Taly Gilat Schmidt

An Inverse-Geometry Volumetric CT System With a Large-Area Scanned Source: A Feasibility Study

We propose an inverse-geometry volumetric CT system for acquiring a 15-cm volume in one rotation with negligible cone-beam artifacts. The system uses a large-area scanned source and a smaller detector array. This note describes two feasibility investigations. The first examines data sufficiency in the transverse planes. The second predicts the signal-to-noise ratio (SNR) compared to a conventional scanner. Results showed sufficient sampling of the full volume in less than 0.5 s and, when compared to a conventional scanner operating at 24 kW with a 0.5-s voxel illumination time (e.g., 0.5-s gantry rotation and pitch of one), predicted a relative SNR of 76%.

CT energy weighting in the presence of scatter and limited energy resolution

PURPOSE Energy-resolved CT has the potential to improve the contrast-to-noise ratio (CNR) through optimal weighting of photons detected in energy bins. In general, optimal weighting gives higher weight to the lower energy photons that contain the most contrast information. However, low-energy photons are generally most corrupted by scatter and spectrum tailing, an effect caused by the limited energy resolution of the detector. This article first quantifies the effects of spectrum tailing on energy-resolved data, which may also be beneficial for material decomposition applications. Subsequently, the combined effects of energy weighting, spectrum tailing, and scatter are investigated through simulations. METHODS The study first investigated the effects of spectrum tailing on the estimated attenuation coefficients of homogeneous slab objects. Next, the study compared the CNR and artifact performance of images simulated with varying levels of scatter and spectrum tailing effects, and reconstructed with energy integrating, photon-counting, and two optimal linear weighting methods: Projection-based and image-based weighting. Realistic detector energy-response functions were simulated based on a previously proposed model. The energy-response functions represent the probability that a photon incident on the detector at a particular energy will be detected at a different energy. Realistic scatter was simulated with Monte Carlo methods. RESULTS Spectrum tailing resulted in a negative shift in the estimated attenuation coefficient of slab objects compared to an ideal detector. The magnitude of the shift varied with material composition, increased with material thickness, and decreased with photon energy. Spectrum tailing caused cupping artifacts and CT number inaccuracies in images reconstructed with optimal energy weighting, and did not impact images reconstructed with photon counting weighting. Spectrum tailing did not significantly impact the CNR in reconstructed images. Scatter reduced the CNR for all energy-weighting methods; however, the effect was greater for optimal energy weighting. For example, optimal energy weighting improved the CNR of iodine and water compared to energy-integrating weighting by a factor of approximately 1.45 in the absence of scatter and by a factor of approximately 1.1 in the presence of scatter (8.9 degrees cone angle, SPR 0.5). Without scatter correction, the difference in CNR resulting from photon-counting and optimal energy weighting was negligible (< 15%) for cone angles greater than 4.4 degrees (SPR > 0.3). Optimal weights combined with deterministic scatter correction provided a 1.3 and 1.1 improvement in CNR compared to energy-integrating and photon-counting weighting, respectively, for the 8.9 degrees cone angle simulation. In the absence of spectrum tailing, image-based weighting demonstrated reduced cupping artifact compared to projection-based weighting; however, both weighting methods exhibited similar cupping artifacts when spectrum tailing was simulated. There were no statistically significant differences in the CNR resulting from projection an image-based weighting for any of the simulated conditions. CONCLUSIONS Optimal linear energy weighting introduces artifacts and CT number inaccuracies due to spectrum tailing. While optimal energy weighting has the potential to improve CNR compared to conventional weighting methods, the benefits are reduced as scatter increases. Efficient methods for reducing scatter and correcting spectrum tailing effects are required to obtain the highest benefit from optimal energy weighting.

An algorithm for constrained one-step inversion of spectral CT data

We develop a primal-dual algorithm that allows for one-step inversion of spectral CT transmission photon counts data to a basis map decomposition. The algorithm allows for image constraints to be enforced on the basis maps during the inversion. The derivation of the algorithm makes use of a local upper bounding quadratic approximation to generate descent steps for non-convex spectral CT data discrepancy terms, combined with a new convex-concave optimization algorithm. Convergence of the algorithm is demonstrated on simulated spectral CT data. Simulations with noise and anthropomorphic phantoms show examples of how to employ the constrained one-step algorithm for spectral CT data.

Simulated scatter performance of an inverse-geometry dedicated breast CT system.

