Affiliation:
1. Department of Mathematics, Rowan University, 201 Mullica Hill Rd., Glassboro, NJ 08028, USA
Abstract
This paper considers a 1D time-domain inverse scattering problem for the Helmholtz equation in which penetrable scatterers are to be determined from boundary measurements of the scattering data. It is formulated as a coefficient identification problem for a wave equation. Using the Laplace transform, the inverse problem is converted into an overdetermined nonlinear system of partial differential equations. To solve this system, a Carleman weighted objective functional, which is proved to be strictly convex in an arbitrary set in a Hilbert space, is constructed. An alternating minimization algorithm is used to minimize the Carleman weighted objective functional. Numerical results are presented to illustrate the performance of the proposed algorithm.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference36 articles.
1. Colton, D., and Kress, R. (2013). Inverse Acoustic and Electromagnetic Scattering Theory, Springer. [3rd ed.].
2. Ammari, H. (2008). An Introduction to Mathematics of Emerging Biomedical Imaging, Springer.
3. Baum, C. (1998). Detection and Identification of Visually Obscured Targets, Taylor and Francis.
4. Buchanan, J.L., Gilbert, R.P., Wirgin, A., and Xu, Y.S. (2004). Marine Acoustics: Direct and Inverse Problems, Society for Industrial and Applied Mathematics.
5. Daniels, D.J. (2004). Ground Penetrating Radar, The Institute of Electrical Engineers.