We survey applications of classical and of time-sequential sampling theory and some of its recent extensions,
respectively, in two complementary areas. First to reduce acquisition requirements for dynamic imaging below
those predicted by classical theory, and second, to reduce the computation for tomographic reconstruction from
O(N3) to O(N2 log N) for an N × N image, with similar acceleration for 3D images. In both areas, the savings
demonstrated in practical examples exceed an order-of-magnitude.