Inverse Scattering of Electromagnetic Waves for A Non-Smooth Conducting Target By Stochastic Optimization
Inverse scattering of the electromagnetic wave plays a very important role in remote sensing. Microwave imaging is a popular approach to achieve this goal. It is basically a complex engineering problem, which is generally very difficult due to the nonlinear electromagnetic integral equations. There have been many numerical techniques for inverse scattering of electromagnetic waves in free space. In general, the computation is time-consuming and difficult due to the nonlinearity and ill-posed problems. Recently, the stochastic optimization has attracted the attention of researchers in nonlinear optimization. Such optimization techniques are often inspired by some intelligent colony behaviors in nature. In particular, the fireworks algorithm  mimics the explosion process of fireworks, and is an important technique of stochastic optimization. It has been proved to outperform the particle swarm optimization algorithm , which is a well-known nature inspiration optimization algorithm. In this study, the firework algorithm is modified and then applied to inverse scattering of a non-smooth conducting cylinder. Based on the Green’s function of electromagnetic waves, scattering integral equation and moment method, the problem of inverse scattering is first transformed into a nonlinear optimization problem. The shape function is divided into many sections and each section is interpolated by a polynomial function. The variables of nonlinear optimization are coefficients of the polynomial function for interpolation within each section of the target shape function. The objective function is defined by comparing scattered electric fields from the guessed and true shapes, respectively. Numerical results show that the target shape reconstructed by our inverse scattering scheme is very accurate and the convergence is fast. In addition, the proposed inverse scattering scheme of electromagnetic waves can tolerate multiple scattering effects between different parts of the non-smooth target.
Keywords - Inverse scattering, Polynomial interpolation, Stochastic optimization.