Injectivity and stability of generalized X-ray transforms on curves

Béla A. Frigyik
University of Washington

Date: May 30, 2006

We consider the generalized X-ray transform on curves in all dimensions. This means we are integrating a function over a family of curves and against a non-zero weight. The standard X-ray transform consists in integrating a function over straight lines. We show that for a generic set (open and dense in an appropriate topology) of curves and weights the generalized X-ray transform is injective. Moreover we prove stability estimates.