Dual-energy CT imaging over non-overlapping, orthogonal arcs of limited-angular ranges.

BACKGROUND: Interest exists in dual-energy computed tomography (DECT) imaging with scanning arcs of limited-angular ranges (LARs) for reducing scan time and radiation dose, and for enabling scan configurations of C-arm CT that can avoid possible collision between the rotating X-ray tube/detector and the imaged subject. OBJECTIVE: In this work, we investigate image reconstruction for a type of configurations of practical DECT interest, referred to as the two-orthogonal-arc configuration, in which low- and high-kVp data are collected over two non-overlapping arcs of equal LAR α, ranging from 30° to 90°, separated by 90°. The configuration can readily be implemented, e.g., on CT with dual sources separated by 90° or with the slow-kVp-switching technique. METHODS: The directional-total-variation (DTV) algorithm developed previously for image reconstruction in conventional, single-energy CT is tailored to enable image reconstruction in DECT with two-orthogonal-arc configurations. RESULTS: Performing visual inspection and quantitative analysis of monochromatic images obtained and effective atomic numbers estimated, we observe that the monochromatic images of the DTV algorithm from LAR data are with substantially reduced LAR artifacts, which are observed otherwise in those of existing algorithms, and thus visually correlate reasonably well, in terms of metrics PCC and nMI, with their reference images obtained from full-angular-range data. In addition, effective atomic numbers estimated from LAR data of DECT with two-orthogonal-arc configurations are in reasonable agreement, with relative errors up to ∼ 10%, with those estimated from full-angular-range data in DECT. CONCLUSIONS: The results acquired in the work may yield insights into the design of LAR configurations of practical dual-energy application relevance in diagnostic CT or C-arm CT imaging.

Compressive sensing in medical imaging.

The promise of compressive sensing, exploitation of compressibility to achieve high quality image reconstructions with less data, has attracted a great deal of attention in the medical imaging community. At the Compressed Sensing Incubator meeting held in April 2014 at OSA Headquarters in Washington, DC, presentations were given summarizing some of the research efforts ongoing in compressive sensing for x-ray computed tomography and magnetic resonance imaging systems. This article provides an expanded version of these presentations. Sparsity-exploiting reconstruction algorithms that have gained popularity in the medical imaging community are studied, and examples of clinical applications that could benefit from compressive sensing ideas are provided. The current and potential future impact of compressive sensing on the medical imaging field is discussed.

Report on the AAPM deep-learning spectral CT Grand Challenge.

BACKGROUND: This Special Report summarizes the 2022 AAPM Grand Challenge on Deep-Learning spectral Computed Tomography (DL-spectral CT) image reconstruction. PURPOSE: The purpose of the challenge is to develop the most accurate image reconstruction algorithm possible for solving the inverse problem associated with a fast kilovolt switching dual-energy CT scan using a three tissue-map decomposition. Participants could choose to use a deep-learning (DL), iterative, or a hybrid approach. METHODS: The challenge is based on a 2D breast CT simulation, where the simulated breast phantom consists of three tissue maps: adipose, fibroglandular, and calcification distributions. The phantom specification is stochastic so that multiple realizations can be generated for DL approaches. A dual-energy scan is simulated where the x-ray source potential of successive views alternates between 50 and 80 kilovolts (kV). A total of 512 views are generated, yielding 256 views for each source voltage. We generate 50 and 80 kV images by use of filtered back-projection (FBP) on negative logarithm processed transmission data. For participants who develop a DL approach, 1000 cases are available. Each case consists of the three 512 × 512 tissue maps, 50 and 80-kV transmission data sets and their corresponding FBP images. The goal of the DL network would then be to predict the material maps from either the transmission data, FBP images, or a combination of the two. For participants developing a physics-based approach, all of the required modeling parameters are made available: geometry, spectra, and tissue attenuation curves. The provided information also allows for hybrid approaches where physics is exploited as well as information about the scanned object derived from the 1000 training cases. Final testing is performed by computation of root-mean-square error (RMSE) for predictions on the tissue maps from 100 new cases. RESULTS: Test phase submission were received from 18 research groups. Of the 18 submissions, 17 were results obtained with algorithms that involved DL. Only the second place finishing team developed a physics-based image reconstruction algorithm. Both the winning and second place teams had highly accurate results where the RMSE was nearly zero to single floating point precision. Results from the top 10 also achieved a high degree of accuracy; and as a result, this special report outlines the methodology developed by each of these groups. CONCLUSIONS: The DL-spectral CT challenge successfully established a forum for developing image reconstruction algorithms that address an important inverse problem relevant for spectral CT.

