Compared with standard computed tomography (CT), dual spectral CT (DSCT) has many advantages for object separation, contrast enhancement, artifact reduction, and material composition assessment. But it is generally difficult to reconstruct images from polychromatic projections acquired by DSCT, because of the nonlinear relation between the polychromatic projections and the images to be reconstructed. This paper first models the DSCT reconstruction problem as a nonlinear system problem; and then extend the classic ART method to solve the nonlinear system. One feature of the proposed method is its flexibility. It fits for any scanning configurations commonly used and does not require consistent rays for different X-ray spectra. Another feature of the proposed method is its high degree of parallelism, which means that the method is suitable for acceleration on GPUs (graphic processing units) or other parallel systems. The method is validated with numerical experiments from simulated noise free and noisy data. High quality images are reconstructed with the proposed method from the polychromatic projections of DSCT. The reconstructed images are still satisfactory even if there are certain errors in the estimated X-ray spectra.

Currently, 3D cone-beam CT image reconstruction speed is still a severe limitation for clinical application. The computational power of modern graphics processing units (GPUs) has been harnessed to provide impressive acceleration of 3D volume image reconstruction. For extra large data volume exceeding the physical graphic memory of GPU, a straightforward compromise is to divide data volume into blocks. Different from the conventional Octree partition method, a new partition scheme is proposed in this paper. This method divides both projection data and reconstructed image volume into subsets according to geometric symmetries in circular cone-beam projection layout, and a fast reconstruction for large data volume can be implemented by packing the subsets of projection data into the RGBA channels of GPU, performing the reconstruction chunk by chunk and combining the individual results in the end. The method is evaluated by reconstructing 3D images from computer-simulation data and real micro-CT data. Our results indicate that the GPU implementation can maintain original precision and speed up the reconstruction process by 110–120 times for circular cone-beam scan, as compared to traditional CPU implementation.

X-ray dual spectral computed tomography (DSCT) scans the measured object with two different x-ray energy spectra and the collected polychromatic projections from this procedure can be used to perform basis material decomposition of the object. An iterative method E-ART was recently proposed to produce highly quantitative basis material images for DSCT, but it has the drawback of slow convergence and huge computational costs. Inspired by the E-ART method, this paper proposes an extended simultaneous algebraic reconstruction technique (E-SART) for the basis material decomposition of DSCT and an accelerating strategy for improve the convergence speed of the iterative reconstruction. Compared with the E-ART method, the proposed method has much faster convergence rate while at the same time it has better noise suppressing feature. The advantages of this method were verified by experiments in which the FORBILD thorax phantom was iteratively reconstructed from noise-free and noisy polychromatic projections. SCANNING 38:599-611, 2016. © 2016 Wiley Periodicals, Inc.

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.

Abstract. The dynamical phenomena of complex networks are not easy to model and to characterize by current methods of mathematics. Newman, Barabási and Watts pointed out the direction of researching complex networks by graph theory, which was successfully applied in current investigation of complex networks, and Newman's network-based methods have been applied to a variety of fields. Some well-known and new methods of mathematics are provided in this article, associated with construction and problems on scale-free models from real networks.