**Can image-domain filtering of FBP CT reconstructions match low-contrast performance of iterative reconstructions?**

S. E. Divel, S. S. Hsieh, J. Wang, N. J. Pelc

SPIE Medical Imaging 2018: Physics of Medical Imaging , vol. 10573, pp. 105731A, 2018

**Abstract**

In large part from concerns about radiation exposure from computed tomography (CT), iterative reconstruction (IR) has emerged as a popular technique for dose reduction. Although IR clearly reduces image noise and improves resolution, its ability to maintain or improve low-contrast detectability over (possibly post-processed) filtered backprojection (FBP) reconstructions is unclear. In this work, we have scanned a low contrast phantom encased in an acrylic oval using two vendors’ scanners at 120 kVp at three dose levels for axial and helical acquisitions with and without automatic exposure control. Using the local noise power spectra of the FBP and IR images to guide the filter design, we developed a two-dimensional angularly-dependent Gaussian filter in the frequency domain that can be optimized to minimize the root-mean-square error between the image-domain filtered FBP and IR reconstructions. The filter is extended to three-dimensions by applying a through-slice Gaussian filter in the image domain. Using this three-dimensional, non-isotropic filtering approach on data with non-uniform statistics from both scanners, we were able to process the FBP reconstructions to closely match the low-contrast performance of IR images reconstructed from the same raw data. From this, we conclude that most or all of the benefits of noise reduction and low-contrast performance of advanced reconstruction can be achieved with adaptive linear filtering of FBP reconstructions in the image domain.

View details for DOI 10.1117/12.2292599

**Generalized linear-systems framework for performance assessment of energy-resolving photon-counting detectors**

M. Persson, P. L. Rajbhandary, N. J. Pelc

SPIE Medical Imaging 2018: Physics of Medical Imaging , vol. 10573, pp. 105731A, 2018

**Abstract**

The development of energy-resolving photon-counting detectors for medical x-ray imaging is attracting considerable attention. Since the image quality can be degraded by different nonidealities such as charge sharing, Compton scatter and fluorescence, there is a need for developing performance metrics in order to compare and optimize detector designs. For conventional, non-energy-resolving detectors, this is commonly done using the linear-systems-theory framework, in which the detector performance is described by noise-equivalent quanta (NEQ) and detective quantum efficiency (DQE) as functions of spatial frequency. However, these metrics do not take the energy-resolving capabilities of multibin photon-counting detectors into account. In this work, we present a unified mathematical framework for quantifying the performance of energy-resolving detectors. We show that the NEQ and DQE can be generalized into matrix-valued quantities, which describe the detector performance for detection tasks with both spatial and energy dependence. With this framework, a small number of simple measurements or simulations are sufficient to compute the dose efficiency of a detector design for any imaging task, taking the effects of detector nonidealities on spatial and energy resolution into account. We further demonstrate that the same framework also can be used for assessing material quantification performance, thereby extending the commonly used performance metrics based on the Cramér-Rao lower bound to spatial-frequency-dependent tasks. The usefulness of the proposed framework is demonstrated using simulations of charge sharing and fluorescence in a CdTe detector.

View details for DOI /10.1117/12.2293402

**Frequency dependent DQE of photon counting detector with spectral degradation and cross-talk**

P. L. Rajbhandary, M. Persson, N. J. Pelc

SPIE Medical Imaging 2018: Physics of Medical Imaging , vol. 10573, pp. 1057312, 2018

**Abstract**

Charge sharing and migration of scattered and fluorescence photons in photon counting detector (PCD) degrade the detector's energy response and cause a single photon to be potentially counted as multiple events in neighboring pixels, leading to correlations of signal and noise. Signal and noise correlations in conventional linear, space-invariant imaging can be usefully characterized by the frequency dependent detective quantum efficiency, DQE(f). The situation is complicated in the PCDs by the spectral dimension. We analyze DQE(f) of CdTe PCDs using a spatial domain method starting from a previously described computation of spatio-energetic cross talk. DQE(f) is estimated as the squared signal-to-noise ratio of the estimate of the amplitude of a small-signal sinusoidal modulation in the object at a frequency f by a given system compared to that with an ideal detector. DQE(f) for spectral and effective monoenergetic imaging are estimated using a multi-pixel Cramer-Rao lower bound for CdTe detectors of different pixel pitch. For a 120 kVp incident spectrum, DQE(0) for a spectral task was ~18%, 25% and 34% for 250 μm, 500 μm and 1 mm pixels, respectively. Positive correlation between same basis material estimates in neighboring pixels from the spatio-energetic cross-talk causes this effect to have least impact at the detector's Nyquist frequency. For effective monoenergetic imaging, DQE(0) at the optimal energy is relatively tolerant of spectral degradation (85-92% depending on pixel size), but is highly dependent on effective energy, with maximum variation (in 250 μm pixels) of 25-85% for effective energies between 30 to 120 keV.

