UNASSIGNED: Dual-energy computed tomography (DECT) is a promising technique, which can provide unique capability for material quantification. The iterative reconstruction of material maps requires spectral information and its accuracy is affected by spectral mismatch. Simultaneously estimating the spectra and reconstructing material maps avoids extra workload on spectrum estimation and the negative impact of spectral mismatch. However, existing methods are not satisfactory in image detail preservation, edge retention, and convergence rate. The purpose of this paper was to mine the similarity between the reconstructed images and the material images to improve the imaging quality, and to design an effective iteration strategy to improve the convergence efficiency.
UNASSIGNED: The material-image subspace decomposition-based iterative reconstruction (MISD-IR) with spectrum estimation was proposed for DECT. MISD-IR is an optimized model combining spectral estimation and material reconstruction with fast convergence speed and promising noise suppression capability. We proposed to reconstruct the material maps based on extended simultaneous algebraic reconstruction techniques and estimation of the spectrum with model spectral. To stabilize the iteration and alleviate the influence of errors, we introduced a weighted proximal operator based on the block coordinate descending algorithm (WP-BCD). Furthermore, the reconstructed computed tomography (CT) images were introduced to suppress the noise based on subspace decomposition, which relies on non-local regularization to prevent noise accumulation.
UNASSIGNED: In numerical experiments, the results of MISD-IR were closer to the ground truth compared with other methods. In real scanning data experiments, the results of MISD-IR showed sharper edges and details. Compared with other one-step iterative methods in the experiment, the running time of MISD-IR was reduced by 75%.
UNASSIGNED: The proposed MISD-IR can achieve accurate material decomposition (MD) without known energy spectrum in advance, and has good retention of image edges and details. Compared with other one-step iterative methods, it has high convergence efficiency.

Objective.In this work, we aim to propose an accurate and robust spectrum estimation method by synergistically combining x-ray imaging physics with a convolutional neural network (CNN).Approach.The approach relies on transmission measurements, and the estimated spectrum is formulated as a convolutional summation of a few model spectra generated using Monte Carlo simulation. The difference between the actual and estimated projections is utilized as the loss function to train the network. We contrasted this approach with the weighted sums of model spectra approach previously proposed. Comprehensive studies were performed to demonstrate the robustness and accuracy of the proposed approach in various scenarios.Main results.The results show the desirable accuracy of the CNN-based method for spectrum estimation. The ME and NRMSE were -0.021 keV and 3.04% for 80 kVp, and 0.006 keV and 4.44% for 100 kVp, superior to the previous approach. The robustness test and experimental study also demonstrated superior performances. The CNN-based approach yielded remarkably consistent results in phantoms with various material combinations, and the CNN-based approach was robust concerning spectrum generators and calibration phantoms.Significance. We proposed a method for estimating the real spectrum by integrating a deep learning model with real imaging physics. The results demonstrated that this method was accurate and robust in estimating the spectrum, and it is potentially helpful for broad x-ray imaging tasks.

UNASSIGNED: The energy spectrum is the property of the X-ray tube that describes the energy fluence per unit interval of photon energy. The existing indirect methods for estimating the spectrum ignore the influence caused by the voltage fluctuation of the X-ray tube.
UNASSIGNED: In this work, we propose a method for estimating the X-ray energy spectrum more accurately by including the voltage fluctuation of the X-ray tube. It expresses the spectrum as the weighted summation of a set of model spectra within a certain voltage fluctuation range. The difference between the raw projection and the estimated projection is considered as the objective function for obtaining the corresponding weight of each model spectrum. The equilibrium optimizer (EO) algorithm is used to find the weight combination that minimizes the objective function. Finally, the estimated spectrum is obtained. We refer to the proposed method as the poly-voltage method. The method is mainly aimed at the cone-beam computed tomography (CBCT) system.
UNASSIGNED: The model spectra mixture evaluation and projection evaluation showed that the reference spectrum can be combined by multiple model spectra. They also showed that it is appropriate to choose about 10% of the preset voltage as the voltage range of the model spectra, which can match the reference spectrum and projection quite well. The phantom evaluation showed that the beam-hardening artifact can be corrected using the estimated spectrum via the poly-voltage method, and the poly-voltage method provides not only the accurate reprojection but also an accurate spectrum. The normalized root mean square error (NRMSE) index between the spectrum generated via the poly-voltage method and the reference spectrum could be kept within 3% according to above evaluations. There existed a 1.77% percentage error between the estimated scatter of polymethyl methacrylate (PMMA) phantom using the two spectra generated via the poly-voltage method and the single-voltage method, and it could be considered for scatter simulation.
UNASSIGNED: Our proposed poly-voltage method could estimate the spectrum more accurately for both ideal and more realistic voltage spectra, and it is robust to the different modes of voltage pulse.

