomical, functional, and molecular levels for radiation treatment beam delivery.

Task-driven optimization of the non-spectral mode of photon counting CT for intracranial hemorrhage assessment

Non-contrast CT (NCCT) is widely employed as the first-line imaging test to evaluate intracranial hemorrhage (ICH). Advances in mutidetector CT (MDCT) technology have greatly improved the image quality of NCCT for the detection of established, relatively large, and acute ICHs. Meanwhile, the reliability of MDCT in detecting microbleeds and chronic hemorrhage, and in predicting hemorrhagic transformation needs to be further improved. The purpose of this work was to investigate the potential use of non-spectral photon counting CT (PCCT) to address these challenges in ICH imaging. Towards this goal, the NCCT protocol of an experimental PCCT system that simulates the geometry of a general-purpose MDCT was optimized. The optimization was driven by three imaging tasks: detection of a 4.0 mm intraparenchymal hemorrhage, detection of a 1.5 mm subarachnoid hemorrhage, and discrimination of a sulcus in the insular cortex from the parenchymal background. These imaging tasks were custom-built into an anthropomorphic head phantom. Under the guidance of the frequency-dependent noise equivalent quanta and the ideal observer model detectability index [Formula: see text], the optimal PCD detection mode, energy threshold, and reconstruction kernel were found to be the anti-charge sharing mode, 15 keV, and an apodized ramp kernel, respectively. Compared with a clinical MDCT operated with an ICH protocol and at a matched dose level, the PCCT system provided at least 20% improvements in [Formula: see text] for all three ICH imaging tasks. These results demonstrated the potential benefits of non-spectral PCCT in ICH assessment.

Resolution characterization of a silicon-based, photon-counting computed tomography prototype capable of patient scanning

Photon-counting detectors are expected to bring a range of improvements to patient imaging with x-ray computed tomography (CT). One is higher spatial resolution. We demonstrate the resolution obtained using a commercial CT scanner where the original energy-integrating detector has been replaced by a single-slice, silicon-based, photon-counting detector. This prototype constitutes the first full-field-of-view silicon-based CT scanner capable of patient scanning. First, the pixel response function and focal spot profile are measured and, combining the two, the system modulation transfer function is calculated. Second, the prototype is used to scan a resolution phantom and a skull phantom. The resolution images are compared to images from a state-of-the-art CT scanner. The comparison shows that for the prototype 19    lp / cm are detectable with the same clarity as 14    lp / cm on the reference scanner at equal dose and reconstruction grid, with more line pairs visible with increasing dose and decreasing image pixel size. The high spatial resolution remains evident in the anatomy of the skull phantom and is comparable to that of other photon-counting CT prototypes present in the literature. We conclude that the deep silicon-based detector used in our study could provide improved spatial resolution in patient imaging without increasing the x-ray dose.

Impacts of photon counting CT to maximum intensity projection (MIP) images of cerebral CT angiography: theoretical and experimental studies

While CTA is an established clinical gold standard for imaging large cerebral arteries and veins, an important challenge that currently remains for CTA is its limited performance in imaging small perforating arteries with diameters below 0.5 mm. The purpose of this work was to theoretically and experimentally study the potential benefits of using photon counting detector (PCD)-based CT (PCCT) to improve the performance of CTA in imaging these small arteries. In particular, the study focused on an important component of the CTA image package known as the maximum intensity projection (MIP) image. To help understand how the physical properties of a detector quantitatively influence the MIP image quality, a theoretical model on the statistical properties of MIP images was developed. After validating this model, it was used to explore the individual and joint contribution of the following detector properties to the MIP signal-to-noise ratio (SNR): inter-slice noise covariance, spatial resolution along the z direction, and native pixel pitch along z. The model demonstrated that superior slice sensitivity, reduced inter-slice noise correlation, and smaller native pixel pitch along z provided by PCDs lead to improved vessel SNR in MIP images. Finally, experiments were performed by scanning an anthropomorphic cerebral angiographic phantom using a benchtop PCCT system and a commercial MDCT system. The experimental MIP results consistently demonstrated that compared with MDCT, PCCT provides superior vessel conspicuity and reduced artifactual stenosis.

