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Abstract BackgroundDual‐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. PurposeThe 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. MethodsThe 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. ResultsIt 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. ConclusionsOptimizing 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. 

Abstract PurposeThe 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. MethodscOSSCIR 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). Images were also compared to a nonspectral TV 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. ResultsNoiseless simulations demonstrated the convergence of the cOSSCIR and MLE+TV 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 algorithm and −154 HU error for the nonspectral TV+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 algorithm, 41 HU for the MLE+TV+Mask algorithm that excluded rays through metal, and 55 HU for the nonspectral TV+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. ConclusionsBy 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.