A Spectral CT Method to Directly Estimate Basis Material Maps From Experimental Photon-Counting Data

Joint Material Decomposition and Scatter Estimation for Spectral CT

Accurate scatter correction is essential to obtain highquality reconstructions in computed tomography. While many correction strategies for this longstanding issue have been developed, additional efforts may be required for spectral CT imaging - which is particularly sensitive to unmodeled biases. In this work we explore a joint estimation approach within a one-step model-based material decomposition framework to simultaneously estimate material densities and scatter profiles in spectral CT. The method is applied to simulated phantom data obtained using a parametric additive scatter mode, and compared to the unmodeled scatter scenario. In these preliminary experiments, We find that this joint estimation approach has the potential to significantly reduce artifacts associated with unmodeled scatter and to improve material density estimates.

Dual energy CT reconstruction using the constrained one step spectral image reconstruction algorithm

BACKGROUND

The constrained one-step spectral CT Image Reconstruction method (cOSSCIR) has been developed to estimate basis material maps directly from spectral CT data using a model of the polyenergetic x-ray transmissions and incorporating convex constraints into the inversion problem. This 'one-step' approach has been shown to stabilize the inversion in the case of photon-counting CT, and may provide similar benefits to dual-kV systems that utilize integrating detectors. Since the approach does not require the same rays be acquired for every spectral measurement, cOSSCIR can apply to dual energy protocols and systems used clinically, such as fast and slow kV switching systems and dual source scanning.

PURPOSE

The purpose of this study is to investigate the use of cOSSCIR applied to dual-kV data, using both registered and unregistered spectral acquisitions, specifically slow and fast kV switching imaging protocols. For this application, cOSSCIR is investigated using inverse crime simulations and dual-kV experiments. This study is the first demonstration of cOSSCIR on the dual-kV reconstruction problem.

METHODS

An integrating detector model was developed for the purpose of reconstructing dual-kV data, and an inverse crime study was used to validate the detector model within the cOSSCIR framework using a simulated pelvic phantom. Experiments were also used to evaluate cOSSCIR on the dual energy problem. Dual-kV data was obtained from a physical phantom containing analogs of adipose, bone, and liver tissues, with the aim of recovering the material coefficients in the bone and adipose basis material maps. cOSSCIR was applied to acquisitions where all rays performed both spectral measurements (registered) and fast and slow kV switching acquisitions (unregistered). cOSSCIR was also compared to two image-domain decomposition approaches, where image-domain methods are the conventional approach for decomposing unregistered spectral data.

RESULTS

Simulations demonstrate the application of cOSSCIR to the dual-kV inversion problem by successfully recovering the material basis maps on ideal data, while further showing that unregistered data presents a more challenging inversion problem. In our experimental reconstructions, the recovered basis material coefficient errors were found to be less than 6.5% in the bone, adipose, and liver regions for both registered and unregistered protocols. Similarly, the errors were less than 4% in the 50 keV virtual mono-energetic images, and the recovered material decomposition vectors nearly overlap their corresponding ground-truth vectors. Additionally, a preliminary two material decomposition study of iodine quantification recovered an average concentration of 9.2 mg/mL from a 10 mg/mL experimental iodine analog.

CONCLUSIONS

Using our integrating detector and spectral models, cOSCCIR is capable of accurately recovering material basis maps from dual-kV data for both registered and unregistered data. The material decomposition quantification compare favorably to the image domain approaches, and our results were not affected by the imaging protocol. Our results also suggest the extension of cOSSCIR to iodine quantification using two material decomposition.

Improving model-data mismatch for photon-counting detector model using global and local model parameters

BACKGROUND

An energy-discriminating capability of a photon counting detector (PCD) can provide many clinical advantages, but several factors, such as charge sharing (CS) and pulse pileup (PP), degrade the capability by distorting the measured x-ray spectrum. To fully exploit the merits of PCDs, it is important to characterize the output of PCDs. Previously proposed PCD output models showed decent agreement with physical PCDs; however, there were still scopes to be improved: a global model-data mismatch and pixel-to-pixel variations.

PURPOSES

In this study, we improve a PCD model by using count-rate-dependent model parameters to address the issues and evaluate agreement against physical PCDs.

METHODS

The proposed model is based on the cascaded model, and we made model parameters condition-dependent and pixel-specific to deal with the global model-data mismatch and the pixel-to-pixel variation. The parameters are determined by a procedure for model parameter estimation with data acquired from different thicknesses of water or aluminum at different x-ray tube currents. To analyze the effects of having proposed model parameters, we compared three setups of our model: a model with default parameters, a model with global parameters, and a model with global-and-local parameters. For experimental validation, we used CdZnTe-based PCDs, and assessed the performance of the models by calculating the mean absolute percentage errors (MAPEs) between the model outputs and the actual measurements from low count-rates to high count-rates, which have deadtime losses of up to 24%.

RESULTS

The outputs of the proposed model visually matched well with the PCD measurements for all test data. For the test data, the MAPEs averaged over all the bins were 49.2-51.1% for a model with default parameters, 8.0-9.8% for a model with the global parameters, and 1.2-2.7% for a model with the global-and-local parameters.

CONCLUSION

The proposed model can estimate the outputs of physical PCDs with high accuracy from low to high count-rates. We expect that our model will be actively utilized in applications where the pixel-by-pixel accuracy of a PCD model is important.