An experimental method to directly measure DQE[Formula: see text] at k = 0 for 2D x-ray imaging systems

The zero-frequency detective quantum efficiency (DQE), viz., DQE0, is defined as the ratio between output and input squared signal-to-noise ratio of an imaging system. In 1963, R. Shaw applied Fourier analysis to generalize DQE0 to the frequency-dependent DQE, i.e. DQE[Formula: see text]. Under conditions specified by Shaw, DQE[Formula: see text] is the same as DQE0 at k  =  0. The experimental measurement of DQE[Formula: see text] involves the measurement of system modulation transfer function (MTF) and noise power spectrum (NPS). Although the measurement of MTF is straightforward, the experimental measurements of NPS[Formula: see text] encountered several challenges. As a result, some experimental methods may yield a nonphysical NPS value at k  =  0, which makes the measured DQE(k)| k=0 deviate from the true zero-frequency DQE. This work presents new results from three aspects: 1) system drift is a significant error source when a large number of independent image acquisitions are involved in measuring NPS and DQE; 2) a cascaded systems analysis shows that the drift induces a global positive offset to the measured autocovariance function, and the offset is quantitatively related to the NPS error at k  =  0; 3) based on the measured autocovariance data, drift-induced offset can be estimated, so that errors in the measured NPS(k)| k=0 and DQE(k)| k=0 can be corrected. Both numerical simulations with known ground truth for DQE0 and experimental studies were performed to validate the proposed measurement method. The results demonstrated that the method mitigates the undesirable influence of system drift in DQE(k)| k=0 and DQE0, allowing the measured values consistent with the classical definition of zero-frequency DQE.

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.

Photon-counting CT: Technical Principles and Clinical Prospects

Photon-counting CT is an emerging technology with the potential to dramatically change clinical CT. Photon-counting CT uses new energy-resolving x-ray detectors, with mechanisms that differ substantially from those of conventional energy-integrating detectors. Photon-counting CT detectors count the number of incoming photons and measure photon energy. This technique results in higher contrast-to-noise ratio, improved spatial resolution, and optimized spectral imaging. Photon-counting CT can reduce radiation exposure, reconstruct images at a higher resolution, correct beam-hardening artifacts, optimize the use of contrast agents, and create opportunities for quantitative imaging relative to current CT technology. In this review, the authors will explain the technical principles of photon-counting CT in nonmathematical terms for radiologists and clinicians. Following a general overview of the current status of photon-counting CT, they will explain potential clinical applications of this technology.

Cascaded systems analysis of shift-variant image quality in slit-scanning breast tomosynthesis

PURPOSE

Digital breast tomosynthesis (DBT) is becoming an important part of breast cancer screening and diagnosis. Compared to two-dimensional mammography, tomosynthesis introduces limited three-dimensional (3D) resolution, but maintains high in-plane resolution, low dose, and allows for similar clinical protocols. The scanning motion and oblique projections of tomosynthesis acquisitions introduce shift-variance to the image quality, in addition to effects such as source blurring and geometric magnification. Shift-variant detector response caused by oblique incidence has been extensively studied previously and is most easily mitigated by letting the source and detector move in sync. In addition, conical reconstruction grids, that is, a grid aligned with the central tomosynthesis projection, have been proposed to compensate for magnification effects. This paper introduces a shift-variant cascaded systems model for tomosynthesis and validates it against measurements. As an example, the model was used to investigate the shift-variance of a tomosynthesis system.