Convergence for nonconvex ADMM, with applications to CT imaging.

The alternating direction method of multipliers (ADMM) algorithm is a powerful and flexible tool for complex optimization problems of the form m i n { f ( x ) + g ( y ) : A x + B y = c } . ADMM exhibits robust empirical performance across a range of challenging settings including nonsmoothness and nonconvexity of the objective functions f and g , and provides a simple and natural approach to the inverse problem of image reconstruction for computed tomography (CT) imaging. From the theoretical point of view, existing results for convergence in the nonconvex setting generally assume smoothness in at least one of the component functions in the objective. In this work, our new theoretical results provide convergence guarantees under a restricted strong convexity assumption without requiring smoothness or differentiability, while still allowing differentiable terms to be treated approximately if needed. We validate these theoretical results empirically, with a simulated example where both f and g are nondifferentiable-and thus outside the scope of existing theory-as well as a simulated CT image reconstruction problem.

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.

Enhancing signal detectability in learning-based CT reconstruction with a model observer inspired loss function.

Deep neural networks used for reconstructing sparse-view CT data are typically trained by minimizing a pixel-wise mean-squared error or similar loss function over a set of training images. However, networks trained with such pixel-wise losses are prone to wipe out small, low-contrast features that are critical for screening and diagnosis. To remedy this issue, we introduce a novel training loss inspired by the model observer framework to enhance the detectability of weak signals in the reconstructions. We evaluate our approach on the reconstruction of synthetic sparse-view breast CT data, and demonstrate an improvement in signal detectability with the proposed loss.

Prototyping optimization-based image reconstructions from limited-angular-range data in dual-energy CT.

Image reconstruction from data collected over full-angular range (FAR) in dual-energy CT (DECT) is well-studied. There exists interest in DECT with advanced scan configurations in which data are collected only over limited-angular ranges (LARs) for meeting unique workflow needs in certain practical imaging applications, and thus in the algorithm development for image reconstruction from such LAR data. The objective of the work is to investigate and prototype image reconstructions in DECT with LAR scans. We investigate and prototype optimization programs with various designs of constraints on the directional-total-variations (DTVs) of virtual monochromatic images and/or basis images, and derive the DTV algorithms to numerically solve the optimization programs for achieving accurate image reconstruction from data collected in a slew of different LAR scans. Using simulated and real data acquired with low- and high-kV spectra over LARs, we conduct quantitative studies to demonstrate and evaluate the optimization programs and their DTV algorithms developed. As the results of the numerical studies reveal, while the DTV algorithms yield images of visual quality and quantitative accuracy comparable to that of the existing algorithms from FAR data, the former reconstruct images with improved visualization, reduced artifacts, and also enhanced quantitative accuracy when applied to LAR data in DECT. Optimization-based, one-step algorithms, including the DTV algorithms demonstrated, can be developed for quantitative image reconstruction from spectral data collected over LARs of extents that are considerably smaller than the FAR in DECT. The theoretical and numerical results obtained can be exploited for prototyping designs of optimization-based reconstructions and LAR scans in DECT, and they may also yield insights into the development of reconstruction procedures in practical DECT applications. The approach and algorithms developed can naturally be applied to investigating image reconstruction from LAR data in multi-spectral and photon-counting CT.

Accurate Reconstruction of Multiple Basis Images Directly From Dual Energy CT Data.

OBJECTIVE: We develop optimization-based algorithms to accurately reconstruct multiple ( 2) basis images directly from dual-energy (DE) data in CT. METHODS: In medical and industrial CT imaging, some basis materials such as bone, metals, and contrast agents of interest are confined often spatially within regions in the image. Exploiting this observation, we develop an optimization-based algorithm to reconstruct, directly from DE data, basis-region images from which multiple ( 2) basis images and virtual monochromatic images (VMIs) can be obtained over the entire image array. RESULTS: We conduct experimental studies using simulated and real DE data in CT, and evaluate basis images and VMIs obtained in terms of visual inspection and quantitative metrics. The study results reveal that the algorithm developed can accurately and robustly reconstruct multiple ( 2) basis images directly from DE data. CONCLUSIONS: The developed algorithm can yield accurate multiple ( 2) basis images, VMIs, and physical quantities of interest from DE data in CT. SIGNIFICANCE: The work may provide insights into the development of practical procedures for reconstructing multiple basis images, VMIs, and physical quantities from DE data in applications. The work can be extended to reconstruct multiple basis images in multi-spectral or photon-counting CT.

