Convex Obstacles from Travelling Times

TL;DR

This paper presents a method to reconstruct multiple convex obstacles in a plane using travel-time data, assuming no line intersects more than two obstacles, advancing inverse problem techniques.

Contribution

It introduces a novel construction for recovering convex obstacles from travel-time information under specific geometric constraints.

Findings

Successful reconstruction of convex obstacles from travel times.

Applicable under the condition that no line intersects more than two obstacles.

Provides a new approach to inverse geometric problems.

Abstract

A construction is given for the recovery of a disjoint union of strictly convex smooth planar obstacles from travelling-time information. The obstacles are required to be such that no Euclidean line meets more than two of them.