The purpose of this work was to quantify the effects of scatter for inverse-geometry dedicated breast CT compared to cone-beam breast CT through simulations. The inverse geometry was previously proposed as an alternative to cone-beam acquisition for volumetric CT. The inverse geometry consists of a large-area scanned-source opposite a detector array that is smaller in the transverse direction. While the gantry rotates, the x-ray beam is rapidly sequenced through an array of positions, acquiring a truncated projection image at each position. Inverse-geometry CT (IGCT) is expected to detect less scatter than cone-beam methods because only a fraction of the object is irradiated at any time and the fast detector isolates the measurements from sequential x-ray beams. An additional scatter benefit is the increased air gap due to the inverted geometry. In this study, we modeled inverse-geometry and cone-beam dedicated breast CT systems of equivalent resolution, field of view, and photon fluence. Monte Carlo simulations generated scatter and primary projections of three cylindrical phantoms of diameters 10, 14, and 18 cm composed of 50% adipose/50% glandular tissue. The scatter-to-primary ratio (SPR) was calculated for each breast diameter. Monte Carlo simulations were combined with analytical simulations to generate inverse-geometry and cone-beam images of breast phantoms embedded with tumors. Noise reprehenting the photon fluence of a realistic breast CT scan was added to the simulated projections. Cone-beam data were reconstructed with and without an ideal scatter correction. The CNR between breast tumor and background was compared for the inverse and cone-beam geometries for the three phantom diameters. Results demonstrated an order of magnitude reduction in SPR for the IGCT system compared to the cone-beam system. For example, the peak IGCT SPRs were 0.05 and 0.09 for the 14 and 18 cm phantoms, respectively, compared to 0.42 and 1 for the cone-beam system. For both geometries, the effects of scatter on contrast-to-noise ratio (CNR) were small for the 10 cm diameter phantom. The inverse-geometry improved the CNR by factors of 1.16 for the 14 cm phantom and 1.48 for the 18 cm phantom compared to a cone-beam acquisition without scatter correction. When an ideal scatter correction was applied to the cone-beam acquisition, the IGCT CNR improvements were 1.03 and 1.25 for the 14 and 18 cm phantoms. Overall, the results suggest that the inverse geometry may be advantageous for dedicated breast CT, an application that requires high-contrast resolution, spatial resolution, and dose efficiency.

A three-dimensional reconstruction algorithm for an inverse-geometry volumetric CT system.

An inverse-geometry volumetric computed tomography (IGCT) system has been proposed capable of rapidly acquiring sufficient data to reconstruct a thick volume in one circular scan. The system uses a large-area scanned source opposite a smaller detector. The source and detector have the same extent in the axial, or slice, direction, thus providing sufficient volumetric sampling and avoiding cone-beam artifacts. This paper describes a reconstruction algorithm for the IGCT system. The algorithm first rebins the acquired data into two-dimensional (2D) parallel-ray projections at multiple tilt and azimuthal angles, followed by a 3D filtered backprojection. The rebinning step is performed by gridding the data onto a Cartesian grid in a 4D projection space. We present a new method for correcting the gridding error caused by the finite and asymmetric sampling in the neighborhood of each output grid point in the projection space. The reconstruction algorithm was implemented and tested on simulated IGCT data. Results show that the gridding correction reduces the gridding errors to below one Hounsfield unit. With this correction, the reconstruction algorithm does not introduce significant artifacts or blurring when compared to images reconstructed from simulated 2D parallel-ray projections. We also present an investigation of the noise behavior of the method which verifies that the proposed reconstruction algorithm utilizes cross-plane rays as efficiently as in-plane rays and can provide noise comparable to an in-plane parallel-ray geometry for the same number of photons. Simulations of a resolution test pattern and the modulation transfer function demonstrate that the IGCT system, using the proposed algorithm, is capable of 0.4 mm isotropic resolution. The successful implementation of the reconstruction algorithm is an important step in establishing feasibility of the IGCT system.

Quantifying the tibiofemoral joint space using x-ray tomosynthesis.

