Spatio-energetic cross-talk in photon counting detectors: N × N binning and sub-pixel masking

Multivariate signal-to-noise ratio as a metric for characterizing spectral computed tomography

Objective.With the introduction of spectral CT techniques into the clinic, the imaging capacities of CT were expanded to multiple energy levels. Due to a variety of factors, the acquired signal in spectral CT datasets is shared between these images. Conventional image quality metrics assume independence between images which is not preserved within spectral CT datasets, limiting their utility for characterizing energy selective images. The purpose of this work was to develop a metrology to characterize energy selective images by incorporating the shared information between images within a spectral CT dataset.Approach.The signal-to-noise ratio (SNR) was extended into a multivariate space where each image within a spectral CT dataset was treated as a separate information channel. The general definition was applied to the specific case of contrast to define a multivariate contrast-to-noise ratio (CNR). The matrix contained two types of terms: a conventional CNR term which characterized image quality within each image in the spectral CT dataset and covariance weighted CNR (Covar-CNR) which characterized the contrast in each image relative to the covariance between images. Experimental data from an investigational photon-counting CT scanner was used to demonstrate the insight of this metrology. A cylindrical water phantom containing vials of iodine and gadolinium (2, 4, and 8 mg ml-1) was imaged under conditions of variable tube current, tube voltage, and energy threshold. Two image series (threshold and bin images) containing two images each were defined based upon the contribution of photons to reconstructed images. Analysis of variance (ANOVA) was calculated between CNR terms and image acquisition variables. A multivariate regression was then fitted to experimental data.Main Results.Image type had a major difference on how Covar-CNR values were distributed. Bin images had a slightly higher mean and wider standard deviation (Covar-CNRlo: 3.38 ±17.25, Covar-CNRhi: 5.77 ± 30.64) compared to threshold images (Covar-CNRlo: 2.08 ±1.89, Covar-CNRhi: 3.45 ± 2.49) across all conditions. ANOVA found that each acquisition variable had a significant relationship with both Covar-CNR terms. The multivariate regression model suggested that material concentration had the largest impact on all CNR terms.Signficance.In this work, we described a theoretical framework to extend the SNR to a multivariate form that is able to characterize images independently and also provide insight regarding the relationship between images. Experimental data was used to demonstrate the insight that this metrology provides about image formation factors in spectral CT.

Development of a separability index for task specific characterization of spectral computed tomography

PURPOSE

In this work, we define a signal detection based metrology to characterize the separability of two different multi-dimensional signals in spectral CT acquisitions.

METHOD

Signal response was modelled as a random process with a deterministic signal and stochastic noise component. A linear Hotelling observer was used to estimate a scalar test statistic distribution that predicts the likelihood of an intensity value belonging to a signal. Two distributions were estimated for two materials of interest and used to derive two metrics separability: a separability index (s') and the area under the curve of the test statistic distributions. Experimental and simulated data of photon-counting CT scanners were used to evaluate each metric. Experimentally, vials of iodine and gadolinium (2, 4, 8 mg/mL) were scanned at multiple tube voltages, tube currents and energy thresholds. Additionally, a simulated dataset with low tube current (10-150 mAs) and material concentrations (0.25-4 mg/mL) was generated.

RESULTS

Experimental data showed that conditions favorable for low noise and expression of k-edge signal produced the highest separability. Material concentration had the greatest impact on separability. The simulated data showed that under more difficult separation conditions, difference in material concentration still had the greatest impact on separability.

CONCLUSION

The results demonstrate the utility of a task specific metrology to measure the overlap in signal between different materials in spectral CT. Using experimental and simulated data, the separability index was shown to describe the relationship between image formation factors and the signal responses of material.

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.

Image-domain Material Decomposition for Spectral CT using a Generalized Dictionary Learning

The spectral computed tomography (CT) has huge advantages by providing accurate material information. Unfortunately, due to the instability or overdetermination of material decomposition model, the accuracy of material decomposition can be compromised in practice. Very recently, the dictionary learning based image-domain material decomposition (DLIMD) can obtain high accuracy for material decompositions from reconstructed spectral CT images. This method can explore the correlation of material components to some extent by training a unified dictionary from all material images. In addition, the dictionary learning based prior as a penalty is applied on material components independently, and many parameters would be carefully elaborated in practice. Because the concentration of contrast agent in clinical applications is low, it can result in data inconsistency for dictionary based representation during the iteration process. To avoid the aforementioned limitations and further improve the accuracy of materials, we first construct a generalized dictionary learning based image-domain material decomposition (GDLIMD) model. Then, the material tensor image is unfolded along the mode-1 to enhance the correlation of different materials. Finally, to avoid the data inconsistency of low iodine contrast, a normalization strategy is employed. Both physical phantom and tissue-synthetic phantom experiments demonstrate the proposed GDLIMD method outperforms the DLIMD and direct inversion (DI) methods.