View details for DOI 10.1117/12.2293922

**Effect of electronic noise and lowest energy threshold selection in photon counting detectors**

P. L. Rajbhandary, N. J. Pelc

SPIE Medical Imaging 2018: Physics of Medical Imaging , vol. 10573, pp. 105734S, 2018

**Abstract**

Photon counting detectors (PCD) are widely credited with having minimum degradation from electronic noise compared to energy integrating detectors. However, they are not immune. We characterized the effect of electronic noise in simulated CdTe PCDs (0.25-1mm pixels) for spectral and effective monoenergetic tasks. Electronic noise was modeled as two separable effects - spectral blurring modeled as convolution with a Gaussian kernel with standard deviation of 7 keV, and false triggering of the lowest energy bin (depending on the threshold). To model false triggering, noise was created by filtering white Gaussian noise with a Gaussian pulse shaping kernel of 40 ns peaking time and, scaled to have a standard deviation of 7 keV, and analyzed numerically to obtain the mean and variance of false triggers at thresholds from 3 to 45 keV with ±3.5 keV hysteresis. PCDs had 5 energy bins, were operated at maximum of 20 % of characteristic count rate unless otherwise specified, and pulse pileup was not modeled. We assume the expected number of false triggers can be predicted and subtracted but that the noise from those events remains. Quantum and false triggering noise were propagated into basis material images using the Cramer-Rao Lower Bound. In basis material images, at the optimal threshold (balancing false triggers and lost true events) there was an 18-24% variance penalty compared to a detector with no electronic noise. For effective monoenergetic imaging, capturing low energy pulses performs asymptotically as well as a detector without electronic noise, with the penalty increasing with increasing energy threshold.

View details for DOI 10.1117/12.2293929

**Energy dependence of SNR and DQE for effective monoenergetic imaging in spectral CT**

P. L. Rajbhandary, N. J. Pelc

SPIE Medical Imaging 2018: Physics of Medical Imaging , vol. 10573, pp. 105731F, 2018

**Abstract**

Synthesized monoenergetic images, generated using linear weighted combination of basis material images, portray the anatomy at a selected effective energy. Images at both high and low effective energies have been proposed as clinically useful. This paper studies the dependence of signal-to-noise ratio (SNR) and detective quantum efficiency (DQE) on the selected energy for CdTe PCDs, and for other spectral CT that uses scintillator detectors. DQE is estimated as the squared of SNR for the system being evaluated divided by that of an ideal PCD. Signal is the unbiased line integral of a material of interest and noise is estimated using propagation of the Cramer-Rao Lower Bound through the weighted sum. SNR and DQE are unimodal with the optimal energy dependent on the mean and width of the measured spectrum, on the spectral response, and system, and weakly on the material of interest. For the CdTe detectors simulated, DQE(0) at the optimal energy is relatively tolerant of spectral degradation (85-92% depending on pixel size), but is highly dependent on effective energy, with maximum variation (in 250 μm pixels) of 22-85% for effective energies between 30 to 120 keV. Study of effect of spectral distribution on DQE shows that a wider spectrum shifts the optimum to lower energy and weakens the energy dependence. In comparison to dual kV and dual layer spectral CT, PCDs have lower optimal effective energy and show higher DQE at low effective energies than energy integrating detectors with dual kV spectra.