Image quality improvement of a one-step spectral CT reconstruction on a prototype photon-counting scanner

Objective. X-ray spectral computed tomography (CT) allows for material decomposition (MD). This study compared a one-step material decomposition MD algorithm with a two-step reconstruction MD algorithm using acquisitions of a prototype CT scanner with a photon-counting detector (PCD).Approach. MD and CT reconstruction may be done in two successive steps, i.e. decompose the data in material sinograms which are then reconstructed in material CT images, or jointly in a one-step algorithm. The one-step algorithm reconstructed material CT images by maximizing their Poisson log-likelihood in the projection domain with a spatial regularization in the image domain. The two-step algorithm maximized first the Poisson log-likelihood without regularization to decompose the data in material sinograms. These sinograms were then reconstructed into material CT images by least squares minimization, with the same spatial regularization as the one step algorithm. A phantom simulating the CT angiography clinical task was scanned and the data used to measure noise and spatial resolution properties. Low dose carotid CT angiographies of 4 patients were also reconstructed with both algorithms and analyzed by a radiologist. The image quality and diagnostic clinical task were evaluated with a clinical score.Main results. The phantom data processing demonstrated that the one-step algorithm had a better spatial resolution at the same noise level or a decreased noise value at matching spatial resolution. Regularization parameters leading to a fair comparison were selected for the patient data reconstruction. On the patient images, the one-step images received higher scores compared to the two-step algorithm for image quality and diagnostic.Significance. Both phantom and patient data demonstrated how a one-step algorithm improves spectral CT image quality over the implemented two-step algorithm but requires a longer computation time. At a low radiation dose, the one-step algorithm presented good to excellent clinical scores for all the spectral CT images.

Constrained one-step material decomposition reconstruction of head CT data from a silicon photon-counting prototype

BACKGROUND

Spectral CT material decomposition provides quantitative information but is challenged by the instability of the inversion into basis materials. We have previously proposed the constrained One-Step Spectral CT Image Reconstruction (cOSSCIR) algorithm to stabilize the material decomposition inversion by directly estimating basis material images from spectral CT data. cOSSCIR was previously investigated on phantom data.

PURPOSE

This study investigates the performance of cOSSCIR using head CT datasets acquired on a clinical photon-counting CT (PCCT) prototype. This is the first investigation of cOSSCIR for large-scale, anatomically complex, clinical PCCT data. The cOSSCIR decomposition is preceded by a spectrum estimation and nonlinear counts correction calibration step to address nonideal detector effects.

METHODS

Head CT data were acquired on an early prototype clinical PCCT system using an edge-on silicon detector with eight energy bins. Calibration data of a step wedge phantom were also acquired and used to train a spectral model to account for the source spectrum and detector spectral response, and also to train a nonlinear counts correction model to account for pulse pileup effects. The cOSSCIR algorithm optimized the bone and adipose basis images directly from the photon counts data, while placing a grouped total variation (TV) constraint on the basis images. For comparison, basis images were also reconstructed by a two-step projection-domain approach of Maximum Likelihood Estimation (MLE) for decomposing basis sinograms, followed by filtered backprojection (MLE + FBP) or a TV minimization algorithm (MLE + TVmin ) to reconstruct basis images. We hypothesize that the cOSSCIR approach will provide a more stable inversion into basis images compared to two-step approaches. To investigate this hypothesis, the noise standard deviation in bone and soft-tissue regions of interest (ROIs) in the reconstructed images were compared between cOSSCIR and the two-step methods for a range of regularization constraint settings.

RESULTS

cOSSCIR reduced the noise standard deviation in the basis images by a factor of two to six compared to that of MLE + TVmin , when both algorithms were constrained to produce images with the same TV. The cOSSCIR images demonstrated qualitatively improved spatial resolution and depiction of fine anatomical detail. The MLE + TVmin algorithm resulted in lower noise standard deviation than cOSSCIR for the virtual monoenergetic images (VMIs) at higher energy levels and constraint settings, while the cOSSCIR VMIs resulted in lower noise standard deviation at lower energy levels and overall higher qualitative spatial resolution. There were no statistically significant differences in the mean values within the bone region of images reconstructed by the studied algorithms. There were statistically significant differences in the mean values within the soft-tissue region of the reconstructed images, with cOSSCIR producing mean values closer to the expected values.

CONCLUSIONS

The cOSSCIR algorithm, combined with our previously proposed spectral model estimation and nonlinear counts correction method, successfully estimated bone and adipose basis images from high resolution, large-scale patient data from a clinical PCCT prototype. The cOSSCIR basis images were able to depict fine anatomical details with a factor of two to six reduction in noise standard deviation compared to that of the MLE + TVmin two-step approach.

Joint Reconstruction and Spectrum Refinement for Photon-Counting-Detector Spectral CT

Photon-counting detector CT (PCD-CT) is a revolutionary technology in decades in the field of CT. Its potential benefits in lowering noise, dose reduction, and material-specific imaging enable completely new clinical applications. Spectral reconstruction of basis material maps requires knowledge of the x-ray spectrum and the spectral response calibration of the detector. However, spectrum estimation errors caused by inaccurate energy threshold calibration will degrade the accuracy of the reconstructions. Existing spectrum estimation methods are not adequately modeled for bias in energy threshold position. Besides, directly solving a big number of variables of the pixel-wise effective spectra for PCD is an ill-conditioned problem so that stable solution is hardly achievable. In this paper, we assumed the effective spectra variation across the detector mainly comes from the calibration error in the energy threshold positions as well as the intrinsic threshold distribution. We propose a joint reconstruction and spectrum refinement algorithm (JoSR) that introduces an innovative spectrum model based on non-negative matrix factorization (NMF) to significantly reduce the dimension of unknowns so that makes the problem well-conditioned. The polychromatic spectral imaging model and the basis material decomposition method together form an optimization objective. The proximal regularized block coordinate descent algorithm is adopted to deal with the non-convex optimization problem to ensure convergence. Simulation studies and experiments on a laboratory PCD-CT system validated the proposed JoSR method. The results demonstrate its advantages on image quality and quantitative accuracy over other state-of-the-art methods in the field.

