A frequency-domain method to inverse moving source problem with unknown radiating moment

TL;DR

This paper presents a multi-frequency factorization method for imaging moving sources using far-field data, enabling the recovery of source support and excitation times with proven uniqueness and numerical validation.

Contribution

It introduces a novel factorization-based inversion scheme that reconstructs source support and excitation instants from sparse far-field data, with proven uniqueness and numerical demonstrations.

Findings

Successfully recovers source support and excitation times from limited data.

Establishes uniqueness of the convex hull and excitation instants.

Validated effectiveness through numerical simulations in 2D and 3D.

Abstract

This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we establish a computational criterion that characterizes both the unknown pulse moments and the narrowest strip (perpendicular to the direction) enclosing the source support. Central to our inversion scheme is the construction of indicator functions, defined pointwise over the spatial and temporal sampling variables. The proposed inversion scheme permits the recovery of the $\Theta$-convex support domain from far-field data at sparse observation directions. Uniqueness in determining the convex hull of the support and the excitation instants-using all observation directions-is also established as a direct consequence of the factorization method. The effectiveness and feasibility of the approach are examined through comprehensive numerical simulations in two and three dimensions.