Simultaneous activity and attenuation estimation in TOF-PET with TV-constrained nonconvex optimization.

An alternating direction method of multipliers (ADMM) framework is developed for nonsmooth biconvex optimization for inverse problems in imaging. In particular, the simultaneous estimation of activity and attenuation (SAA) problem in time-of-flight positron emission tomography (TOF-PET) has such a structure when maximum likelihood estimation (MLE) is employed. The ADMM framework is applied to MLE for SAA in TOF-PET, resulting in the ADMM-SAA algorithm. This algorithm is extended by imposing total variation (TV) constraints on both the activity and attenuation map, resulting in the ADMM-TVSAA algorithm. The performance of this algorithm is illustrated using the penalized maximum likelihood activity and attenuation estimation (P-MLAA) algorithm as a reference. Additional results on step-size tuning and on the use of unconstrained ADMM-SAA are presented in the previous arXiv submission: arXiv:2303.17042v1.

Optimizing dual-energy CT technique for iodine-based contrast-to-noise ratio, a theoretical study.

BACKGROUND: Dual-energy CT (DECT) systems provide valuable material-specific information by simultaneously acquiring two spectral measurements, resulting in superior image quality and contrast-to-noise ratio (CNR) while reducing radiation exposure and contrast agent usage. The selection of DECT scan parameters, including x-ray tube settings and fluence, is critical for the stability of the reconstruction process and hence the overall image quality. PURPOSE: The goal of this study is to propose a systematic theoretical method for determining the optimal DECT parameters for minimal noise and maximum CNR in virtual monochromatic images (VMIs) for fixed subject size and total radiation dose. METHODS: The noise propagation in the process of projection based material estimation from DECT measurements is analyzed. The main components of the study are the mean pixel variances for the sinogram and monochromatic image and the CNR, which were shown to depend on the Jacobian matrix of the sinograms-to-DECT measurements map. Analytic estimates for the mean sinogram and monochromatic image pixel variances and the CNR as functions of tube potentials, fluence, and VMI energy are derived, and then used in a virtual phantom experiment as an objective function for optimizing the tube settings and VMI energy to minimize the image noise and maximize the CNR. RESULTS: It was shown that DECT measurements corresponding to kV settings that maximize the square of Jacobian determinant values over a domain of interest lead to improved stability of basis material reconstructions. Instances of non-uniqueness in DECT were addressed, focusing on scenarios where the Jacobian determinant becomes zero within the domain of interest despite significant spectral separation. The presence of non-uniqueness can lead to singular solutions during the inversion of sinograms-to-DECT measurements, underscoring the importance of considering uniqueness properties in parameter selection. Additionally, the optimal VMI energy and tube potentials for maximal CNR was determined. When the x-ray beam filter material was fixed at 2 mm of aluminum and the photon fluence for low and high kV scans were considered equal, the tube potential pair of 60/120 kV led to the maximal iodine CNR in the VMI at 53 keV. CONCLUSIONS: Optimizing DECT scan parameters to maximize the CNR can be done in a systematic way. Also, choosing the parameters that maximize the Jacobian determinant over the set of expected line integrals leads to more stable reconstructions due to the reduced amplification of the measurement noise. Since the values of the Jacobian determinant depend strongly on the imaging task, careful consideration of all of the relevant factors is needed when implementing the proposed framework.

Accurate reconstruction of 4D spectral-spatial images from sparse-view data in continuous-wave EPRI.

In continuous-wave electron paramagnetic resonance imaging (CW EPRI), data are collected generally at densely sampled views sufficient for achieving accurate reconstruction of a four dimensional spectral-spatial (4DSS) image by use of the conventional filtered-backprojection (FBP) algorithm. It is desirable to minimize the scan time by collection of data only at sparsely sampled views, referred to as sparse-view data. Interest thus remains in investigation of algorithms for accurate reconstruction of 4DSS images from sparse-view data collected for potentially enabling fast data acquisition in CW EPRI. In this study, we investigate and demonstrate optimization-based algorithms for accurate reconstruction of 4DSS images from sparse-view data. Numerical studies using simulated and real sparse-view data acquired in CW EPRI are conducted that reveal, in terms of image visualization and physical-parameter estimation, the potential of the algorithms developed for yielding accurate 4DSS images from sparse-view data in CW EPRI. The algorithms developed may be exploited for enabling sparse-view scans with minimized scan time in CW EPRI for yielding 4DSS images of quality comparable to, or better than, that of the FBP reconstruction from data collected at densely sampled views.