METHODS

The shift-variant cascaded systems model was validated on a slit-scanning photon-counting DBT system, with synchronous source-detector movement, using simple back-projection in a conical reconstruction volume. The modulation transfer function (MTF), normalized noise-power spectrum (NNPS), and detective quantum efficiency (DQE) were used as figures of merit. Simulations were performed for single points while measurements were done over a finite volume, assuming local shift invariance. To investigate the full extent of shift-variance, 80 locations across the volume were simulated, and the MTF and DQE at 2.5 lp/mm were calculated as a function of position.

RESULTS

The simulated metrics generally agreed well with their corresponding measurements. The frequency at 50% MTF along the scan direction showed a relatively small variation, ranging from 2.1 to 2.4 lp/mm for the different locations. The frequency at 50% MTF along the chest-mammilla direction showed a larger variation, ranging from 2.9 to 3.8 lp/mm. All points exhibited a similarly shaped NNPS but the noise magnitude varied with slice height. The zero-frequency DQE in reconstructed slices was lower than that of the projections, an effect likely caused by noise-aliasing increasing the zero-frequency noise.

CONCLUSIONS

A shift-variant cascaded systems model has been developed for slit-scanning tomosynthesis using simple back-projection. The model was successfully validated against measurements. Even though the study was performed on a slit-scanning system, several parts of the framework can be applied and extended to other tomosynthesis geometries. The conical reconstruction grid has low variation in image quality in the scan direction where the 3D information is acquired, but source and geometric magnification still dominate in the slit direction, causing a larger variation in image quality. We conclude that image quality is close to shift-invariant in the scan direction, but not in the height and chest-mammilla directions, and we recommend that small measurement volumes are used when measuring image quality in these directions to minimize the effects of shift variance.

Impact of anti-charge sharing on the zero-frequency detective quantum efficiency of CdTe-based photon counting detector system: cascaded systems analysis and experimental validation

Inter-pixel communication and anti-charge sharing (ACS) technologies have been introduced to photon counting detector (PCD) systems to address the undesirable charge sharing problem. In addition to improving the energy resolution of PCD, ACS may also influence other aspects of PCD performance such as detector multiplicity (i.e. the number of pixels triggered by each interacted photon) and detective quantum efficiency (DQE). In this work, a theoretical model was developed to address how ACS impacts the multiplicity and zero-frequency DQE [DQE(0)] of PCD systems. The work focused on cadmium telluride (CdTe)-based PCD that often involves the generation and transport of K-fluorescence photons. Under the parallel cascaded systems analysis framework, the theory takes both photoelectric and scattering effects into account, and it also considers both the reabsorption and escape of photons. In a new theoretical treatment of ACS, it was considered as a modified version of the conventional single pixel (i.e. non-ACS) mode, but with reduced charge spreading distance and K-fluorescence travel distance. The proposed theoretical model does not require prior knowledge of the detailed ACS implementation method for each specific PCD, and its parameters can be experimentally determined using a radioisotope without invoking any Monte-Carlo simulation. After determining the model parameters, independent validation experiments were performed using a diagnostic x-ray tube and four different polychromatic beams (from 50 to 120 kVp). Both the theoretical and experimental results demonstrate that ACS increased the first and second moments of multiplicity for a majority of the x-ray energy and threshold levels tested, except when the threshold level was much lower than the x-ray energy level. However, ACS always improved DQE(0) at all energy and threshold levels tested.

Modeling the frequency-dependent detective quantum efficiency of photon-counting x-ray detectors

PURPOSE

To find a simple model for the frequency-dependent detective quantum efficiency (DQE) of photon-counting detectors in the low flux limit.

METHODS

Formula for the spatial cross-talk, the noise power spectrum and the DQE of a photon-counting detector working at a given threshold are derived. Parameters are probabilities for types of events like single counts in the central pixel, double counts in the central pixel and a neighboring pixel or single count in a neighboring pixel only. These probabilities can be derived in a simple model by extensive use of Monte Carlo techniques: The Monte Carlo x-ray propagation program MOCASSIM is used to simulate the energy deposition from the x-rays in the detector material. A simple charge cloud model using Gaussian clouds of fixed width is used for the propagation of the electric charge generated by the primary interactions. Both stages are combined in a Monte Carlo simulation randomizing the location of impact which finally produces the required probabilities. The parameters of the charge cloud model are fitted to the spectral response to a polychromatic spectrum measured with our prototype detector.