Comprehensive evaluations of a prototype full field-of-view photon counting CT system through phantom studies

Objective. Photon counting CT (PCCT) has been a research focus in the last two decades. Recent studies and advancements have demonstrated that systems using semiconductor-based photon counting detectors (PCDs) have the potential to provide better contrast, noise and spatial resolution performance compared to conventional scintillator-based systems. With multi-energy threshold detection, PCD can simultaneously provide the photon energy measurement and enable material decomposition for spectral imaging. In this work, we report a performance evaluation of our first CdZnTe-based prototype full-size PCCT system through various phantom imaging studies.Approach.This prototype system supports a 500 mm scan field-of-view and 10 mmz-coverage at isocenter. Phantom scans were acquired using 120 kVp from 50 to 400 mAs to assess the imaging performance on: CT number accuracy, uniformity, noise, spatial resolution, material differentiation and quantification.Main results.Both qualitative and quantitative evaluations show that PCCT, under the tested conditions, has superior imaging performance with lower noise and improved spatial resolution compared to conventional energy integrating detector (EID)-CT. Using projection domain material decomposition approach with multiple energy bin measurements, PCCT virtual monoenergetic images have lower noise, and good accuracy in quantifying iodine and calcium concentrations. These results lead to increased contrast-to-noise ratio (CNR) for both high and low contrast study objects compared to EID-CT at matched dose and spatial resolution. PCCT can also generate super-high resolution images using much smaller detector pixel size than EID-CT and greatly improve image spatial resolution.Significance.Improved spatial resolution and quantification accuracy with reduced image noise of the PCCT images can potentially lead to better diagnosis at reduced radiation dose compared to conventional EID-CT. Increased CNR achieved by PCCT suggests potential reduction in iodine contrast media load, resulting in better patient safety and reduced cost.

Dual- and multi-energy CT for particle stopping-power estimation: current state, challenges and potential

Range uncertainty has been a key factor preventing particle radiotherapy from reaching its full physical potential. One of the main contributing sources is the uncertainty in estimating particle stopping power (ρ_s) within patients. Currently, theρ_sdistribution in a patient is derived from a single-energy CT (SECT) scan acquired for treatment planning by converting CT number expressed in Hounsfield units (HU) of each voxel toρ_susing a Hounsfield look-up table (HLUT), also known as the CT calibration curve. HU andρ_sshare a linear relationship with electron density but differ in their additional dependence on elemental composition through different physical properties, i.e. effective atomic number and mean excitation energy, respectively. Because of that, the HLUT approach is particularly sensitive to differences in elemental composition between real human tissues and tissue surrogates as well as tissue variations within and among individual patients. The use of dual-energy CT (DECT) forρ_sprediction has been shown to be effective in reducing the uncertainty inρ_sestimation compared to SECT. The acquisition of CT data over different x-ray spectra yields additional information on the material elemental composition. Recently, multi-energy CT (MECT) has been explored to deduct material-specific information with higher dimensionality, which has the potential to further improve the accuracy ofρ_sestimation. Even though various DECT and MECT methods have been proposed and evaluated over the years, these approaches are still only scarcely implemented in routine clinical practice. In this topical review, we aim at accelerating this translation process by providing: (1) a comprehensive review of the existing DECT/MECT methods forρ_sestimation with their respective strengths and weaknesses; (2) a general review of uncertainties associated with DECT/MECT methods; (3) a general review of different aspects related to clinical implementation of DECT/MECT methods; (4) other potential advanced DECT/MECT applications beyondρ_sestimation.

Spectral calibration of photon-counting detectors at high photon flux

BACKGROUND

Calibration of photon-counting detectors (PCDs) is necessary for quantitatively accurate spectral computed tomography (CT), but the calibration process can be complicated by nonlinear flux-dependent physical factors such as pulse pile-up.

PURPOSE

This work develops a method for spectral sensitivity calibration of a PCD-based spectral CT system that incorporates nonlinear flux dependence and can thus be employed at high photon flux.

METHODS

A calibration model for the spectral response and polynomial flux dependence is proposed, which incorporates prior x-ray source spectrum and PCD models and that has a small set of parameters for adjusting to the spectral CT system of interest. The model parameters are determined by fitting transmission data from a known object of known composition: a step-wedge phantom composed of different thicknesses of aluminum, a bone equivalent, and polymethyl methacrylate (PMMA), a soft-tissue equivalent. This fitting employs Tikhonov regularization, and the regularization strength and the polynomial order for the intensity modeling are determined by bias and variance analysis. The spectral calibration and nonlinear intensity correction is validated on transmission measurements through a third material, Teflon, at different x-ray photon flux levels.

RESULTS

The nonlinear intensity dependence is determined to be accurately accounted for with a third-order polynomial. The calibrated spectral CT model accurately predicts Teflon transmission to within 1% for flux levels up to 50% of the detector maximum.