Simultaneous Activity and Attenuation Estimation in TOF-PET With TV-Constrained Nonconvex Optimization.

An alternating direction method of multipliers (ADMM) framework is developed for nonsmooth biconvex optimization for inverse problems in imaging. In particular, the simultaneous estimation of activity and attenuation (SAA) problem in time-of-flight positron emission tomography (TOF-PET) has such a structure when maximum likelihood estimation (MLE) is employed. The ADMM framework is applied to MLE for SAA in TOF-PET, resulting in the ADMM-SAA algorithm. This algorithm is extended by imposing total variation (TV) constraints on both the activity and attenuation map, resulting in the ADMM-TVSAA algorithm. The performance of this algorithm is illustrated using the penalized maximum likelihood activity and attenuation estimation (P-MLAA) algorithm as a reference.

A directional total variation minimization algorithm for isotropic resolution in digital breast tomosynthesis.

An optimization-based image reconstruction algorithm is developed for contrast enhanced digital breast tomosynthesis (DBT) using dual-energy scanning. The algorithm minimizes directional total variation (TV) with a data discrepancy and non-negativity constraints. Iodinated contrast agent (ICA) imaging is performed by reconstructing images from dual-energy DBT data followed by weighted subtraction. Physical DBT data is acquired with a Siemens Mammomat scanner of a structured breast phantom with ICA inserts. Results are shown for both directional TV minimization and filtered back-projection for reference. It is seen that directional TV is able to substantially reduce depth blur for the ICA objects.

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.

4D-image reconstruction directly from limited-angular-range data in continuous-wave electron paramagnetic resonance imaging.

OBJECTIVE: We investigate and develop optimization-based algorithms for accurate reconstruction of four-dimensional (4D)-spectral-spatial (SS) images directly from data collected over limited angular ranges (LARs) in continuous-wave (CW) electron paramagnetic resonance imaging (EPRI). METHODS: Basing on a discrete-to-discrete data model devised in CW EPRI employing the Zeeman-modulation (ZM) scheme for data acquisition, we first formulate the image reconstruction problem as a convex, constrained optimization program that includes a data fidelity term and also constraints on the individual directional total variations (DTVs) of the 4D-SS image. Subsequently, we develop a primal-dual-based DTV algorithm, simply referred to as the DTV algorithm, to solve the constrained optimization program for achieving image reconstruction from data collected in LAR scans in CW-ZM EPRI. RESULTS: We evaluate the DTV algorithm in simulated- and real-data studies for a variety of LAR scans of interest in CW-ZM EPRI, and visual and quantitative results of the studies reveal that 4D-SS images can be reconstructed directly from LAR data, which are visually and quantitatively comparable to those obtained from data acquired in the standard, full-angular-range (FAR) scan in CW-ZM EPRI. CONCLUSION: An optimization-based DTV algorithm is developed for accurately reconstructing 4D-SS images directly from LAR data in CW-ZM EPRI. Future work includes the development and application of the optimization-based DTV algorithm for reconstructions of 4D-SS images from FAR and LAR data acquired in CW EPRI employing schemes other than the ZM scheme. SIGNIFICANCE: The DTV algorithm developed may be exploited potentially for enabling and optimizing CW EPRI with minimized imaging time and artifacts by acquiring data in LAR scans.

Investigation of discrete imaging models and iterative image reconstruction in differential X-ray phase-contrast tomography.

Differential X-ray phase-contrast tomography (DPCT) refers to a class of promising methods for reconstructing the X-ray refractive index distribution of materials that present weak X-ray absorption contrast. The tomographic projection data in DPCT, from which an estimate of the refractive index distribution is reconstructed, correspond to one-dimensional (1D) derivatives of the two-dimensional (2D) Radon transform of the refractive index distribution. There is an important need for the development of iterative image reconstruction methods for DPCT that can yield useful images from few-view projection data, thereby mitigating the long data-acquisition times and large radiation doses associated with use of analytic reconstruction methods. In this work, we analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction in DPCT. We also investigate the use of one of the models with a modern image reconstruction algorithm for performing few-view image reconstruction of a tissue specimen.

