Level Set Algorithm for Shape Reconstruction of Non-Overlapping Three-Dimensional Penetrable Targets

This paper presents a 3-D shape reconstruction algorithm based on the level set method. Multiple dielectric and non-overlapping objects are considered. The level set algorithm is a gradient-type optimization approach that aims to minimize a cost function between measurements and computer-simulated data. The algorithm is capable of retrieving the shape and location of multiple targets made of two different and slightly lossy materials. An appropriate form of the deformation velocity based on the forward and adjoint fields is calculated. The method of moment surface integral equation is implemented to calculate the deformation velocity of the evolving objects. Two sets of Hamilton-Jacobi equations, associated with the two dielectric materials, are solved simultaneously to update the evolving objects. During the inversion scheme, the marching cubes method is employed to restore the surface meshes necessary for the forward solver. The algorithm is tested on corrupted synthetic data with signal-to-noise ratio of 10 dB.