Optimal dynamic tomography for wide-sense stationary spatial random fields

Dynamic tomography is concerned with the image formation of a temporally changing object from its line integral projections. The problem remains challenging because of its high dimensionality. In this paper, we identify a sufficient class of dynamic tomography problems that can be solved by a state estimator that requires only linear shift-invariant filtering operations. This class includes rigid-body motion, common in biomedical imaging scenarios. The new state estimator is far less computationally demanding than classic methods such as the Kalman filter. Whereas the Kalman filter requires O(N²) memory storage and O(N³) processing for anN-dimensional problem, the state estimator derived in this work requires only O(N) storage and O(N logN) processing.