Reconstructing plane sets from projections

Abstract

We give some uniqueness results for the problem of determining a finite set in the plane knowing its projections along m directions. We apply the results to the problem of the reconstruction of a homogeneous convex body with a finite set of spherical disjoint holes. If m X-ray pictures with directions in some plane are given, then the problem is well posed provided the number of the holes is less than or equal to m and the set of the directions satisfies a suitable condition. © 1990 Springer-Verlag New York Inc.