In this paper, we propose a method, which combines a particle swarm optimization (PSO) algorithm with a Newton–Kantorovitch algorithm for image reconstruction of perfectly conducting objects. First, the inverse problem is recast as a global nonlinear optimization problem, which is solved by a PSO. Then, the solution obtained by the PSO is taken as an initial guess for the Newton–Kantorovitch algorithm to obtain the more accuracy solution in a few iterations.
The inversion algorithm which is based on the rigorous mathematics makes use of the received scattered field and appropriate boundary condition to derive a set of nonlinear integral equations. The moment method is used to transform the nonlinear integral equations into matrix form. Then the pseudoinverse transformation is employed to overcome the ill-posedness to obtain a convergent and stable solution.
The particle swarm optimization algorithm is employed to find out the global extreme solution of the object function. Numerical results show that the performance of this cascaded method is better than the individual PSO and the individual Newton–Kantorovitch algorithm. Satisfactory reconstruction has been obtained by using this cascaded method.
Applied Mathematics and Computation 219(11), pp.6093–6105