RESULTS

Based on the Monte Carlo model, the DQE of photon-counting detectors as a function of spatial frequency is calculated for various pixel sizes, photon energies, and thresholds.

CONCLUSION

The frequency-dependent DQE of a photon-counting detector in the low flux limit can be described with an equation containing only a small set of probabilities as input. Estimates for the probabilities can be derived from a simple model of the detector physics.

Estimation of Basis Line-Integrals in a Spectral Distortion-Modeled Photon Counting Detector Using Low-Rank Approximation-Based X-Ray Transmittance Modeling: K-Edge Imaging Application

Photon counting detectors (PCDs) provide multiple energy-dependent measurements for estimating basis line-integrals. However, the measured spectrum is distorted from the spectral response effect (SRE) via charge sharing, K-fluorescence emission, and so on. Thus, in order to avoid bias and artifacts in images, the SRE needs to be compensated. For this purpose, we recently developed a computationally efficient three-step algorithm for PCD-CT without contrast agents by approximating smooth X-ray transmittance using low-order polynomial bases. It compensated the SRE by incorporating the SRE model in a linearized estimation process and achieved nearly the minimum variance and unbiased (MVU) estimator. In this paper, we extend the three-step algorithm to K-edge imaging applications by designing optimal bases using a low-rank approximation to model X-ray transmittances with arbitrary shapes (i.e., smooth without the K-edge or discontinuous with the K-edge). The bases can be used to approximate the X-ray transmittance and to linearize the PCD measurement modeling and then the three-step estimator can be derived as in the previous approach: estimating the x-ray transmittance in the first step, estimating basis line-integrals including that of the contrast agent in the second step, and correcting for a bias in the third step. We demonstrate that the proposed method is more accurate and stable than the low-order polynomial-based approaches with extensive simulation studies using gadolinium for the K-edge imaging application. We also demonstrate that the proposed method achieves nearly MVU estimator, and is more stable than the conventional maximum likelihood estimator in high attenuation cases with fewer photon counts.

Feasibility of Dose-reduced Chest CT with Photon-counting Detectors: Initial Results in Humans

Purpose To investigate whether photon-counting detector (PCD) technology can improve dose-reduced chest computed tomography (CT) image quality compared with that attained with conventional energy-integrating detector (EID) technology in vivo. Materials and Methods This was a HIPAA-compliant institutional review board-approved study, with informed consent from patients. Dose-reduced spiral unenhanced lung EID and PCD CT examinations were performed in 30 asymptomatic volunteers in accordance with manufacturer-recommended guidelines for CT lung cancer screening (120-kVp tube voltage, 20-mAs reference tube current-time product for both detectors). Quantitative analysis of images included measurement of mean attenuation, noise power spectrum (NPS), and lung nodule contrast-to-noise ratio (CNR). Images were qualitatively analyzed by three radiologists blinded to detector type. Reproducibility was assessed with the intraclass correlation coefficient (ICC). McNemar, paired t, and Wilcoxon signed-rank tests were used to compare image quality. Results Thirty study subjects were evaluated (mean age, 55.0 years ± 8.7 [standard deviation]; 14 men). Of these patients, 10 had a normal body mass index (BMI) (BMI range, 18.5-24.9 kg/m²; group 1), 10 were overweight (BMI range, 25.0-29.9 kg/m²; group 2), and 10 were obese (BMI ≥30.0 kg/m², group 3). PCD diagnostic quality was higher than EID diagnostic quality (P = .016, P = .016, and P = .013 for readers 1, 2, and 3, respectively), with significantly better NPS and image quality scores for lung, soft tissue, and bone and with fewer beam-hardening artifacts (all P < .001). Image noise was significantly lower for PCD images in all BMI groups (P < .001 for groups 1 and 3, P < .01 for group 2), with higher CNR for lung nodule detection (12.1 ± 1.7 vs 10.0 ± 1.8, P < .001). Inter- and intrareader reproducibility were good (all ICC > 0.800). Conclusion Initial human experience with dose-reduced PCD chest CT demonstrated lower image noise compared with conventional EID CT, with better diagnostic quality and lung nodule CNR. ^© RSNA, 2017 Online supplemental material is available for this article.

