Inverse Scattering of Three-Dimensional Pec Objects Using the Level-Set Method

Abstract

Abstract-A 3D shape reconstruction algorithm for multiple PEC objects immersed in air is presented. The Hamilton-Jacobi PDE is solved in the entire computational domain with employing the marching cubes method to retrieve the unknown objects. The method of moment surface integral equation is used as the forward solver. An appropriate form of the deformation velocity, based on the forward and adjoint fields, is implemented to minimize the mismatch between the measurements and simulated scattered fields from the evolving objects. The inversion algorithm demonstrated good shape reconstruction results even when using limited view data or noisy corrupted data with SNR of 5 dB.

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.…”