Tomographic reconstruction from limited angular data.

Abstract

The nth moment of a projection Mn(phi) = rnp(r, phi) dr must be a trigonometric polynomial of degree less than or equal to n. Measuring Mn(phi i) for n + 1 arbitrary angles phi i allows reconstruction of Mn(phi) for all phi. Thus in principle, the exact knowledge of the shadow function within an arbitrarily narrow sector allows reconstruction of the complete shadow. The algorithm doing this is very simple, but its applicability is severely limited by noise in the data.