View details for DOI 0.1117/12.2293932

**Implementation of a piecewise-linear dynamic attenuator**

P. Shunhavanich, N. R. Bennett, S. S. Hsieh, N. J. Pelc

SPIE Medical Imaging 2018: Physics of Medical Imaging, vol. 10573, pp. 105730T, 2018

**Abstract**

A dynamic bowtie filter can modulate flux along both fan and view angles for reduced dose, scatter, and required detector dynamic range. Reducing the dynamic range requirement is crucial for photon counting detectors. One approach, the piecewise-linear attenuator (Hsieh and Pelc, Med Phys 2013), has shown promising results both in simulations and an initial prototype. Multiple wedges, each covering a different range of fan angle, are moved in the axial direction to change their attenuating thickness as seen in an axial slice. We report on an implementation of a filter with precision components and a control algorithm targeted for operation on a table-top system. Algorithms for optimizing wedge position and mA modulation and for correcting bowtie-specific beam-hardening artifacts are proposed. In experiments, the error between expected and observed bowtie transmission was ~2% on average and ~7% at maximum for a chest phantom. Within object boundaries, the observed flux dynamic ranges of 42, for a chest phantom, and 25, for an abdomen phantom were achieved, corresponding to a reduction factor of 5 and 11 from the object scans without the bowtie. With beam hardening correction, the mean CT number in soft tissue regions was improved by 79 HU on average, and deviated by 7 HU on average from clinical scanner CT images. The implemented piecewise-linear attenuator is able to dynamically adjust its thickness with high precision to achieve flexible flux control.

View details for DOI 10.1117/12.2293525

**Segmented targeted least squares estimator for material decomposition in multibin photon-counting detectors**

P. L. Rajbhandary, S. S. Hsieh, N. J. Pelc

Journal of Medical Imaging , vol. 4, no. 2, pp. 023503, 2017

**Abstract**

We present a fast, noise-efficient, and accurate estimator for material separation using photon-counting x-ray detectors (PCXDs) with multiple energy bin capability. The proposed targeted least squares estimator (TLSE) is an improvement of a previously described A-table method by incorporating dynamic weighting that allows the variance to be closer to the Cramér–Rao lower bound (CRLB) throughout the operating range. We explore Cartesian and average-energy segmentation of the basis material space for TLSE and show that, compared with Cartesian segmentation, the average-energy method requires fewer segments to achieve similar performance. We compare the average-energy TLSE to other proposed estimators—including the gold standard maximum likelihood estimator (MLE) and the A-table—in terms of variance, bias, and computational efficiency. The variance and bias were simulated in the range of 0 to 6 cm of aluminum and 0 to 50 cm of water with Monte Carlo methods. The Average-energy TLSE achieves an average variance within 2% of the CRLB and mean absolute error of 3.68±0.06×10^{−6 } cm. Using the same protocol, the MLE showed variance within 1.9% of the CRLB ratio and average absolute error of 3.10±0.06×10^{−6} cm but was 50 times slower in our implementations. Compared with the A-table method, TLSE gives a more homogenously optimal variance-to-CRLB ratio in the operating region. We show that variance in basis material estimates for TLSE is lower than that of the A-table method by as much as ∼36% in the peripheral region of operating range (thin or thick objects). The TLSE is a computationally efficient and fast method for material separation with PCXDs, with accuracy and precision comparable to the MLE.

View details for DOI 10.1117/1.JMI.4.2.023503

**Method for decreasing CT simulation time of complex phantoms and systems through separation of material specific projection data**

S. E. Divel, S. Christensen, M. Wintermark, M. G. Lansberg, N.J. Pelc

SPIE Medical Imaging 2017: Physics of Medical Imaging, vol. 10132, pp. 1013259, 2017

**Abstract**

Computer simulation is a powerful tool in CT; however, long simulation times of complex phantoms and systems, especially when modeling many physical aspects (e.g., spectrum, finite detector and source size), hinder the ability to realistically and efficiently evaluate and optimize CT techniques. Long simulation times primarily result from the tracing of hundreds of line integrals through each of the hundreds of geometrical shapes defined within the phantom. However, when the goal is to perform dynamic simulations or test many scan protocols using a particular phantom, traditional simulation methods inefficiently and repeatedly calculate line integrals through the same set of structures although only a few parameters change in each new case. In this work, we have developed a new simulation framework that overcomes such inefficiencies by dividing the phantom into material specific regions with the same time attenuation profiles, acquiring and storing monoenergetic projections of the regions, and subsequently scaling and combining the projections to create equivalent polyenergetic sinograms. The simulation framework is especially efficient for the validation and optimization of CT perfusion which requires analysis of many stroke cases and testing hundreds of scan protocols on a realistic and complex numerical brain phantom. Using this updated framework to conduct a 31-time point simulation with 80 mm of z-coverage of a brain phantom on two 16-core Linux serves, we have reduced the simulation time from 62 hours to under 2.6 hours, a 95% reduction.