Spatio-energetic cross talk in photon counting detectors: Detector model and correlated Poisson data generator

PURPOSE

An x-ray photon interacts with photon counting detectors (PCDs) and generates an electron charge cloud or multiple clouds. The clouds (thus, the photon energy) may be split between two adjacent PCD pixels when the interaction occurs near pixel boundaries, producing a count at both of the pixels. This is called double-counting with charge sharing. (A photoelectric effect with K-shell fluorescence x-ray emission would result in double-counting as well). As a result, PCD data are spatially and energetically correlated, although the output of individual PCD pixels is Poisson distributed. Major problems include the lack of a detector noise model for the spatio-energetic cross talk and lack of a computationally efficient simulation tool for generating correlated Poisson data. A Monte Carlo (MC) simulation can accurately simulate these phenomena and produce noisy data; however, it is not computationally efficient.

METHODS

In this study, the authors developed a new detector model and implemented it in an efficient software simulator that uses a Poisson random number generator to produce correlated noisy integer counts. The detector model takes the following effects into account: (1) detection efficiency; (2) incomplete charge collection and ballistic effect; (3) interaction with PCDs via photoelectric effect (with or without K-shell fluorescence x-ray emission, which may escape from the PCDs or be reabsorbed); and (4) electronic noise. The correlation was modeled by using these two simplifying assumptions: energy conservation and mutual exclusiveness. The mutual exclusiveness is that no more than two pixels measure energy from one photon. The effect of model parameters has been studied and results were compared with MC simulations. The agreement, with respect to the spectrum, was evaluated using the reduced χ² statistics or a weighted sum of squared errors, χ_red²(≥1), where χ_red²=1 indicates a perfect fit.

RESULTS

The model produced spectra with flat field irradiation that qualitatively agree with previous studies. The spectra generated with different model and geometry parameters allowed for understanding the effect of the parameters on the spectrum and the correlation of data. The agreement between the model and MC data was very strong. The mean spectra with 90 keV and 140 kVp agreed exceptionally well: χ_red² values were 1.049 with 90 keV data and 1.007 with 140 kVp data. The degrees of cross talk (in terms of the relative increase from single pixel irradiation to flat field irradiation) were 22% with 90 keV and 19% with 140 kVp for MC simulations, while they were 21% and 17%, respectively, for the model. The covariance was in strong agreement qualitatively, although it was overestimated. The noisy data generation was very efficient, taking less than a CPU minute as opposed to CPU hours for MC simulators.

CONCLUSIONS

The authors have developed a novel, computationally efficient PCD model that takes into account double-counting and resulting spatio-energetic correlation between PCD pixels. The MC simulation validated the accuracy.

Signal and noise characteristics of a CdTe-based photon counting detector: Cascaded systems analysis and experimental studies