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.

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.

A Clinically Driven Task-Based Comparison of Photon Counting and Conventional Energy Integrating CT for Soft Tissue, Vascular, and High-Resolution Tasks

Photon-counting CT detectors are the next step in advancing CT system development and will replace the current energy integrating detectors (EID) in CT systems in the near future. In this context, the performance of PCCT was compared to EID CT for three clinically relevant tasks: abdominal soft tissue imaging, where differentiating low contrast features is important; vascular imaging, where iodine detectability is critical; and, high-resolution skeletal and lung imaging. A multi-tiered phantom was imaged on an investigational clinical PCCT system (Siemens Healthineers) across different doses using three imaging modes: macro and ultra-high resolution (UHR) PCCT modes and EID CT. Images were reconstructed using filtered backprojection and soft tissue (B30f), vascular (B46f), or high-resolution (B70f; U70f for UHR) kernels. Noise power spectra, task transfer functions, and detectability index were evaluated. For a soft tissue task, PCCT modes showed comparable noise and resolution with improved contrast-to-noise ratio. For a vascular task, PCCT modes showed lower noise and improved iodine detectability. For a high resolution task, macro mode showed lower noise and comparable resolution while UHR mode showed higher noise but improved spatial resolution for both air and bone. PCCT offers competitive advantages to EID CT for clinical tasks.

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.

Assessment of Multienergy Interpixel Coincidence Counters (MEICC) for Charge Sharing Correction or Compensation for Photon Counting Detectors With Boxcar Signals

Recently, multi-energy inter-pixel coincidence counter (MEICC) has been proposed for charge sharing correction and compensation for photon counting detectors (PCDs), which uses energy-dependent coincidence counters to record coincident events between multiple energy windows of a pixel-of-interest and those of neighboring pixels. A Monte Carlo (MC) simulation study was performed to assess the performance of MEICC; however, the performance might have been overestimated in a previous study. The charge sharing increases the number of photons recorded at a PCD pixel at the expense of the spatial resolution, and therefore, when spatially uniform flat-field x-ray signals are used, it gives PCDs with charge sharing more signals than a PCD without charge sharing. In this paper, we propose to use spatially modulated boxcar signals for evaluating the performances for high spatial frequency tasks because they provide consistent signals regardless of the presence of absence of charge sharing. The flat-field signals must be used for low spatial frequency tasks. We assessed the performances of MEICC and other PCDs with both flat-field signals and boxcar signals, with optimal threshold energies, and with two different pixel sizes. As it is expected, normalized Cramér-Rao lower bounds (nCRLBs) measured with the boxcar signals were worse than those with flat-field signals in general. The nCRLBs of MEICC with 225-μm pixel were close to the current 450-μm PCD. We studied a combination of flat-field signals and N×N super-pixels, where the output of N×N pixels were added, using an MC simulation and a simple charge sharing counting model. The study showed that charge sharing had two opposing impacts on the conventional CT imaging-a negative impact with double-counting among N×N pixels and a positive impact with single-counting spill-in and spill-out across the super-pixel boundary-and the positive impact diminished with increasing N. A use of large N×N super-pixels such as N≥25 was suggested to approximate the zero-frequency detection quantum efficiency of PCD with charge sharing.

Multi-energy inter-pixel coincidence counters for charge sharing correction and compensation in photon counting detectors

PURPOSE

Smaller pixel sizes of x-ray photon counting detectors (PCDs) are advantageous for count rate capabilities but disadvantageous for charge sharing. With charge sharing, the energy of an x-ray photon may be split and one photon may produce two or more counts at adjacent pixels, both at lower energies than the incident energy. This "double-counting" increases noise variance and degrades the spectral response. Overall, it has a significantly negative impact on the performance of PCD-based computed tomography (CT). Charge sharing is induced by the detection physics and occurs regardless of count rates; thus, it is impossible to avoid. We propose in this paper a method that has a potential to address both noise and bias added by charge sharing.

METHODS

We propose applying a multi-energy inter-pixel coincidence counter (MEICC) technique, which uses energy-dependent coincidence counters, keeps the book of charge sharing events during data acquisition, and provides the exact number of charge sharing occurrences, which can be used to either correct or compensate for them after the acquisition is completed. MEICC does not interfere with the primary counting process; therefore, PCDs with MEICC will remain as fast as those without MEICC. MEICC can be implemented using current electronics technology because its inter-pixel coincidence counters used to handle digital data are rather simple. We evaluated Cramér-Rao lower bound (CRLB) of PCDs with and without MEICC using a Monte Carlo simulation.

