Reconstruction and uniqueness of moving obstacles

TL;DR

This paper presents a method for reconstructing the shape and trajectory of a moving obstacle in an inhomogeneous medium using ultrasonic travel time data, demonstrating high accuracy and efficiency.

Contribution

It introduces a novel numerical approach for obstacle reconstruction from travel times, with proven uniqueness and high-resolution results.

Findings

High-resolution shape and trajectory reconstruction achieved.

Method is computationally efficient and parallelizable.

Reconstruction is accurate with known sound speed and initial data.

Abstract

We study the uniqueness and accuracy of the numerical solution of the problem of reconstruction of the shape and trajectory of a reflecting obstacle moving in an inhomogeneous medium from travel times, start and end points, and initial angles of ultrasonic rays reflecting at the obstacle. The speed of sound in the domain when there is no obstacle present is known and provided as an input parameter which together with the other initial data enables the algorithm to trace ray paths and find their reflection points. The reflection points determine with high-resolution the shape and trajectory of the obstacle. The method has predictable computational complexity and performance and is very efficient when it is parallelized and optimized because only a small portion of the domain is reconstructed.