**Improvements in low contrast detectability with iterative reconstruction and the effect of slice thickness**

S. S. Hsieh, N. J. Pelc, N. J.

SPIE Medical Imaging 2017: Physics of Medical Imaging, vol. 10132, pp. 1013253, 2017

**Abstract**

Iterative reconstruction has become a popular route for dose reduction in CT scans. One method for assessing the dose reduction of iterative reconstruction is to use a low contrast detectability phantom. The apparent improvement in detectability can be very large on these phantoms, with many studies showing dose reduction in excess of 50%. In this work, we show that much of the advantage of iterative reconstruction in this context can be explained by differences in slice thickness. After adjusting the effective reconstruction kernel by blurring filtered backprojection images to match the shape of the noise power spectrum of iterative reconstruction, we produce thick slices and compare the two reconstruction algorithms. The remaining improvement from iterative reconstruction, at least in scans with relatively uniform statistics in the raw data, is significantly reduced. Hence, the effective slice thickness in iterative reconstruction may be larger than that of filtered backprojection, explaining some of the improvement in image quality.

**Sensitivity analysis of pulse pileup model parameter in photon counting detectors**

P. Shunhavanich, N. J. Pelc

SPIE Medical Imaging 2017: Physics of Medical Imaging, vol. 10132, pp. 101323M, 2017

**Abstract**

Photon counting detectors (PCDs) may provide several benefits over energy-integrating detectors (EIDs), including spectral information for tissue characterization and the elimination of electronic noise. PCDs, however, suffer from pulse pileup, which distorts the detected spectrum and degrades the accuracy of material decomposition. Several analytical models have been proposed to address this problem. The performance of these models are dependent on the assumptions used, including the estimated pulse shape whose parameter values could differ from the actual physical ones. As the incident flux increases and the corrections become more significant the needed parameter value accuracy may be more crucial. In this work, the sensitivity of model parameter accuracies is analyzed for the pileup model of Taguchi et al. The spectra distorted by pileup at different count rates are simulated using either the model or Monte Carlo simulations, and the basis material thicknesses are estimated by minimizing the negative log-likelihood with Poisson or multivariate Gaussian distributions. From simulation results, we find that the accuracy of the deadtime, the height of pulse negative tail, and the timing to the end of the pulse are more important than most other parameters, and they matter more with increasing count rate. This result can help facilitate further work on parameter calibrations.

**Effect of spatio-energy correlation in PCD due to charge sharing, scatter, and secondary photons**

P. L. Rajbhandary, S. S. Hsieh, N. J. Pelc

SPIE Medical Imaging 2017: Physics of Medical Imaging, vol. 10132, pp. 101320V, 2017

**Abstract**

Charge sharing, scatter and fluorescence events in a photon counting detector (PCD) can result in multiple counting of a single incident photon in neighboring pixels. This causes energy distortion and correlation of data across energy bins in neighboring pixels (spatio-energy correlation). If a “macro-pixel” is formed by combining multiple small pixels, it will exhibit correlations across its energy bins. Charge sharing and fluorescence escape are dependent on pixel size and detector material. Accurately modeling these effects can be crucial for detector design and for model based imaging applications. This study derives a correlation model for the multi-counting events and investigates the effect in virtual non-contrast and effective monoenergetic imaging. Three versions of 1 mm^{2} square CdTe macro-pixel were compared: a 4×4 grid, 2×2 grid, or 1×1 composed of pixels with side length 250 μm, 500 μm, or 1 mm, respectively. The same flux was applied to each pixel, and pulse pile-up was ignored. The mean and covariance matrix of measured photon counts is derived analytically using pre-computed spatio-energy response functions (SERF) estimated from Monte Carlo simulations. Based on the Cramer-Rao Lower Bound, a macro-pixel with 250×250 μm^{2} sub-pixels shows ~2.2 times worse variance than a single 1 mm^{2} pixel for spectral imaging, while its penalty for effective monoenergetic imaging is <10% compared to a single 1 mm^{2} pixel.