PURPOSE Digital x-ray tomosynthesis (DTS) has the potential to provide 3D information about the knee joint in a load-bearing posture, which may improve diagnosis and monitoring of knee osteoarthritis compared with projection radiography, the current standard of care. Manually quantifying and visualizing the joint space width (JSW) from 3D tomosynthesis datasets may be challenging. This work developed a semiautomated algorithm for quantifying the 3D tibiofemoral JSW from reconstructed DTS images. The algorithm was validated through anthropomorphic phantom experiments and applied to three clinical datasets. METHODS A user-selected volume of interest within the reconstructed DTS volume was enhanced with 1D multiscale gradient kernels. The edge-enhanced volumes were divided by polarity into tibial and femoral edge maps and combined across kernel scales. A 2D connected components algorithm was performed to determine candidate tibial and femoral edges. A 2D joint space width map (JSW) was constructed to represent the 3D tibiofemoral joint space. To quantify the algorithm accuracy, an adjustable knee phantom was constructed, and eleven posterior-anterior (PA) and lateral DTS scans were acquired with the medial minimum JSW of the phantom set to 0-5 mm in 0.5 mm increments (VolumeRad™, GE Healthcare, Chalfont St. Giles, United Kingdom). The accuracy of the algorithm was quantified by comparing the minimum JSW in a region of interest in the medial compartment of the JSW map to the measured phantom setting for each trial. In addition, the algorithm was applied to DTS scans of a static knee phantom and the JSW map compared to values estimated from a manually segmented computed tomography (CT) dataset. The algorithm was also applied to three clinical DTS datasets of osteoarthritic patients. RESULTS The algorithm segmented the JSW and generated a JSW map for all phantom and clinical datasets. For the adjustable phantom, the estimated minimum JSW values were plotted against the measured values for all trials. A linear fit estimated a slope of 0.887 (R² = 0.962) and a mean error across all trials of 0.34 mm for the PA phantom data. The estimated minimum JSW values for the lateral adjustable phantom acquisitions were found to have low correlation to the measured values (R² = 0.377), with a mean error of 2.13 mm. The error in the lateral adjustable-phantom datasets appeared to be caused by artifacts due to unrealistic features in the phantom bones. JSW maps generated by DTS and CT varied by a mean of 0.6 mm and 0.8 mm across the knee joint, for PA and lateral scans. The tibial and femoral edges were successfully segmented and JSW maps determined for PA and lateral clinical DTS datasets. CONCLUSIONS A semiautomated method is presented for quantifying the 3D joint space in a 2D JSW map using tomosynthesis images. The proposed algorithm quantified the JSW across the knee joint to sub-millimeter accuracy for PA tomosynthesis acquisitions. Overall, the results suggest that x-ray tomosynthesis may be beneficial for diagnosing and monitoring disease progression or treatment of osteoarthritis by providing quantitative images of JSW in the load-bearing knee.

Experimental Comparison of Empirical Material Decomposition Methods for Spectral CT

Material composition can be estimated from spectral information acquired using photon counting x-ray detectors with pulse height analysis. Non-ideal effects in photon counting x-ray detectors such as charge-sharing, k-escape, and pulse-pileup distort the detected spectrum, which can cause material decomposition errors. This work compared the performance of two empirical decomposition methods: a neural network estimator and a linearized maximum likelihood estimator with correction (A-table method). The two investigated methods differ in how they model the nonlinear relationship between the spectral measurements and material decomposition estimates. The bias and standard deviation of material decomposition estimates were compared for the two methods, using both simulations and experiments with a photon-counting x-ray detector. Both the neural network and A-table methods demonstrated a similar performance for the simulated data. The neural network had lower standard deviation for nearly all thicknesses of the test materials in the collimated (low scatter) and uncollimated (higher scatter) experimental data. In the experimental study of Teflon thicknesses, non-ideal detector effects demonstrated a potential bias of 11-28%, which was reduced to 0.1-11% using the proposed empirical methods. Overall, the results demonstrated preliminary experimental feasibility of empirical material decomposition for spectral CT using photon-counting detectors.

Few-view single photon emission computed tomography (SPECT) reconstruction based on a blurred piecewise constant object model

A sparsity-exploiting algorithm intended for few-view single photon emission computed tomography (SPECT) reconstruction is proposed and characterized. The algorithm models the object as piecewise constant subject to a blurring operation. To validate that the algorithm closely approximates the true object in the noiseless case, projection data were generated from an object assuming this model and using the system matrix. Monte Carlo simulations were performed to provide more realistic data of a phantom with varying smoothness across the field of view and a cardiac phantom. Reconstructions were performed across a sweep of two primary design parameters. The results demonstrate that the algorithm recovers the object in a noiseless simulation case. While the algorithm assumes a specific blurring model, the results suggest that the algorithm may provide high reconstruction accuracy even when the object does not match the assumed blurring model. Generally, increased values of the blurring parameter and total variation weighting parameters reduced streaking artifacts, while decreasing spatial resolution. The proposed algorithm demonstrated higher correlation with respect to the true phantom compared to maximum-likelihood expectation maximization (MLEM) reconstructions. Images reconstructed with the proposed algorithm demonstrated reduced streaking artifacts when reconstructing from few views compared to MLEM. The proposed algorithm introduced patchy artifacts in some reconstructed images, depending on the noise level and the selected algorithm parameters. Overall, the results demonstrate preliminary feasibility of a sparsity-exploiting reconstruction algorithm which may be beneficial for few-view SPECT.

