The application of a multiscale strategy integrated with a stochastic technique to the solution of nonlinear inverse scattering problems is presented. The approach allows the explicit and effective handling of many difficulties associated with such problems ranging from ill-conditioning to nonlinearity and false solutions drawback. The choice of a finite dimensional representation for the unknowns, due to the upper bound to the essential dimension of the data, is iteratively accomplished by means of an adaptive multiresolution model, which offers a considerable flexibility for the use of the information on the scattering domain acquired during the iterative steps of the multiscaling process. Even though a suitable representation of the unknowns could limit the local minima problem, the multiresolution strategy is integrated with a customized stochastic optimizer based on the behavior of a particle swarm, which prevents the solution from being trapped into false solutions without a large increasing of the overall computational burden. Selected examples concerned with a two-dimensional microwave imaging problem are presented for illustrating the key features of the integrated stochastic multiscaling strategy.

An Integrated Multiscaling Strategy Based on a Particle Swarm Algorithm for Inverse Scattering Problems

Donelli, Massimo;Franceschini, Gabriele;Martini, Anna;Massa, Andrea
2006-01-01

Abstract

The application of a multiscale strategy integrated with a stochastic technique to the solution of nonlinear inverse scattering problems is presented. The approach allows the explicit and effective handling of many difficulties associated with such problems ranging from ill-conditioning to nonlinearity and false solutions drawback. The choice of a finite dimensional representation for the unknowns, due to the upper bound to the essential dimension of the data, is iteratively accomplished by means of an adaptive multiresolution model, which offers a considerable flexibility for the use of the information on the scattering domain acquired during the iterative steps of the multiscaling process. Even though a suitable representation of the unknowns could limit the local minima problem, the multiresolution strategy is integrated with a customized stochastic optimizer based on the behavior of a particle swarm, which prevents the solution from being trapped into false solutions without a large increasing of the overall computational burden. Selected examples concerned with a two-dimensional microwave imaging problem are presented for illustrating the key features of the integrated stochastic multiscaling strategy.
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Donelli, Massimo; Franceschini, Gabriele; Martini, Anna; Massa, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/71434
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