A sampling type method in an electromagnetic waveguide

Abstract

We propose a sampling type method to image scatterer in an electromagnetic waveguide. The waveguide terminates at one end and the measurements are on the other end and in the far field. The imaging function is based on integrating the measurements and a known function over the measurement surface directly. The design and analysis of such imaging function are based on a factorization of a data operator given by the measurements. We show by analysis that the imaging function peaks inside the scatterer, where the coercivity of the factorized operator and the design of the known function play a central role. Finally, numerical examples are provided to demonstrate the performance of the imaging method.

Shape and parameter identification by the linear sampling method for a restricted Fourier integral operator

“…It is also possible to establish a semi-explicit convergence result for parameter identification with both noiseless and noisy data, this is ongoing work and will be reported in a forthcoming paper. Finally we remark that the prolate-based linear sampling method shares a similar spirit to the modal formulation of the linear sampling method in waveguide [7]; see also [21]. given at LGL quadrature nodes {t p } N p=0 and {s q } N q=0 .…”

“…The key observation is that one of the factorized operator has (disk) PSWFs as its eigenfunctions. The prolate-based linear sampling method shares a similar spirit to the modal formulation of the linear sampling method in waveguide [7]; see also [21]. In this way we obtain a reduced indicator function in a finite dimensional subspace.…”

Monotonicity-based shape reconstruction for an inverse scattering problem in a waveguide

“…Nevertheless, inverse scattering problems in waveguides are of practical relevance and have thus received increasing attention in recent years. For instance, sampling-type reconstruction methods, which are closely related to the approach considered in this work, have been discussed in [6][7][8][9]42] (see also [40,44] for inverse scattering problems modeled by Maxwell's equations). A sampling method for a multi-frequency inverse scattering problem has recently been proposed in [41], and a timedomain sampling method has been established in [43].…”