Recent advances in single photon counting detectors (PCDs) are opening up new opportunities in medical imaging. However, the performance of PCDs is not flawless. Problems such as charge sharing may deteriorate the performance of PCD. This work studied the dependence of the signal and noise properties of a cadmium telluride (CdTe)-based PCD on the charge sharing effect and the anti-charge sharing (ACS) capability offered by the PCD. Through both serial and parallel cascaded systems analysis, a theoretical model was developed to trace the origin of charge sharing in CdTe-based PCD, which is primarily related to remote k-fluorescence re-absorption and spatial spreading of charge cloud. The ACS process was modeled as a sub-imaging state prior to the energy thresholding stage, and its impact on the noise power spectrum (NPS) of PCD can be qualitatively determined by the theoretical model. To validate the theoretical model, experimental studies with a CdTe-based PCD system (XC-FLITE X1, XCounter AB) was performed. Two x-ray radiation conditions, including an RQA-5 beam and a 40 kVp beam, were used for the NPS measurements. Both theoretical predictions and experimental results showed that ACS makes the NPS of the CdTe-based PCD flatter, which corresponds to reduced noise correlation length. The flatness of the NPS is further boosted by increasing the energy threshold or reducing the x-ray energy, both of which reduce the likelihood of registering multiple counts from the same incidenting x-ray photon.

Estimation of Basis Line-Integrals in a Spectral Distortion-Modeled Photon Counting Detector Using Low-Order Polynomial Approximation of X-ray Transmittance

Photon counting detector (PCD)-based computed tomography exploits spectral information from a transmitted x-ray spectrum to estimate basis line-integrals. The recorded spectrum, however, is distorted and deviates from the transmitted spectrum due to spectral response effect (SRE). Therefore, the SRE needs to be compensated for when estimating basis line-integrals. One approach is to incorporate the SRE model with an incident spectrum into the PCD measurement model and the other approach is to perform a calibration process that inherently includes both the SRE and the incident spectrum. A maximum likelihood estimator can be used to the former approach, which guarantees asymptotic optimality; however, a heavy computational burden is a concern. Calibration-based estimators are a form of the latter approach. They can be very efficient; however, a heuristic calibration process needs to be addressed. In this paper, we propose a computationally efficient three-step estimator for the former approach using a low-order polynomial approximation of x-ray transmittance. The low-order polynomial approximation can change the original non-linear estimation method to a two-step linearized approach followed by an iterative bias correction step. We show that the calibration process is required only for the bias correction step and prove that it converges to the unbiased solution under practical assumptions. Extensive simulation studies validate the proposed method and show that the estimation results are comparable to those of the ML estimator while the computational time is reduced substantially.

Technical Note: spektr 3.0-A computational tool for x-ray spectrum modeling and analysis

PURPOSE

A computational toolkit (spektr 3.0) has been developed to calculate x-ray spectra based on the tungsten anode spectral model using interpolating cubic splines (TASMICS) algorithm, updating previous work based on the tungsten anode spectral model using interpolating polynomials (TASMIP) spectral model. The toolkit includes a matlab (The Mathworks, Natick, MA) function library and improved user interface (UI) along with an optimization algorithm to match calculated beam quality with measurements.

METHODS

The spektr code generates x-ray spectra (photons/mm(2)/mAs at 100 cm from the source) using TASMICS as default (with TASMIP as an option) in 1 keV energy bins over beam energies 20-150 kV, extensible to 640 kV using the TASMICS spectra. An optimization tool was implemented to compute the added filtration (Al and W) that provides a best match between calculated and measured x-ray tube output (mGy/mAs or mR/mAs) for individual x-ray tubes that may differ from that assumed in TASMICS or TASMIP and to account for factors such as anode angle.

RESULTS

The median percent difference in photon counts for a TASMICS and TASMIP spectrum was 4.15% for tube potentials in the range 30-140 kV with the largest percentage difference arising in the low and high energy bins due to measurement errors in the empirically based TASMIP model and inaccurate polynomial fitting. The optimization tool reported a close agreement between measured and calculated spectra with a Pearson coefficient of 0.98.

CONCLUSIONS

The computational toolkit, spektr, has been updated to version 3.0, validated against measurements and existing models, and made available as open source code. Video tutorials for the spektr function library, UI, and optimization tool are available.