CONCLUSIONS

The proposed PCD calibration method enables accurate physical modeling necessary for quantitative imaging in spectral CT. Furthermore, the model applies to high flux settings so that acquisition times will not be limited by restricting the spectral CT system to low flux levels.

One-step iterative reconstruction approach based on eigentissue decomposition for spectral photon-counting computed tomography

Purpose: We propose a one-step tissue characterization method for spectral photon-counting computed tomography (SPCCT) using eigentissue decomposition (ETD), tailored for highly accurate human tissue characterization in radiotherapy. Methods: The approach combines a Poisson likelihood, a spatial prior, and a quantitative prior constraining eigentissue fractions based on expected values for tabulated tissues. There are two regularization parameters: α for the quantitative prior, and β for the spatial prior. The approach is validated in a realistic simulation environment for SPCCT. The impact of α and β is evaluated on a virtual phantom. The framework is tested on a virtual patient and compared with two sinogram-based two-step methods [using respectively filtered backprojection (FBP) and an iterative method for the second step] and a post-reconstruction approach with the same quantitative prior. All methods use ETD. Results: Optimal performance with respect to bias or RMSE is achieved with different combinations of α and β on the cylindrical phantom. Evaluated in tissues of the virtual patient, the one-step framework outperforms two-step and post-reconstruction approaches to quantify proton-stopping power (SPR). The mean absolute bias on the SPR is 0.6% (two-step FBP), 0.6% (two-step iterative), 0.6% (post-reconstruction), and 0.2% (one-step optimized for low bias). Following the same order, the RMSE on the SPR is 13.3%, 2.5%, 3.2%, and 1.5%. Conclusions: Accurate and precise characterization with ETD can be achieved with noisy SPCCT data without the need to rely on post-reconstruction methods. The one-step framework is more accurate and precise than two-step methods for human tissue characterization.

Model-based pulse pileup and charge sharing compensation for photon counting detectors: A simulation study

Purpose

We aim at developing a model‐based algorithm that compensates for the effect of both pulse pileup (PP) and charge sharing (CS) and evaluates the performance using computer simulations.

Methods

The proposed PCP algorithm for PP and CS compensation uses cascaded models for CS and PP we previously developed, maximizes Poisson log‐likelihood, and uses an efficient three‐step exhaustive search. For comparison, we also developed an LCP algorithm that combines models for a loss of counts (LCs) and CS. Two types of computer simulations, slab‐ and computed tomography (CT)‐based, were performed to assess the performance of both PCP and LCP with 200 and 800 mA, (300 µm)² × 1.6‐mm cadmium telluride detector, and a dead‐time of 23 ns. A slab‐based assessment used a pair of adipose and iodine with different thicknesses, attenuated X‐rays, and assessed the bias and noise of the outputs from one detector pixel; a CT‐based assessment simulated a chest/cardiac scan and a head‐and‐neck scan using 3D phantom and noisy cone‐beam projections.

Results

With the slab simulation, the PCP had little or no biases when the expected counts were sufficiently large, even though a probability of count loss (PCL) due to dead‐time loss or PP was as high as 0.8. In contrast, the LCP had significant biases (>±2 cm of adipose) when the PCL was higher than 0.15. Biases were present with both PCP and LCP when the expected counts were less than 10–120 per datum, which was attributed to the fact that the maximum likelihood did not approach the asymptote. The noise of PCP was within 8% from the Cramér–Rao lower bounds for most cases when no significant bias was present. The two CT studies essentially agreed with the slab simulation study. PCP had little or no biases in the estimated basis line integrals, reconstructed basis density maps, and synthesized monoenergetic CT images. But the LCP had significant biases in basis line integrals when X‐ray beams passed through lungs and near the body and neck contours, where the PCLs were above 0.15. As a consequence, basis density maps and monoenergetic CT images obtained by LCP had biases throughout the imaged space.

Conclusion

We have developed the PCP algorithm that uses the PP–CS model. When the expected counts are more than 10–120 per datum, the PCP algorithm is statistically efficient and successfully compensates for the effect of the spectral distortion due to both PP and CS providing little or no biases in basis line integrals, basis density maps, and monoenergetic CT images regardless of count‐rates. In contrast, the LCP algorithm, which models an LC due to pileup, produces severe biases when incident count‐rates are high and the PCL is 0.15 or higher.

Addressing CT metal artifacts using photon-counting detectors and one-step spectral CT image reconstruction

PURPOSE

The constrained one-step spectral CT image reconstruction (cOSSCIR) algorithm with a nonconvex alternating direction method of multipliers optimizer is proposed for addressing computed tomography (CT) metal artifacts caused by beam hardening, noise, and photon starvation. The quantitative performance of cOSSCIR is investigated through a series of photon-counting CT simulations.

METHODS

cOSSCIR directly estimates basis material maps from photon-counting data using a physics-based forward model that accounts for beam hardening. The cOSSCIR optimization framework places constraints on the basis maps, which we hypothesize will stabilize the decomposition and reduce streaks caused by noise and photon starvation. Another advantage of cOSSCIR is that the spectral data need not be registered, so that a ray can be used even if some energy window measurements are unavailable. Photon-counting CT acquisitions of a virtual pelvic phantom with low-contrast soft tissue texture and bilateral hip prostheses were simulated. Bone and water basis maps were estimated using the cOSSCIR algorithm and combined to form a virtual monoenergetic image for the evaluation of metal artifacts. The cOSSCIR images were compared to a "two-step" decomposition approach that first estimated basis sinograms using a maximum likelihood algorithm and then reconstructed basis maps using an iterative total variation constrained least-squares optimization (MLE+TVmin $_{\text{min}}$ ). Images were also compared to a nonspectral TVmin $_{\text{min}}$ reconstruction of the total number of counts detected for each ray with and without normalized metal artifact reduction (NMAR) applied. The simulated metal density was increased to investigate the effects of increasing photon starvation. The quantitative error and standard deviation in regions of the phantom were compared across the investigated algorithms. The ability of cOSSCIR to reproduce the soft-tissue texture, while reducing metal artifacts, was quantitatively evaluated.

