In x-ray multispectral (or photon-counting) computed tomography (MCT), the object of interest is scanned under multiple x-ray spectra, and it can acquire more information about the scanned object than conventional CT, in which only one x-ray spectrum is used. The obtained polychromatic projections are utilized to perform material-selective and energy-selective image reconstruction. Compared with the conventional single spectral CT, MCT has a superior material distinguishability. Therefore, it has wide potential applications in both medical and industrial areas. However, the nonlinearity and ill condition of the MCT problem make it difficult to get high-quality and fast convergence of images for existing MCT reconstruction algorithms. In this paper, we proposed an iterative reconstruction algorithm based on an oblique projection modification technique (OPMT) for fast basis material decomposition of MCT. In the case of geometric inconsistency, along the current x-ray path, the oblique projection modification direction not only relates to the polychromatic projection equation of the known spectrum, but it also comprehensively refers to the polychromatic projection equation information of the unknown spectra. Moreover, the ray-by-ray correction makes it applicable to geometrically consistent projection data. One feature of the proposed algorithm is its fast convergence speed. The OPMT considers the information from multiple polychromatic projection equations, which greatly speeds up the convergence of MCT reconstructed images. Another feature of the proposed algorithm is its high flexibility. The ray-by-ray correction will be suitable for any common MCT scanning mode. The proposed algorithm is validated with numerical experiments from both simulated and real data. Compared with the ASD-NC-POCS and E-ART algorithms, the proposed algorithm achieved high-quality reconstructed images while accelerating the convergence speed of them.

Medical CT imaging often encounters metallic implants or some metal interventional therapy apparatus. These metallic objects can produce metal artifacts in reconstruction images, which severely degrade image quality. In this paper, we analyze the difference between polychromatic projection data and Radon transform data and develop an analytical method to reduce metal artifacts. Approximate features of metal artifacts can be obtained by a simplified energy spectrum function of x-ray beam. The developed method can reduce most artifacts, and preserve more original details. It does not require prior knowledge of x-ray energy spectrum and original projection data, avoiding iterative calculation and saving reconstruction time. Simulation experimental results show that the method can greatly remove metal artifacts.

Multi-source computed tomography (CT) imaging has unique technical advantages not only for dynamic objects, but also for large-size objects by designing its imaging scan mode. Using the triple-source fan-beam imaging scan mode under three circular trajectories with two different radii, we in this study developed and analyzed theoretically several exact reconstruction algorithms in terms of full-scan and short-scan for three sets of truncated projection data. This triple-source scan configuration in different radii cases is easier to be simulated by a single-source scan configuration in an industrial CT system. The proposed algorithms are based on the idea of filtering-back-projection (FBP) algorithm, and can reconstruct the large-size objects under the same CT devices. The developed algorithms avoid data rebinning and can provide exact and fast image reconstruction. The results of the numerical simulation based data analysis verified that new algorithms were accurate and effective.

In planar objects computed tomography (CT), restricted to the scanning environment, projections can only be collected from limited angles. Moreover, limited by the emitting power of the x-ray source, only a few photons penetrate the long side of the planar objects, which results in the noise increasing in projections. Planar objects CT reconstruction based on these two conditions is mathematically corresponding to solving an ill-posed inverse problem. Although several iterative reconstruction algorithms of limited-angle CT were proposed, high-quality planar objects CT reconstruction algorithms with fast convergence are still the goals of many researchers. In order to address the aforementioned problems, we proposed a new optimization model for planar objects CT reconstruction. Inspired by the theory of ‘visible boundary and invisible boundary’ in limited-angle CT and the differentiation property of Fourier transform, a new optimization objective function is proposed in this paper. Based on the statistical noise model of existing CT system, the convex set constraint of the optimization model is given. Besides, the optimization model is solved by convex set projection and Fourier transform differentiation property. The proposed algorithm was evaluated with both simulated data and real data. The experimental results show that the proposed algorithm can achieve the effect of noise suppression, limited-angle artifacts reduction, and fast structure reconstruction when it applies to planar objects CT.

Beam-hardening and scatter are two significant factors leading to contrast reduction and gray value inaccuracy in CT images. The cupping artifacts and obscure boundaries in reconstructed images are also caused mainly by both beam-hardening and scattering. It is difficult to get high-quality CT images with only one of them to make correction. In this paper, we proposed an x-ray CT polychromatic attenuation model with scatter effect, and an iterative method for simultaneous reduction on beam-hardening and scatter artifacts. In this model, the measured data of the detector comprise two parts: an attenuation term and a scatter term. The former is defined by an exponential rational fraction to fit the traditional attenuation process, and the latter is defined by a convolutional scatter intensity. The coefficients of the rational fraction in the attenuation term and the scatter term kernel are all calculated from a calibration phantom which is scanned to get corresponding equations. Based on the polychromatic attenuation model, we proposed an iterative artifacts reduction method combining deconvolution technique with linearized back-projection (iDLB method). This method makes the nonlinear polychromatic attenuation model become easily solvable by linearizing transformation, which simplifies the residuals allocation process. Experiments of both numerical simulation and practical data show the iDLB method has the ability to reduce beam-hardening and scatter artifacts simultaneously, improve the contrast of CT images, and it is highly parallelized for lower computational cost.