The Level Set Shape Reconstruction Algorithm Applied to 2d Pec Targets Hidden Behind a Wall

Abstract

Abstract-The level set algorithm is extended to handle the reconstruction of the shape and location of objects hidden behind a dielectric wall. The Green's function of stratified media is used to modify the method of moments and the surface integral equation forward solver. Due to the oscillatory nature of the Sommerfeld integrals, the stationary phase approximation is implemented here to achieve fast and accurate reconstruction results, especially when the targets are located adequately far from the wall. Transverse Magnetic (TM) plane waves are employed for excitation with limited view for transmitting and receiving the waves in the far field at one side of the wall. The results show the capability of the level set method for retrieving the shape and location of multiple 2D PEC objects of arbitrary shapes even when there are located at a small distance from the wall. To reduce the computational expenses of the algorithm in the case of multiple hidden objects, the MPI parallelization technique is implemented leading to a reduction in the CPU time from hours on a single processor to few minutes using 128 processors on the NCSA Supercomputer Center.

Inverse Scattering Shape Reconstruction of 3d Bacteria Using the Level Set Algorithm

“…The current work expands the previous published work on the level set method [7][8][9][10]. The contribution can be summarized as: (i) demonstrating the capability of the level set algorithm for the shape reconstruction of 3D bacteria, leading to use very high frequencies, (ii) testing the convergence of the algorithm at frequencies up to 300 THz, and (iii) investigating and analyzing the effect of two specific parameters on the algorithm convergence at these high frequencies; these parameters are the time step and the resolution of the marching cubes method.…”

“…The level set inverse scattering technique has proven its capability in retrieving the shapes of multiple unknown targets based on their scattered fields in the microwave range of frequency (100 MHz-10 GHz) [7][8][9][10]. The scattered fields are measured at multiple receiving directions when the target is excited from multiple incident directions and at multiple frequencies (see Fig.…”

“…The algorithm starts with an initial guess which then evolves to the true target. The main idea behind the level set technique is that the evolving object is implicitly modeled as the zero level of a higher order function [7][8][9][10]. The zero level of a higher order function φ is given as:…”

“…The deformation velocity function F (r) normal to the surface is the force which drives the initial surface to converge to the true one. The values of the normal deformation velocity are calculated by minimizing the mismatch between the simulated fields scattered from the evolving object and the synthetic measured fields, see details in [7][8][9][10]. In order to calculate F (r), the method of moments surface current densities and the marching cubes computer graphics method are used.…”

“…The initial values of the level set function, φ 0 , at each pixel in the computational domain are assigned equal to the signed distance function which is defined as the minimum distance between each pixel and the surface (or contour) of the initial guess [7][8][9][10]. The signed distance function is negative if the pixel is inside the initial guess surface, positive if the pixel is outside the initial guess surface and zero if the pixel is on the surface of the initial guess.…”