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.

Limited-angle computed tomography is a very challenging problem in applications. Due to a high degree of ill-posedness, conventional reconstruction algorithms will introduce blurring along the directions perpendicular to the missing projection lines, as well as streak artifacts when applied on limited-angle data. Various models and algorithms have been proposed to improve the reconstruction quality by incorporating priors, among which the total variation, i.e. l 1 norm of gradient, and l 0 norm of the gradient are the most popular ones. These models and algorithms partially solve the blurring problem under certain situations. However, the fundamental difficulty remains. In this paper, we propose a reconstruction model for limited-angle computed tomography, which incorporates two regularization terms that play the role of edge-preserving diffusion and smoothing along the x-direction and y -direction respectively. Then, an alternating minimization algorithm is proposed to solve the model approximately. The proposed model is inspired by the theory of visible and invisible singularities of limited-angle data, developed by Quinto et al. By incorporating visible singularities as priors into an iterative procedure, the proposed algorithm could produce promising results and outperforms state-of-the-art algorithms for certain limited-angle computed tomography applications. Extensive experiments on both simulated data and real data are provided to validate our model and algorithm.

Purpose: Sparse-data computed tomography (CT) frequently occurs, such as breast tomosynthesis, Carm CT, on-board four-dimensional cone-beam CT (4D CBCT), and industrial CT. However, sparse-data image reconstruction remains challenging due to highly undersampled data. This work develops a datadriven image reconstruction method for sparse-data CT using deep neural networks (DNN). Methods: The new method so-called AirNet is designed to incorporate the benefits from analytical reconstruction method (AR), iterative reconstruction method (IR), and DNN. It is built upon fused analytical and iterative reconstruction (AIR) that synergizes AR and IR via the optimization framework of modified proximal forward-backward splitting (PFBS). By unrolling PFBS into IR updates of CT data fidelity and DNN regularization with residual learning, AirNet utilizes AR such as FBP during the data fidelity, introduces dense connectivity into DNN regularization, and learns PFBS coefficients and DNN parameters that minimize the loss function during the training stage; and then AirNet with trained parameters can be used for end-to-end image reconstruction. Results: A CT atlas of 100 prostate scans was used to validate the AirNet in comparison with stateof-art DNN-based postprocessing and image reconstruction methods. The validation loss in AirNet had the fastest decreasing rate, owing to inherited fast convergence from AIR. AirNet was robust to noise in projection data and content differences between the training set and the images to be reconstructed. The impact of image quality on radiotherapy treatment planning was evaluated for both photon and proton therapy, and AirNet achieved the best treatment plan quality, especially for proton therapy. For example, with limited-angle data, the maximal target dose for AirNet was 109.5% in comparison with the ground truth 109.1%, while it was significantly elevated to 115.1% and 128.1% for FBPConvNet and LEARN, respectively.

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