Improved subspace migration for imaging of small and arc-like perfectly conducting cracks

Abstract

This paper considers the fast, effective imaging of a perfectly conducting crack(s) in a 2-D homogeneous medium using data measured on its boundary. Based on the structure of singular vectors of the Multi-Static Response (MSR) matrix, whose elements are normalized by a suitable test function at several frequencies, we introduce a weighted subspace migration imaging functional. Based on the relation with the Bessel functions of integer order, it is verified that this is an improved version of traditional subspace migration. Numerical experiments for small and extended cracks from noisy synthetic data support our analysis.

Keywords:

• subspace migration
• perfectly conducting cracks
• multi-static response (MSR) matrix
• Bessel functions
• numerical experiments

Acknowledgments

The author would like to acknowledge anonymous reviewer for valuable comments. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2011-0007705), and the research program of Kookmin University in Korea.