Inversions of the windowed ray transform

Abstract

The windowed ray transform is the generalization of the "Analytic-Signal Transform" which was developed to extend arbitrary functions from R-n to C-n in a natural way. The X-ray transform is also a special case of this transform. Similar to the X-ray transform, the problem of inverting this transform is overdetermined. Hence it is possible to prove the existence of several inversion formulas. Kaiser obtained one such inversion formula in 1993. We present several inversion formulas here. One of them is similar to that of Kaiser, but it requires a weaker condition. The others are new.