An FFT-Accelerated Particle Swarm Optimization Method for Solving Far-Field Inverse Scattering Problems

Electromagnetic inverse scattering problems are nonlinear and ill-posed. They are often transformed into optimization problems and solved by deterministic or stochastic algorithms. In this article, an inversion method combining a customized particle swarm optimization (PSO) algorithm and the fast Fourier transform (FFT) is proposed. Stochastic algorithms tackle optimization problems in a global manner, which is an important feature in reducing the risk of optimization falling into local extrema. Another feature utilized here is that constraints can be easily applied in the optimization process, yielding better results. Based on this consideration, a customized PSO algorithm incorporating the mutation operator is proposed to further enrich the swarm diversity. However, the large-scale search in the solution space also increases the computational burden, which is the major limitation of stochastic algorithms being applied in microwave imaging problems. In this article, a novel cost function of inversion optimization problems is derived based on the Born approximation so that the evaluation of individual fitness can be performed by the FFT. Reconstructions are performed using both synthetic and experimental data to illustrate the key features of the proposed approach, and good results have been obtained in terms of imaging accuracy and robustness.