1,720,971 research outputs found
The linear sampling method without sampling
No full textWe present a new implementation of the linear sampling method in which the set of discretized far-field equations for all sampling points is replaced by a single functional equation formulated in a Hilbert space defined as a direct sum of L2 spaces. The squared norm of the regularized solution of such equation is used as indicator function and is analytically determined together with its Fourier transform. This provides some theoretical hints about the spatial resolution achievable by the metho
Inverse scattering and edge detection: the threshold problem for the linear sampling method
No full textApplication of the inhomogeneous Lippmann-Schwinger equation to inverse scattering problems
No full textIn this paper we present a hybrid approach to numerically solving two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is “hybrid” in that it merges a qualitative and a quantita- tive method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to im- plement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the “inhomogeneous Lippmann–Schwinger equation”; the latter is a generalization of the classical Lippmann–Schwinger equation to the case of an inhomogeneous background, and in our paper is deduced from the differential formulation of the direct scattering problem to provide the reconstruction algorithm with an appropriate theoretical basis. Then the point values of the refractive index are computed only in the region identified by the linear sampling method at the previous step. The effectiveness of this hybrid approach is supported by numerical simulations presented at the end of the paper
Post-processing of the linear sampling method by means of deformable models
No full textThe linear sampling method is a qualitative procedure for the visualization of both impenetrable and inhomogeneous scatterers, which requires the regularized solution of a linear ill- posed integral equation of the first kind. An open issue in this technique is the one of determining the optimal scatterer profile from the visualization maps in an automatic manner. In the present paper this problem is addressed in two steps. First, linear sampling is optimized by using a new regularization algorithm for the solution of the integral equation, which provides more accurate maps for different levels of the noise affecting the data. Then an edge detection technique based on active contours is applied to the optimized maps. Our computation exploits a recently introduced implementation of the linear sampling method which enhances both the accuracy and the numerical effectiveness of the approach
Inverse scattering and edge detection: the threshold problem for the linear sampling method
No full textA fully no-sampling formulation of the linear sampling method for three-dimensional inverse electromagnetic scattering problems
No full textWe describe a very fast and automatic formulation of the linear sampling method for three-dimensional electromagnetic inverse scattering problems. This formulation is an extension of a no-sampling implementation recently proposed for two- dimensional configurations. In this 3D framework, regularization occurs independently not only of the sampling point but even of the polarization of the fundamental solution used as known term. Furthermore, a very effective automatic procedure for the selection of the optimal surface describing the scatterer is introduced
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