Gilman, Mikhail; Tsynkov, Semyon A mathematical model for SAR imaging beyond the first Born approximation. (English) Zbl 1334.78027 SIAM J. Imaging Sci. 8, No. 1, 186-225 (2015). The paper generalizes the conventional synthetic aperture radar (SAR) ambiguity theory in view of removing inconsistencies presented in the conventional theory. The authors propose a new model for radar targets that exploits a horizontally inhomogeneous dielectric half-space. In the framework of this model, one can consider the linearized scattering without assuming that it is weak (as in the conventional theory). The physical observable is a slowly varying amplitude of the Bragg resonant harmonic in the spectrum of electric permittivity computed on a resolution size window. The model represents the scattered field as a surface (rather than volumetric) retarded potential. Moreover, the linearization can be performed against various background solutions rather than only the unobstructed incident field in free space. It is also shown that in the case of weak scattering, the results following from the new model are equivalent to those from the classical theory. Reviewer: Dmitry Shepelsky (Kharkov) Cited in 5 Documents MSC: 78A45 Diffraction, scattering 35B20 Perturbations in context of PDEs 35R30 Inverse problems for PDEs 45Q05 Inverse problems for integral equations 78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory 78A55 Technical applications of optics and electromagnetic theory 78M34 Model reduction in optics and electromagnetic theory 78M35 Asymptotic analysis in optics and electromagnetic theory 86A22 Inverse problems in geophysics 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory 94A12 Signal theory (characterization, reconstruction, filtering, etc.) Keywords:synthetic aperture imaging; SAR ambiguity theory; linearized scattering; linearized inverse problem; backscattering; Bragg resonance; weak scattering; strong scattering PDFBibTeX XMLCite \textit{M. Gilman} and \textit{S. Tsynkov}, SIAM J. Imaging Sci. 8, No. 1, 186--225 (2015; Zbl 1334.78027) Full Text: DOI Link