A comprehensive model for quantum noise characterization in digital mammography

A version of cascaded systems analysis was developed specifically with the aim of studying quantum noise propagation in x-ray detectors. Signal and quantum noise propagation was then modelled in four types of x-ray detectors used for digital mammography: four flat panel systems, one computed radiography and one slot-scan silicon wafer based photon counting device. As required inputs to the model, the two dimensional (2D) modulation transfer function (MTF), noise power spectra (NPS) and detective quantum efficiency (DQE) were measured for six mammography systems that utilized these different detectors. A new method to reconstruct anisotropic 2D presampling MTF matrices from 1D radial MTFs measured along different angular directions across the detector is described; an image of a sharp, circular disc was used for this purpose. The effective pixel fill factor for the FP systems was determined from the axial 1D presampling MTFs measured with a square sharp edge along the two orthogonal directions of the pixel lattice. Expectation MTFs were then calculated by averaging the radial MTFs over all possible phases and the 2D EMTF formed with the same reconstruction technique used for the 2D presampling MTF. The quantum NPS was then established by noise decomposition from homogenous images acquired as a function of detector air kerma. This was further decomposed into the correlated and uncorrelated quantum components by fitting the radially averaged quantum NPS with the radially averaged EMTF(2). This whole procedure allowed a detailed analysis of the influence of aliasing, signal and noise decorrelation, x-ray capture efficiency and global secondary gain on NPS and detector DQE. The influence of noise statistics, pixel fill factor and additional electronic and fixed pattern noises on the DQE was also studied. The 2D cascaded model and decompositions performed on the acquired images also enlightened the observed quantum NPS and DQE anisotropy.

Volumetric CT with sparse detector arrays (and application to Si-strip photon counters)

Novel x-ray medical imaging sensors, such as photon counting detectors (PCDs) and large area CCD and CMOS cameras can involve irregular and/or sparse sampling of the detector plane. Application of such detectors to CT involves undersampling that is markedly different from the commonly considered case of sparse angular sampling. This work investigates volumetric sampling in CT systems incorporating sparsely sampled detectors with axial and helical scan orbits and evaluates performance of model-based image reconstruction (MBIR) with spatially varying regularization in mitigating artifacts due to sparse detector sampling. Volumetric metrics of sampling density and uniformity were introduced. Penalized-likelihood MBIR with a spatially varying penalty that homogenized resolution by accounting for variations in local sampling density (i.e. detector gaps) was evaluated. The proposed methodology was tested in simulations and on an imaging bench based on a Si-strip PCD (total area 5 cm  ×  25 cm) consisting of an arrangement of line sensors separated by gaps of up to 2.5 mm. The bench was equipped with translation/rotation stages allowing a variety of scanning trajectories, ranging from a simple axial acquisition to helical scans with variable pitch. Statistical (spherical clutter) and anthropomorphic (hand) phantoms were considered. Image quality was compared to that obtained with a conventional uniform penalty in terms of structural similarity index (SSIM), image uniformity, spatial resolution, contrast, and noise. Scan trajectories with intermediate helical width (~10 mm longitudinal distance per 360° rotation) demonstrated optimal tradeoff between the average sampling density and the homogeneity of sampling throughout the volume. For a scan trajectory with 10.8 mm helical width, the spatially varying penalty resulted in significant visual reduction of sampling artifacts, confirmed by a 10% reduction in minimum SSIM (from 0.88 to 0.8) and a 40% reduction in the dispersion of SSIM in the volume compared to the constant penalty (both penalties applied at optimal regularization strength). Images of the spherical clutter and wrist phantoms confirmed the advantages of the spatially varying penalty, showing a 25% improvement in image uniformity and 1.8  ×  higher CNR (at matched spatial resolution) compared to the constant penalty. The studies elucidate the relationship between sampling in the detector plane, acquisition orbit, sampling of the reconstructed volume, and the resulting image quality. They also demonstrate the benefit of spatially varying regularization in MBIR for scenarios with irregular sampling patterns. Such findings are important and integral to the incorporation of a sparsely sampled Si-strip PCD in CT imaging.

