X-ray spectrum plays a very important role in dual energy computed tomography (DECT) reconstruction. Because it is difficult to measure x-ray spectrum directly in practice, efforts have been devoted into spectrum estimation by using transmission measurements. These measurement methods are independent of the image reconstruction, which bring extra cost and are time consuming. Furthermore, the estimated spectrum mismatch would degrade the quality of the reconstructed images. In this paper, we propose a spectrum estimation-guided iterative reconstruction algorithm for DECT which aims to simultaneously recover the spectrum and reconstruct the image. The proposed algorithm is formulated as an optimization framework combining spectrum estimation based on model spectra representation, image reconstruction, and regularization for noise suppression. To resolve the multi-variable optimization problem of simultaneously obtaining the spectra and images, we introduce the block coordinate descent (BCD) method into the optimization iteration. Both the numerical simulations and physical phantom experiments are performed to verify and evaluate the proposed method. The experimental results validate the accuracy of the estimated spectra and reconstructed images under different noise levels. The proposed method obtains a better image quality compared with the reconstructed images from the known exact spectra and is robust in noisy data applications.

Random walk is a popular and efficient algorithm for image segmentation, especially for extracting regions of interest (ROIs). One difficulty with the random walk algorithm is the requirement for solving a huge sparse linear system when applied to large images. Another limitation is its sensitivity to seeds distribution, i.e., the segmentation result depends on the number of seeds as well as their placement, which puts a burden on users. In this paper, we first propose a continuous random walk model with explicit coherence regularization (CRWCR) for the extracted ROI, which helps to reduce the seeds sensitivity, so as to reduce the user interactions. Then, a very efficient algorithm to solve the CRWCR model will be developed, which helps to remove the difficulty of solving huge linear systems. Our algorithm consists of two stages: initialization by performing one-dimensional random walk sweeping based on user-provided seeds, followed by the alternating direction scheme, i.e., Peaceman-Rachford scheme for further correction. The first stage aims to provide a good initial guess for the ROI, and it is very fast since we just solve a limited number of one-dimensional random walk problems. Then, this initial guess is evolved to the ideal solution by applying the second stage, which should also be very efficient since it fits well for GPU computing, and 10 iterations are usually sufficient for convergence. Numerical experiments are provided to validate the proposed model as well as the efficiency of the two-stage algorithm.

Compared with traditional CT, dual energy CT (DECT) has the capability to improve material differentiation and reduce beam hardening artifacts, and thus has wide prospects of applications. In this paper, by linearizing the polychromatic projections with their first-order Taylor expansions, we derive an iterative reconstruction method for DECT. The method updates the basis material images by adding the residual images reconstructed from the residual projections to the current estimated basis material images, i.e., the iteration process of the proposed method is carried out in image domain, so it is applicable to both geometrically consistent and inconsistent projections. In addition, as the filtered back-projection method is used in the reconstruction of the residual images, the proposed method has a high degree of parallelism. Both numerical simulation and real-data experiments are performed, and the results confirm the effectiveness of the proposed reconstruction method.