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.
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