Report on the AAPM deep-learning sparse-view CT grand challenge.

PURPOSE: The purpose of the challenge is to find the deep-learning (DL) technique for sparse-view computed tomography (CT) image reconstruction that can yield the minimum root mean square error (RMSE) under ideal conditions, thereby addressing the question of whether or not DL can solve inverse problems in imaging. METHODS: The challenge setup involves a 2D breast CT simulation, where the simulated breast phantom has random fibro-glandular structure and high-contrast specks. The phantom allows for arbitrarily large training sets to be generated with perfectly known truth. The training set consists of 4000 cases where each case consists of the truth image, 128-view sinogram data, and the corresponding 128-view filtered back-projection (FBP) image. The networks are trained to predict the truth image from either the sinogram or FBP data. Geometry information is not provided. The participating algorithms are tested on a data set consisting of 100 new cases. RESULTS: About 60 groups participated in the challenge at the validation phase, and 25 groups submitted test-phase results along with reports on their DL methodology. The winning team improved reconstruction accuracy by two orders of magnitude over our previous convolutional neural network (CNN)-based study on a similar test problem. CONCLUSIONS: The DL-sparse-view challenge provides a unique opportunity to examine the state-of-the-art in DL techniques for solving the sparse-view CT inverse problem.

Image reconstruction from data over two orthogonal arcs of limited-angular ranges.

PURPOSE: Computed tomography (CT) scanning over limited-angular ranges (LARs) is of practical interest in possible reduction of imaging dose and time and in design of nonstandard scans. This work aims to investigate image reconstruction for two nonoverlapping arcs of LARs, and to demonstrate that they may allow more accurate image reconstruction than may a single arc of LAR. METHODS: We consider a configuration with two nonoverlapping arcs of LARs α 1 $\alpha _1$ and α 2 $\alpha _2$ , whose centers are separated by 90 ∘ $90^\circ$ , and refer to it as a two-orthogonal-arc configuration. Data are generated from a chest phantom with two-orthogonal-arc configurations over total angular coverage α τ = α 1 + α 2 $\alpha _\tau =\alpha _1+\alpha _2$ ranging from 18 ∘ $18^\circ$ to 180 ∘ $180^\circ$ , and images are reconstructed subsequently by use of the directional-total-variation (DTV) algorithm. For comparison, we also consider image reconstruction for a single-arc configuration of angular range α τ $\alpha _\tau$ . Quantitative metrics such as the normalized root-mean-square-error (nRMSE) are used for evaluation of image reconstruction accuracy. RESULTS: Visual inspection and quantitative analysis of images reconstructed reveal that a two-orthogonal-arc configuration generally yields more accurate image reconstruction than does its single-arc counterpart. As total angular range α τ $\alpha _\tau$ increases, the DTV algorithm yields image reconstruction with enhanced accuracy, as expected. Also, if α τ $\alpha _\tau$ remains constant, the two-orthogonal-arc configuration with α 1 = α 2 $\alpha _1 = \alpha _2$ generally leads to image reconstruction more accurate than those of two-orthogonal-arc configurations with α 1 ≠ α 2 $\alpha _1 \ne \alpha _2$ , as the nRMSE of the former can be lower than that of the latter for up to more than one order of magnitude. CONCLUSIONS: Appropriately designed two-orthogonal-arc configurations may be exploited for improving image-reconstruction accuracy in CT imaging with reduced angular coverage. This study may yield insights into the design of innovative CT scans for lowering scan time and radiation dose, and/or for avoiding scan collision in, for example, C-arm CT.

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.

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+TV min $_{\text{min}}$ ). Images were also compared to a nonspectral TV min $_{\text{min}}$ 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+TV min $_{\text{min}}$ 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+TV min $_{\text{min}}$ algorithm and -154 HU error for the nonspectral TV min $_{\text{min}}$ +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+TV min $_{\text{min}}$ algorithm, 41 HU for the MLE+TV min $_{\text{min}}$ +Mask algorithm that excluded rays through metal, and 55 HU for the nonspectral TV min $_{\text{min}}$ +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.