Beijing Institute of Mathematical Sciences and Applications

Xiaoming John Zhang

David Omogbhe

A6-101

Zoom 204 323 0165 (BIMSA)

This talk concerns the inversion of the attenuated ray transform for symmetric 2-tensor fields on a bounded domain in two-dimensional Euclidean space. The data consist of line integrals (all straight lines intersecting the domain) of the components of a symmetric 2-tensor. This problem arises naturally from the linearized boundary rigidity problem in the at case: determining a perturbation of the Euclidean metric from boundary distance measurements reduces to inverting this tensor ray transform. We present a constructive inversion method based on A-analytic theory originally developed for scalar fields, and extend it to symmetric 2-tensors. By identifying the tensor field with a suitable complex-valued function and applying A-analytic function theory, the inversion reduces to solving a boundary value problem on a planar domain. This talk is part of the ICMRA program.