Multi-frequency imaging of perfectly conducting cracks via boundary measurements

TL;DR

This paper introduces a non-iterative, multi-frequency boundary measurement method for imaging perfectly conducting cracks in 2D media, demonstrating effective results even with noisy data.

Contribution

It presents a novel multi-frequency imaging functional based on the MSR matrix structure, enabling accurate crack detection without iterative procedures.

Findings

Effective imaging of cracks from noisy data

Successful detection of single and multiple cracks

Non-iterative approach reduces computational complexity

Abstract

Imaging of perfectly conducting crack(s) in a 2-D homogeneous medium using boundary data is studied. Based on the singular structure of the Multi-Static Response (MSR) matrix whose elements are normalized by an adequate test function at several frequencies, an imaging functional is introduced and analyzed. A non-iterative imaging procedure is proposed. Numerical experiments from noisy synthetic data show that acceptable images of single and multiple cracks are obtained.