RESULTS

Noiseless simulations demonstrated the convergence of the cOSSCIR and MLE+TVmin $_{\text{min}}$ algorithms to the correct basis maps in the presence of beam-hardening effects. When noise was simulated, cOSSCIR demonstrated a quantitative error of -1 HU, compared to 2 HU error for the MLE+TVmin $_{\text{min}}$ algorithm and -154 HU error for the nonspectral TVmin $_{\text{min}}$ +NMAR algorithm. For the cOSSCIR algorithm, the standard deviation in the central iodine region of interest was 20 HU, compared to 299 HU for the MLE+TVmin $_{\text{min}}$ algorithm, 41 HU for the MLE+TVmin $_{\text{min}}$ +Mask algorithm that excluded rays through metal, and 55 HU for the nonspectral TVmin $_{\text{min}}$ +NMAR algorithm. Increasing levels of photon starvation did not impact the bias or standard deviation of the cOSSCIR images. cOSSCIR was able to reproduce the soft-tissue texture when an appropriate regularization constraint value was selected.

CONCLUSIONS

By directly inverting photon-counting CT data into basis maps using an accurate physics-based forward model and a constrained optimization algorithm, cOSSCIR avoids metal artifacts due to beam hardening, noise, and photon starvation. The cOSSCIR algorithm demonstrated improved stability and accuracy compared to a two-step method of decomposition followed by reconstruction.

DIRECT-Net: A unified mutual-domain material decomposition network for quantitative dual-energy CT imaging

PURPOSE

The purpose of this paper is to present an end-to-end deep convolutional neural network to improve the dual-energy CT (DECT) material decomposition performance.

METHODS

In this study, we proposes a unified mutual-domain (sinogram domain and CT domain) material decomposition network (DIRECT-Net) for DECT imaging. By design, the DIRECT-Net has immediate access to mutual-domain data, and utilizes stacked convolution neural network layers for noise reduction and material decomposition. The training data are numerically generated following the fundamental DECT imaging physics. Numerical simulation of the XCAT digital phantom, experiments of a biological specimen, a calcium chloride phantom and an iodine solution phantom are carried out to evaluate the performance of DIRECT-Net. Comparisons are performed with different DECT decomposition algorithms.

RESULTS

Results demonstrate that the proposed DIRECT-Net can generate water and bone basis images with less artifacts compared to the other decomposition methods. Additionally, the quantification errors of the calcium chloride (75-375 mg/cm³ ) and the iodine (2-20 mg/cm³ ) are less than 4%.

CONCLUSIONS

An end-to-end material decomposition network is proposed for quantitative DECT imaging. The qualitative and quantitative results demonstrate that this new DIRECT-Net has promising benefits in improving the DECT image quality.

High-resolution model-based material decomposition in dual-layer flat-panel CBCT

PURPOSE

Spectral CT uses energy-dependent measurements that enable material discrimination in addition to reconstruction of structural information. Flat-panel detectors (FPDs) have been widely used in dedicated and interventional systems to deliver high spatial resolution, volumetric cone-beam CT (CBCT) in compact and OR-friendly designs. In this work, we derive a model-based method that facilitates high-resolution material decomposition in a spectral CBCT system equipped with a prototype dual-layer FPD. Through high-fidelity modeling of multilayer detector, we seek to avoid resolution loss that is present in more traditional processing and decomposition approaches.

METHOD

A physical model for spectral measurements in dual-layer flat-panel CBCT is developed including layer-dependent differences in system geometry, spectral sensitivities, and detector blur (e.g., due to varied scintillator thicknesses). This forward model is integrated into a model-based material decomposition (MBMD) method based on minimization of a penalized weighted least-squared (PWLS) objective function. The noise and resolution performance of this approach was compared with traditional projection-domain decomposition (PDD) and image-domain decomposition (IDD) approaches as well as one-step MBMD with lower-fidelity models that use approximated geometry, projection interpolation, or an idealized system geometry without system blur model. Physical studies using high-resolution three-dimensional (3D)-printed water-iodine phantoms were conducted to demonstrate the high-resolution imaging performance of the compared decomposition methods in iodine basis images and synthetic monoenergetic images.

RESULTS

Physical experiments demonstrate that the MBMD methods incorporating an accurate geometry model can yield higher spatial resolution iodine basis images and synthetic monoenergetic images than PDD and IDD results at the same noise level. MBMD with blur modeling can further improve the spatial-resolution compared with the decomposition results obtained with IDD, PDD, and MBMD methods with lower-fidelity models. Using the MBMD without or with blur model can increase the absolute modulation at 1.75 lp/mm by 10% and 22% compared with IDD at the same noise level.

