A decoupling-based imaging method for inverse medium scattering for Maxwell's equations

• Published in: Inverse problems Vol. 26; no. 1; pp. 015007 - 015007 (17)
• Main Author: Lakhal, A
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.01.2010; Institute of Physics
• Subjects: Algorithms; Approximation; Electric fields; Electromagnetic properties; Exact sciences and technology; Illumination; Imaging; IMP; Inverse; Iterative methods; Mathematical analysis; Mathematical models; Maxwell equation; Maxwell's equations; Nonlinearity; Physics; Reconstruction; Scalars; Scattering; Three dimensional; Uniqueness; Vectors (mathematics); Near field; Scattering medium; Digital simulation; Inverse scattering problem; Maxwell equations; Algorithms; Decoupling; Inverse problems; Inverse scattering; Illumination; Nonlinearity; Non linear approximation; Iterative methods; Electric fields; Electromagnetic properties; Vector equation
• ISSN: 0266-5611; 1361-6420
• DOI: 10.1088/0266-5611/26/1/015007

We present an iterative reconstruction method for an inverse medium scattering problem (IMP) for the three-dimensional time-harmonic Maxwell equations. The goal here is to determine the electromagnetic properties of a nonmagnetic unknown inhomogeneous object. The data are near-field measurements of scattered electric fields for multiple illuminations at a fixed frequency. We use the concept of the generalized induced source (GIS) to recast the intertwined vector equations of Maxwell into decoupled scalar scattering problems. To treat the nonlinearity of the IMP, we apply the localized nonlinear approximation due to Habashy and co-workers. In this framework, we derive a fast reconstruction method based on the Kaczmarz algorithm. Besides, for the underlying approximation we present a uniqueness result for determining the contrast function. Numerical experiments in 3D with synthetic and real data show the scope and limitations of the method.