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.
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