CONCLUSION

The proposed model-based material decomposition method for a dual-layer flat-panel CBCT system has demonstrated an ability to extend high-resolution performance through sophisticated detector modeling including the layer-dependent blur. The proposed work has the potential to not only facilitate high-resolution spectral CT in interventional and dedicated CBCT systems, but may also provide the opportunity to evaluate different flat-panel design trade-offs including multilayer FPDs with mismatched geometries, scintillator thicknesses, and spectral sensitivities.

An experimental method to correct low-frequency concentric artifacts in photon counting CT

Large-area photon counting detectors (PCDs) are usually built by tiling multiple semiconductor panels that often have slightly different spectral responses to input x-rays. As a result of this spectral inconsistency, experimental PCD-CT images of large, human-sized objects may show high-frequency ring artifacts and low-frequency band artifacts. Due to the much larger width of the bands compared with the rings, the concentric artifact problem in PCD-CT images of human-sized objects cannot be adequately addressed by conventional CT ring correction methods. This work presents an experimental method to correct the concentric artifacts in PCD-CT. The method is applicable to not only energy-discriminating PCDs with multiple bins but also PCDs with only a single threshold controller. Its principle is similar to the two-step beam hardening correction method, except that the proposed method uses pixel-specific polynomial functions to address the spectral inconsistency problem across the detector plane. The pixel-specific polynomial coefficients were experimentally calibrated using 15 acrylic sheets and 6 aluminum sheets of known thicknesses. The pixel-specific polynomial functions were used to convert the measured PCD-CT projection data to acrylic- and aluminum-equivalent thicknesses that are energy-independent. The proposed method was experimentally evaluated using a human cadaver head and multiple physical phantoms: two of them contain iodine and one phantom contains dual K-edge contrast materials (gadolinium and iodine). The results show that the proposed method can effectively remove the low-frequency concentric artifacts in PCD-CT images while reducing beam hardening artifacts. In contrast, the conventional CT ring correction algorithm did not adequately address the low-frequency band artifacts. Compared with the direct material decomposition-based correction method, the proposed method not only relaxes the requirement of multi-energy bins but also generates images with lower noise and fewer concentric artifacts.

Photon Counting CT: Clinical Applications and Future Developments

The use of a photon counting detector in CT (PCD CT) is currently the subject of intense investigation and development. In this review article, we will describe potential clinical applications of this technology with a particular focus on the experience of our own institution with a prototype PCD CT scanner. PCDs have three primary advantages over conventional, energy integrating detectors (EIDs): they provide spectral information without need for a dedicated dual energy protocol; they are immune to electronic noise; and they can be made very high resolution without significant compromises to quantum efficiency. These advantages translate into several clinical applications. Metal artifacts, beam hardening artifacts, and noise streaks from photon starvation can be better mitigated using PCD CT. Certain incidental findings can be better characterized using the spectral information from PCD CT. High-contrast, high-resolution structures such as the temporal bone can be better visualized using PCD CT and at greatly reduced dose. We also discuss new possibilities on the horizon, including new contrast agents, and how anticipated improvements in PCD CT will translate to performance in these applications.

Regularization by denoising sub-sampled Newton method for spectral CT multi-material decomposition

Spectral Computed Tomography (CT) is an emerging technology that enables us to estimate the concentration of basis materials within a scanned object by exploiting different photon energy spectra. In this work, we aim at efficiently solving a model-based maximum-a-posterior problem to reconstruct multi-materials images with application to spectral CT. In particular, we propose to solve a regularized optimization problem based on a plug-in image-denoising function using a randomized second order method. By approximating the Newton step using a sketching of the Hessian of the likelihood function, it is possible to reduce the complexity while retaining the complex prior structure given by the data-driven regularizer. We exploit a non-uniform block sub-sampling of the Hessian with inexact but efficient conjugate gradient updates that require only Jacobian-vector products for denoising term. Finally, we show numerical and experimental results for spectral CT materials decomposition. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

A signal detection model for quantifying overregularization in nonlinear image reconstruction

Many useful image quality metrics for evaluating linear image reconstruction techniques do not apply to or are difficult to interpret for nonlinear image reconstruction. The vast majority of metrics employed for evaluating nonlinear image reconstruction are based on some form of global image fidelity, such as image root mean square error (RMSE). Use of such metrics can lead to overregularization in the sense that they can favor removal of subtle details in the image. To address this shortcoming, we develop an image quality metric based on signal detection that serves as a surrogate to the qualitative loss of fine image details. The metric is demonstrated in the context of a breast CT simulation, where different equal-dose configurations are considered. The configurations differ in the number of projections acquired. Image reconstruction is performed with a nonlinear algorithm based on total variation constrained least-squares (TV-LSQ). The resulting images are studied as a function of three parameters: number of views acquired, total variation constraint value, and number of iterations. The images are evaluated visually, with image RMSE, and with the proposed signal-detection-based metric. The latter uses a small signal, and computes detectability in the sinogram and in the reconstructed image. Loss of signal detectability through the image reconstruction process is taken as a quantitative measure of loss of fine details in the image. Loss of signal detectability is seen to correlate well with the blocky or patchy appearance due to overregularization with TV-LSQ, and this trend runs counter to the image RMSE metric, which tends to favor the over-regularized images. The proposed signal detection-based metric provides an image quality assessment that is complimentary to that of image RMSE. Using the two metrics in concert may yield a useful prescription for determining CT algorithm and configuration parameters when nonlinear image reconstruction is used.

