The directional total variation algorithm (DTV) reported in the literature achieves promising results for limited angle reconstructions, especially when the scanning angular range is very small. However, the visible edge prior for limited-angle CT is not explicitly considered by DTV. In this paper, a variant of the DTV model is proposed which explicitly builds into the visible edge prior developed by Quinto et al. Numerical experiments show that the proposed model and algorithm produce very competitive results compared to DTV.
The directional total variation algorithm (DTV) reported in the literature achieves promising results for limited angle reconstructions, especially when the scanning angular range is very small. However, the visible edge prior for limited-angle CT is not explicitly considered by DTV. In this paper, a variant of the DTV model is proposed which explicitly builds into the visible edge prior developed by Quinto et al. Numerical experiments show that the proposed model and algorithm produce very competitive results compared to DTV.
Dynamic tomography finds its usage in certain important applications. The reconstruction problem could be cast in the Bayes framework as a time series analysis problem, such that the Kalman filter (KF) could come into play. A series of drawback of such an approach lies in its high computational and storage complexity. Dimension reduction Kalman filter (DR-KF) method has been proposed in the literature to relieve such a pain. However, our tests show that DR-KF results in heavy ringing artifacts. To solve this dilemma, in this paper, we propose to approximate the regularization term involving the precision matrix with a spatial regularization term plus a temporal regularization term, such that the space and time complexity are greatly reduced. Besides, to get the original Kalman filter into play, we propose a blocked KF for backward smoothing, i.e. split the reconstructed image slices into small overlapping blocks, and the KF is applied on each block. The blocked KF has much smaller computational and storage complexity, and fits well for parallel computations. Numerical experiments show that the proposed approach achieves better reconstructions while calling for much smaller computational resources.
Low-dose CT reconstructions suffer from severe noise and artifacts. Many methods have been proposed to increase the ratio between image quality and radiation dose through incorporating various priors. By learning priors in labelled data-set, neural network methods have achieved great success for this purpose. In CT applications, however, paired training data-sets are rarely available or difficult to obtain. Recently, unsupervised learning has attracted a lot of attention. Along this line, Noise2Inverse, an unsupervised neural network architecture, has shown the possibility of applying unsupervised learning for low-dose CT reconstructions. When the training data-sets (unlabelled) are not large enough or the training is insufficient, however, Noise2Inverse might perform not well. Another important issue is that network methods might suffer from intrinsic instability. In this regard, we propose to hybrid neural networks, especially the Noise2Inverse architecture, with traditional optimization models such that hand-crafted priors come into play as a remedy. Numerical experiments show that the proposed architecture improves Noise2Inverse in terms of both quality measures PSNR and SSIM, especially in the case of inadequate training.
The Chambolle-Pock (CP) algorithm has been successfully applied for solving optimization problems involving various data fidelity and regularization terms. However, when applied to CT image reconstruction, its efficiency is still far from being satisfactory. Another problem is that unmatched forward and backward operators are commonly used for CT reconstruction, in which case, the CP algorithm might fail to converge well. In this paper, based on a operator-splitting perspective of the simultaneous algebraic reconstruction technique (SART), the CP algorithm is generalized to incorporate the ordered subsets technique for fast convergence. The energy functional associated with the optimization problem is split into multiple terms, and the CP algorithm is employed to minimize each of them in an iterative manner. Numerical experiments show that the proposed algorithm could gain more than ten times faster convergence speed compared to the classical CP algorithm.
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