Any change in the light-source spectrum modifies the color information of an object. The spectral distribution of the light source can be optimized to enhance specific details of the obtained images; thus, using information-enhanced images is expected to improve the image recognition performance via machine vision. However, no studies have applied light spectrum optimization to reduce the training loss in modern machine vision using deep learning. Therefore, we propose a method for optimizing the light-source spectrum to reduce the training loss using neural networks. A two-class classification of one-vs-rest among the classes, including enamel as a healthy condition and dental lesions, was performed to validate the proposed method. The proposed convolutional neural network-based model, which accepts a 5 × 5 small patch image, was compared with an alternating optimization scheme using a linear-support vector machine that optimizes classification weights and lighting weights separately. Furthermore, it was compared with the proposed neural network-based algorithm, which inputs a pixel and consists of fully connected layers. The results of the five-fold cross-validation revealed that, compared to the previous method, the proposed method improved the F1-score and was superior to the models that were using the immutable standard illuminant D65.

This article addresses the problem of estimating the spectral correlation function (SCF), which provides quantitative characterization in the frequency domain of wide-sense cyclostationary properties of random processes which are considered to be the theoretical models of observed time series or discrete-time signals. The theoretical framework behind the SCF estimation is briefly reviewed so that an important difference between the width of the resolution cell in bifrequency plane and the step between the centers of neighboring cells is highlighted. The outline of the proposed double-number fast Fourier transform algorithm (2N-FFT) is described in the paper as a sequence of steps directly leading to a digital signal processing technique. The 2N-FFT algorithm is derived from the time-smoothing approach to cyclic periodogram estimation where the spectral interpolation based on doubling the FFT base is employed. This guarantees that no cyclic frequency is left out of the coverage grid so that at least one resolution element intersects it. A numerical simulation involving two processes, a harmonic amplitude modulated by stationary noise and a binary-pulse amplitude-modulated train, demonstrated that their cyclic frequencies are estimated with a high accuracy, reaching the size of step between resolution cells. In addition, the SCF components estimated by the proposed algorithm are shown to be similar to the curves provided by the theoretical models of the observed processes. The comparison between the proposed algorithm and the well-known FFT accumulation method in terms of computational complexity and required memory size reveals the cases where the 2N-FFT algorithm offers a reasonable trade-off.

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.
OBJECTIVE: 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.

Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation.

An x-ray energy spectrum plays an essential role in computed tomography (CT) imaging and related tasks. Because of the high photon flux of clinical CT scanners, most of the spectrum estimation methods are indirect and usually suffer from various limitations. In this study, we aim to provide a segmentation-free, indirect transmission measurement-based energy spectrum estimation method using dual-energy material decomposition. The general principle of this method is to minimize the quadratic error between the polychromatic forward projection and the raw projection to calibrate a set of unknown weights, which are used to express the unknown spectrum together with a set of model spectra. The polychromatic forward projection is performed using material-specific images, which are obtained using dual-energy material decomposition. The algorithm was evaluated using numerical simulations, experimental phantom data, and realistic patient data. The results show that the estimated spectrum matches the reference spectrum quite well and the method is robust. Extensive studies suggest that the method provides an accurate estimate of the CT spectrum without dedicated physical phantom and prolonged workflow. This paper may be attractive for CT dose calculation, artifacts reduction, polychromatic image reconstruction, and other spectrum-involved CT applications.