Multi-energy computed tomography and material quantification: Current barriers and opportunities for advancement

Computed tomography (CT) technology has rapidly evolved since its introduction in the 1970s. It is a highly important diagnostic tool for clinicians as demonstrated by the significant increase in utilization over several decades. However, much of the effort to develop and advance CT applications has been focused on improving visual sensitivity and reducing radiation dose. In comparison to these areas, improvements in quantitative CT have lagged behind. While this could be a consequence of the technological limitations of conventional CT, advanced dual-energy CT (DECT) and photon-counting detector CT (PCD-CT) offer new opportunities for quantitation. Routine use of DECT is becoming more widely available and PCD-CT is rapidly developing. This review covers efforts to address an unmet need for improved quantitative imaging to better characterize disease, identify biomarkers, and evaluate therapeutic response, with an emphasis on multi-energy CT applications. The review will primarily discuss applications that have utilized quantitative metrics using both conventional and DECT, such as bone mineral density measurement, evaluation of renal lesions, and diagnosis of fatty liver disease. Other topics that will be discussed include efforts to improve quantitative CT volumetry and radiomics. Finally, we will address the use of quantitative CT to enhance image-guided techniques for surgery, radiotherapy and interventions and provide unique opportunities for development of new contrast agents.

High-Resolution Model-based Material Decomposition for Multi-Layer Flat-Panel Detectors

In this work we compare a novel model-based material decomposition (MBMD) approach against a standard approach in high-resolution spectral CT using multi-layer flat-panel detectors. Physical experiments were conducted using a prototype dual-layer detector and a custom high-resolution iodine-enhanced line-pair phantom. Reconstructions were performed using three methods: traditional filtered back-projection (FBP) followed by image-domain decomposition, idealized MBMD with no blur modeling (iMBMD), and MBMD with system blur modeling (bMBMD). We find that both MBMD methods yielded higher resolution decompositions with lower noise than the FBP method, and that bMBMD further improves spatial resolution over iMBMD due to the additional blur modeling. These results demonstrate the advantages of MBMD in resolution performance and noise control over traditional methods for spectral CT. Model-based material decomposition hence has great potential in high-resolution spectral CT applications.

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.

Spectrum Estimation-Guided Iterative Reconstruction Algorithm for Dual Energy CT

X-ray spectrum plays a very important role in dual energy computed tomography (DECT) reconstruction. Because it is difficult to measure x-ray spectrum directly in practice, efforts have been devoted into spectrum estimation by using transmission measurements. These measurement methods are independent of the image reconstruction, which bring extra cost and are time consuming. Furthermore, the estimated spectrum mismatch would degrade the quality of the reconstructed images. In this paper, we propose a spectrum estimation-guided iterative reconstruction algorithm for DECT which aims to simultaneously recover the spectrum and reconstruct the image. The proposed algorithm is formulated as an optimization framework combining spectrum estimation based on model spectra representation, image reconstruction, and regularization for noise suppression. To resolve the multi-variable optimization problem of simultaneously obtaining the spectra and images, we introduce the block coordinate descent (BCD) method into the optimization iteration. Both the numerical simulations and physical phantom experiments are performed to verify and evaluate the proposed method. The experimental results validate the accuracy of the estimated spectra and reconstructed images under different noise levels. The proposed method obtains a better image quality compared with the reconstructed images from the known exact spectra and is robust in noisy data applications.

Block matching frame based material reconstruction for spectral CT

Spectral computed tomography (CT) has a great potential in material identification and decomposition. To achieve high-quality material composition images and further suppress the x-ray beam hardening artifacts, we first propose a one-step material reconstruction model based on Taylor's first-order expansion. Then, we develop a basic material reconstruction method named material simultaneous algebraic reconstruction technique (MSART). Considering the local similarity of each material image, we incorporate a powerful block matching frame (BMF) into the material reconstruction (MR) model and generate a BMF based MR (BMFMR) method. Because the BMFMR model contains the L 0-norm problem, we adopt a split-Bregman method for optimization. The numerical simulation and physical phantom experiment results validate the correctness of the material reconstruction algorithms and demonstrate that the BMF regularization outperforms the total variation and no-local mean regularizations.

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.

Photon-Counting Computed Tomography for Vascular Imaging of the Head and Neck: First In Vivo Human Results

PURPOSE

The purpose of this study was to evaluate image quality of a spectral photon-counting detector (PCD) computed tomography (CT) system for evaluation of major arteries of the head and neck compared with conventional single-energy CT scans using energy-integrating detectors (EIDs).

METHODS

In this institutional review board-approved study, 16 asymptomatic subjects (7 men) provided informed consent and received both PCD and EID contrast-enhanced CT scans of the head and neck (mean age, 58 years; range, 46-75 years). Tube settings were (EID: 120 kVp/160 mA vs PCD: 140 kVp/108 mA) for all volunteers. Quantitative analysis included measurements of mean attenuation, image noise, and contrast-to-noise ratio (CNR). Spectral PCD data were used to reconstruct virtual monoenergetic images and iodine maps. A head phantom was used to validate iodine concentration measurements in PCD images only. Two radiologists blinded to detector type independently scored the image quality of different segments of the arteries, as well as diagnostic acceptability, image noise, and severity of artifacts of the PCD and EID images. Reproducibility was assessed with intraclass correlation coefficient. Linear mixed models that account for within-subject correlation of analyzed arterial segments were used. Linear regression and Bland-Altman analysis with 95% limits of agreement were used to calculate the accuracy of material decomposition.

