Approximate backpropagation (ABP) methods are used to identify the shape of acoustic and electromagnetic scatterers in the resonance region from full aperture data. Said methods rely on a heuristic relation i.e., ABP, between the expansion coefficients, which represent the scattered wave in the far zone and, respectively, on the obstacle boundary, Γ. The unknown is the shape parameter vector, ψ, which must be in a suitable admissible set. The objective function to be minimized is the L2(Γ)-norm of the boundary defect. A sample numerical result is given, which comes from the inversion of an IPSWICH data set. In order to justify the well-posedness of ABP some related problems are examined. An error hound is given, which compares the far zone to the least squares boundary coefficients. The approximate forward propagation (AFP) map is defined and its consistency on disks and spheres is stated. Finally, a property of forward propagation in the infinite dimensional case (l2) is provided
Crosta, G. (1998). Forward and backward propagation algorithms applied to the electromagnetic scattering by an impenetrable obstacle. A progress report. In J. Jin (a cura di), 14th Annual Review of Progress in Applied Computational Electromagnetics (Naval Postgraduate School Monterey, CA, March 16-20, 1998) - Conference Proceedings, vol. II (pp. 210-215). Monterey, CA, United States : Applied Computational Electromagnetics Soc.
Forward and backward propagation algorithms applied to the electromagnetic scattering by an impenetrable obstacle. A progress report
Crosta, GFF
1998
Abstract
Approximate backpropagation (ABP) methods are used to identify the shape of acoustic and electromagnetic scatterers in the resonance region from full aperture data. Said methods rely on a heuristic relation i.e., ABP, between the expansion coefficients, which represent the scattered wave in the far zone and, respectively, on the obstacle boundary, Γ. The unknown is the shape parameter vector, ψ, which must be in a suitable admissible set. The objective function to be minimized is the L2(Γ)-norm of the boundary defect. A sample numerical result is given, which comes from the inversion of an IPSWICH data set. In order to justify the well-posedness of ABP some related problems are examined. An error hound is given, which compares the far zone to the least squares boundary coefficients. The approximate forward propagation (AFP) map is defined and its consistency on disks and spheres is stated. Finally, a property of forward propagation in the infinite dimensional case (l2) is provided
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