RESULTS

When the number of energy windows was four or larger and eight neighboring pixels were used, the CRLBs of 225-µm PCD with MEICC normalized by those of the current PCD with the same number of windows were 0.361-0.383 for water density images of two basis functions, which was only 5.7-16.4% worse than those of a PCD without charge sharing (which were at 0.329-0.358). In contrast, the normalized CRLBs of the PCD with one coincidence counter were 0.466-0.499, which were 37.3-45.6% worse than the PCD without charge sharing. The use of eight neighboring pixels provided ~10% better CRLB values than four neighboring pixels for MEICC. With four energy windows, decreasing the number of coincidence counters from 16 to 9 only slightly increased the CRLB from 0.255 to 0.269 (which corresponded to as little as a 5.5% change). The normalized CRLBs of MEICC for K-edge imaging (gold) were 0.295-0.426, while those of the one coincidence counter were 0.926-0.959 and the ideal PCDs were 0.126-0.146.

CONCLUSIONS

The proposed MEICC provides spectral information that can be used to address charge sharing problems in PCDs and is expected to satisfy the requirements for clinical x-ray CT. MEICC is very effective, especially for K-edge imaging, which requires accurate spectral information.

Investigation of spectral performance for single-scan contrast-enhanced breast CT using photon-counting technology: A phantom study

PURPOSE

Contrast-enhanced imaging of the breast is frequently used in breast MRI and has recently become more common in mammography. The purpose of this study was to make single-scan contrast-enhanced imaging feasible for photon-counting breast CT (pcBCT) and to assess the spectral performance of a pcBCT scanner by evaluating iodine maps and virtual non-contrast (VNC) images.

METHODS

We optimized the settings of a pcBCT to maximize the signal-to-noise ratio between iodinated contrast agent and breast tissue. Therefore, an electronic energy threshold dividing the x-ray spectrum used into two energy bins was swept from 23.17 keV to 50.65 keV. Validation measurements were performed by placing syringes with contrast agent (2.5 mg/ml to 40 mg/ml) in phantoms with 7.5 cm and 12 cm in diameter. Images were acquired at different tube currents and reconstructed with 300 μm isotropic voxel size. Iodine maps and VNC images were generated using image-based material decomposition. Iodine concentrations and CT values were measured for each syringe and compared to the known concentrations and reference CT values.

RESULTS

Maximal signal-to-noise ratios were found at a threshold position of 32.59 keV. Accurate iodine quantification (average root mean square error of 0.56 mg/ml) was possible down to a concentration of 2.5 mg/ml for all tube currents investigated. The enhancement has been sufficiently removed in the VNC images, so they can be interpreted as unenhanced CT images. Only minor changes of CT values compared to a conventional CT scan were observed. Noise was increased by the decomposition by a factor of 2.62 and 4.87 (7.5 cm and 12 cm phantoms) but did not compromise the accuracy of the iodine quantification.

CONCLUSIONS

Accurate iodine quantification and generation of VNC images can be achieved using contrast-enhanced pcBCT from a single CT scan in the absence of temporal or spatial misalignment. Using iodine maps and VNC images, pcBCT has the potential to reduce dose, shorten examination and reading time, and to increase cancer detection rates.

Development of a scanner-specific simulation framework for photon-counting computed tomography

The aim of this study was to develop and validate a simulation platform that generates photon-counting CT images of voxelized phantoms with detailed modeling of manufacturer-specific components including the geometry and physics of the x-ray source, source filtrations, anti-scatter grids, and photon-counting detectors. The simulator generates projection images accounting for both primary and scattered photons using a computational phantom, scanner configuration, and imaging settings. Beam hardening artifacts are corrected using a spectrum and threshold dependent water correction algorithm. Physical and computational versions of a clinical phantom (ACR) were used for validation purposes. The physical phantom was imaged using a research prototype photon-counting CT (Siemens Healthcare) with standard (macro) mode, at four dose levels and with two energy thresholds. The computational phantom was imaged with the developed simulator with the same parameters and settings used in the actual acquisition. Images from both the real and simulated acquisitions were reconstructed using a reconstruction software (FreeCT). Primary image quality metrics such as noise magnitude, noise ratio, noise correlation coefficients, noise power spectrum, CT number, in-plane modulation transfer function, and slice sensitivity profiles were extracted from both real and simulated data and compared. The simulator was further evaluated for imaging contrast materials (bismuth, iodine, and gadolinium) at three concentration levels and six energy thresholds. Qualitatively, the simulated images showed similar appearance to the real ones. Quantitatively, the average relative error in image quality measurements were all less than 4% across all the measurements. The developed simulator will enable systematic optimization and evaluation of the emerging photon-counting computed tomography technology.