Spectral CT of the Extremities with a Silicon Strip Photon Counting Detector

PURPOSE

Photon counting x-ray detectors (PCXDs) are an important emerging technology for spectral imaging and material differentiation with numerous potential applications in diagnostic imaging. We report development of a Si-strip PCXD system originally developed for mammography with potential application to spectral CT of musculoskeletal extremities, including challenges associated with sparse sampling, spectral calibration, and optimization for higher energy x-ray beams.

METHODS

A bench-top CT system was developed incorporating a Si-strip PCXD, fixed anode x-ray source, and rotational and translational motions to execute complex acquisition trajectories. Trajectories involving rotation and translation combined with iterative reconstruction were investigated, including single and multiple axial scans and longitudinal helical scans. The system was calibrated to provide accurate spectral separation in dual-energy three-material decomposition of soft-tissue, bone, and iodine. Image quality and decomposition accuracy were assessed in experiments using a phantom with pairs of bone and iodine inserts (3, 5, 15 and 20 mm) and an anthropomorphic wrist.

RESULTS

The designed trajectories improved the sampling distribution from 56% minimum sampling of voxels to 75%. Use of iterative reconstruction (viz., penalized likelihood with edge preserving regularization) in combination with such trajectories resulted in a very low level of artifacts in images of the wrist. For large bone or iodine inserts (>5 mm diameter), the error in the estimated material concentration was <16% for (50 mg/mL) bone and <8% for (5 mg/mL) iodine with strong regularization. For smaller inserts, errors of 20-40% were observed and motivate improved methods for spectral calibration and optimization of the edge-preserving regularizer.

CONCLUSION

Use of PCXDs for three-material decomposition in joint imaging proved feasible through a combination of rotation-translation acquisition trajectories and iterative reconstruction with optimized regularization.

Cascaded systems analysis of photon counting detectors

PURPOSE

Photon counting detectors (PCDs) are an emerging technology with applications in spectral and low-dose radiographic and tomographic imaging. This paper develops an analytical model of PCD imaging performance, including the system gain, modulation transfer function (MTF), noise-power spectrum (NPS), and detective quantum efficiency (DQE).

METHODS

A cascaded systems analysis model describing the propagation of quanta through the imaging chain was developed. The model was validated in comparison to the physical performance of a silicon-strip PCD implemented on an experimental imaging bench. The signal response, MTF, and NPS were measured and compared to theory as a function of exposure conditions (70 kVp, 1-7 mA), detector threshold, and readout mode (i.e., the option for coincidence detection). The model sheds new light on the dependence of spatial resolution, charge sharing, and additive noise effects on threshold selection and was used to investigate the factors governing PCD performance, including the fundamental advantages and limitations of PCDs in comparison to energy-integrating detectors (EIDs) in the linear regime for which pulse pileup can be ignored.

RESULTS

The detector exhibited highly linear mean signal response across the system operating range and agreed well with theoretical prediction, as did the system MTF and NPS. The DQE analyzed as a function of kilovolt (peak), exposure, detector threshold, and readout mode revealed important considerations for system optimization. The model also demonstrated the important implications of false counts from both additive electronic noise and charge sharing and highlighted the system design and operational parameters that most affect detector performance in the presence of such factors: for example, increasing the detector threshold from 0 to 100 (arbitrary units of pulse height threshold roughly equivalent to 0.5 and 6 keV energy threshold, respectively), increased the f50 (spatial-frequency at which the MTF falls to a value of 0.50) by ∼30% with corresponding improvement in DQE. The range in exposure and additive noise for which PCDs yield intrinsically higher DQE was quantified, showing performance advantages under conditions of very low-dose, high additive noise, and high fidelity rejection of coincident photons.

CONCLUSIONS

The model for PCD signal and noise performance agreed with measurements of detector signal, MTF, and NPS and provided a useful basis for understanding complex dependencies in PCD imaging performance and the potential advantages (and disadvantages) in comparison to EIDs as well as an important guide to task-based optimization in developing new PCD imaging systems.