Region‐of‐interest material decomposition from truncated energy‐resolved CT

PURPOSE Energy-resolved CT using photon-counting detectors has the potential to provide improved material decomposition compared to dual-kVp approaches. However, available photon-counting detectors are susceptible to pulse-pileup artifacts, especially at the periphery of the field of view (FOV) where the object attenuation is low compared to the center of the FOV. Pulse pileup may be avoided by imaging a region-of-interest (ROI) where the dynamic range is expected to be limited. This work investigated performing material decomposition and reconstructing ROI basis images from truncated energy-resolved data. METHODS A method is proposed to reconstruct images of basis functions primarily contained within the ROI, such as targeted or localized K-edge contrast agents. Material decomposition is performed independently for each ray in the sinogram, followed by filtered backprojection from the truncated data encompassing the ROI. A second method is proposed that uses a prior conventional energy-integrating image to estimate energy-resolved data outside the ROI. The measured and estimated energy-resolved data are decomposed into basis projections and merged into basis sinograms of the full FOV. Basis images of the ROI are then reconstructed through filtered backprojection. This method is most easily applied to objects that do not contain K-edge contrast agents outside the ROI. Simulations of a voxelized thorax phantom with iodine in the blood pool and a detector with five energy bins were performed. Full FOV, truncated, and truncated data merged with data estimated from the prior energy-integrating image were decomposed into Compton, photoelectric, and iodine basis functions. An empirical weighting factor was determined to blend the merged sinogram at the boundary of the truncated data. The effects of noise and misalignment in the prior image were also quantified. Basis images of the central 15 cm × 15 cm ROI containing the heart were reconstructed via filtered backprojection. Basis image accuracy was quantified relative to gold-standard basis images reconstructed from full FOV energy-resolved data. RESULTS The error in the iodine basis image reconstructed from truncated energy-resolved data without prior information was less than 1% for the central 7 cm of the 7.5-cm-radius ROI and 3% at the edge of the ROI. When the truncated and estimated basis sinograms were blended, the error was below 1% throughout the ROI for photoelectric basis images and ranged from 1% at the center of the ROI to 4% at the edge for the Compton basis image. CONCLUSIONS The density of localized K-edge contrast agents can be estimated to within 1% error using filtered back projection without prior information. For noncontrast and localized-contrast scans, ROI images of general basis functions can be reconstructed to within a few percent error using a prior energy-integrating image. The ability to perform material decomposition for a limited ROI may facilitate energy-resolved CT with available photon-counting detectors.

The effects of extending the spectral information acquired by a photon-counting detector for spectral CT

Photon-counting x-ray detectors with pulse-height analysis provide spectral information that may improve material decomposition and contrast-to-noise ratio (CNR) in CT images. The number of energy measurements that can be acquired simultaneously on a detector pixel is equal to the number of comparator channels. Some spectral CT designs have a limited number of comparator channels, due to the complexity of readout electronics. The spectral information could be extended by changing the comparator threshold levels over time, sub pixels, or view angle. However, acquiring more energy measurements than comparator channels increases the noise and/or dose, due to differences in noise correlations across energy measurements and decreased dose utilisation. This study experimentally quantified the effects of acquiring more energy measurements than comparator channels using a bench-top spectral CT system. An analytical and simulation study modeling an ideal detector investigated whether there was a net benefit for material decomposition or optimal energy weighting when acquiring more energy measurements than comparator channels. Experimental results demonstrated that in a two-threshold acquisition, acquiring the high-energy measurement independently from the low-energy measurement increased noise standard deviation in material-decomposition basis images by factors of 1.5-1.7 due to changes in covariance between energy measurements. CNR in energy-weighted images decreased by factors of 0.92-0.71. Noise standard deviation increased by an additional factor of [Formula: see text] due to reduced dose utilisation. The results demonstrated no benefit for two-material decomposition noise or energy-weighted CNR when acquiring more energy measurements than comparator channels. Understanding the noise penalty of acquiring more energy measurements than comparator channels is important for designing spectral detectors and for designing experiments and interpreting data from prototype systems with a limited number of comparator channels.