Multi-frequency subspace migration for imaging of perfectly conducting, arc-like cracks in full- and limited-view inverse scattering problems.pdfVIP

Journal of Computational Physics 283 (2015) 52–80 Contents lists available at ScienceDirect Journal of Computational Physics /locate/jcp Multi-frequency subspace migration for imaging of perfectly conducting, arc-like cracks in full- and limited-view inverse scattering problems Won-Kwang Park Department of Mathematics, Kookmin University, Seoul 136-702, Korea article info Article history: Received 23 July 2014 Received in revised form 23 November 2014 Accepted 26 November 2014 Available online 3 December 2014 Keywords: Full- and limited-view inverse scattering problems Multi-frequency subspace migration Perfectly conducting cracks Multi-Static Response (MSR) matrix Numerical experiments abstract Multi-frequency subspace migration imaging techniques are usually adopted for the noniterative imaging of unknown electromagnetic targets, such as cracks in concrete walls or bridges and anti-personnel mines in the ground, in the inverse scattering problems. It is con?rmed that this technique is very fast, effective, robust, and can not only be applied to full- but also to limited-view inverse problems if a suitable number of incidents and corresponding scattered ?elds are applied and collected. However, in many works, the application of such techniques is heuristic. With the motivation of such heuristic application, this study analyzes the structure of the imaging functional employed in the subspace migration imaging technique in two-dimensional full- and limited-view inverse scattering problems when the unknown targets are arbitrary-shaped, arc-like perfectly conducting cracks located in the two-dimensional homogeneous space. In contrast to the statistical approach based on statistical hypothesis testing, our approach is based on the fact that the subspace migration imaging functional can be expressed by a linear combination of the Bessel functions of integer order of the ?rst kind. This is based on the structure of the Multi-Static Response (MSR) matrix collected in the f