Limited Angle Reconstruction in Tomography via Squashing

Abstract

We give a new algorithm for reconstructing a density f in the plane from its projections along those lines making an angle greater than a fixed delta > 0 with the x axis. Of course, the performance of the algorithm depends on delta and on the smoothness of f, but it appears to give a practical and simple solution to the problem whenever one exists. The basic idea, which seems to be new, is to make an affine (squashing) scale change of f to g for which the projections are then known at n equally spaced angles, so that we know how to find g, and then we obtain f from g by inverting the scale change.