Stability for Time Dependent X-ray Transforms and Applications

Abstract

We prove a logarithmic stability estimate for the time dependent X-ray transform on ${\mathbb{R}}_t^{+}\times {\mathbb{R}}^n$. To do so, we extend a known result by Begmatov for the stability of the time dependent X-ray transform in ${\mathbb{R}}_t^{+}\times {\mathbb{R}}^2$. We give some examples of stability and injectivity results in relationship to the Dirichlet-to-Neumann problem. In particular, under the Geometric Control Condtion, we derive inverse logarithmic stability estimates for time dependent conformal factors.

this arxiv submission has been split into two separate submissions by separate authors, http://arxiv.org/abs/1406.4854 and the current version. the new version contains a extension to conformal factors

References in corpus (1)

• The inverse problem for the local geodesic ray transform

Cited by in corpus (1)

• Support Theorem for the Light Ray Transform on Minkowski Spaces