RESULTS

Photon-counting detector image quality scores were significantly higher compared with EID image quality scores with lower image noise (P < 0.01) and less image artifacts (P < 0.001). Photon-counting detector image noise was 9.1% lower than EID image noise (8.0 ± 1.3 HU vs 8.8 ± 1.5 HU, respectively, P < 0.001). Arterial segments showed artifacts on EID images due to beam hardening that were not present on PCD images. On PCD images of the head phantom, there was excellent correlation (R = 0.998) between actual and calculated iodine concentrations without significant bias (bias: -0.4 mg/mL [95% limits of agreements: -1.1 to 0.4 mg/mL]). Iodine maps had 20.7% higher CNR compared with nonspectral PCD (65.2 ± 9.0 vs 54.0 ± 4.5, P = 0.01), and virtual monoenergetic image at 70 keV showed similar CNR to nonspectral images (52.6 ± 4.2 vs 54.0 ± 4.5, P = 0.39).

CONCLUSIONS

Photon-counting CT has the potential to improve the image quality of carotid and intracranial CT angiography compared with single-energy EID CT.

Estimating the spectrum in computed tomography via Kullback-Leibler divergence constrained optimization

PURPOSE

We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x-ray spectrum that can accurately model the x-ray transmission curves and reflects a realistic shape of the typical energy spectra of the CT system.

METHODS

Spectrum estimation is posed as an optimization problem with x-ray spectrum as unknown variables, and a Kullback-Leibler (KL)-divergence constraint is employed to incorporate prior knowledge of the spectrum and enhance numerical stability of the estimation process. The formulated constrained optimization problem is convex and can be solved efficiently by use of the exponentiated-gradient (EG) algorithm. We demonstrate the effectiveness of the proposed approach on the simulated and experimental data. The comparison to the expectation-maximization (EM) method is also discussed.

RESULTS

In simulations, the proposed algorithm is seen to yield x-ray spectra that closely match the ground truth and represent the attenuation process of x-ray photons in materials, both included and not included in the estimation process. In experiments, the calculated transmission curve is in good agreement with the measured transmission curve, and the estimated spectra exhibits physically realistic looking shapes. The results further show the comparable performance between the proposed optimization-based approach and EM.

CONCLUSIONS

Our formulation of a constrained optimization provides an interpretable and flexible framework for spectrum estimation. Moreover, a KL-divergence constraint can include a prior spectrum and appears to capture important features of x-ray spectrum, allowing accurate and robust estimation of x-ray spectrum in CT imaging.

Multicolour imaging with spectral photon-counting CT: a phantom study

Background

To evaluate the feasibility of multicolour quantitative imaging with spectral photon-counting computed tomography (SPCCT) of different mixed contrast agents.

Methods

Phantoms containing eleven tubes with mixtures of varying proportions of two contrast agents (i.e. two selected from gadolinium, iodine or gold nanoparticles) were prepared so that the attenuation of each tube was about 280 HU. Scans were acquired at 120 kVp and 100 mAs using a five-bin preclinical SPCCT prototype, generating conventional, water, iodine, gadolinium and gold images. The correlation between prepared and measured concentrations was assessed using linear regression. The cross-contamination was measured for each material as the root mean square error (RMSE) of its concentration in the other material images, where no signal was expected. The contrast-to-noise ratio (CNR) relative to a phosphate buffered saline tube was calculated for each contrast agent.

Results

The solutions had similar attenuations (279 ± 10 HU, mean ± standard deviation) and could not be differentiated on conventional images. However, a distinction was observed in the material images within the same samples, and the measured and prepared concentrations were strongly correlated (R² ≥ 0.97, 0.81 ≤ slope ≤ 0.95, -0.68 ≤ offset ≤ 0.89 mg/mL). Cross-contamination in the iodine images for the mixture of gold and gadolinium contrast agents (RMSE = 0.34 mg/mL) was observed. CNR for 1 mg/mL of contrast agent was better for the mixture of iodine and gadolinium (CNR_iodine = 3.20, CNR_gadolinium = 2.80) than gold and gadolinium (CNR_gadolinium = 1.67, CNR_gold = 1.37).

Conclusions

SPCCT enables multicolour quantitative imaging. As a result, it should be possible to perform imaging of multiple uptake phases of a given tissue/organ within a single scan by injecting different contrast agents sequentially.

A General CT Reconstruction Algorithm for Model-Based Material Decomposition

Material decomposition in CT has the potential to reduce artifacts and improve quantitative accuracy by utilizing spectral models and multi-energy scans. In this work we present a novel Model-Based Material Decomposition (MBMD) method based on an existing iterative reconstruction algorithm derived from a general non-linear forward model. A digital water phantom with inserts containing different concentrations of calcium was scanned on a kV switching system. We used the presented method to simultaneously reconstruct water and calcium material density images, and compared the results to an image domain and a projection domain decomposition method. When switching voltage every other frame, MBMD resulted in more accurate water and calcium concentration values than the image domain decomposition method, and was just as accurate as the projection domain decomposition method. In a second, slower, kV switching scheme (changing voltage every ten frames) which precluded the use of traditional projection domain based methods, MBMD continued to produce quantitatively accurate reconstructions. Finally, we present a preliminary study applying MBMD to a water phantom containing vials of different concentrations of K₂HPO₄ which was scanned on a cone-beam CT test bench. Both the fast and slow (emulated) kV switching schemes resulted in similar reconstructions, indicating MBMD's robustness to challenging acquisition schemes. Additionally, the K₂HPO₄ concentration ratios between the vials were accurately represented in the reconstructed K₂HPO₄ density image.