Identification of Multilayered Particles from Scattering Data by a Clustering Method

A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the scatterer in a non-Born region of scattering. Local de-terministic and global probabilistic minimization methods are studied. A special Reduction Procedure is introduced to reduce the dimensionality of the minimization space. Deep's and the Multilevel Single-Linkage methods for global minimization are used for the solution of the inverse problem. Their performance is analyzed for various multilayer configurations. 1. INTRODUCTION Many practical problems require an identification of the internal structure of an object given some measurements on its surface. In this paper we study such an identification for a multilayered particle illuminated by acoustic or electromagnetic plane waves. Thus the problem discussed here is an inverse scattering problem. A similar problem for the particle identification from the light scattering data is studied in [29]. The precise formulation of the problem is postponed till Section 2. Our approach is to reduce the inverse problem to the best fit to data multidimensional minimization. This is done in Section 3. It is also shown there that more than one frequency of the incoming waves is required to provide a stable identification. The resulting minimization is a challenging problem, since the objective function has many narrow local minima. Finding a global minimum (the sought identification) is the main subject of the study here. In Section 4 we analyze various local minimization methods and develop a special Local Minimization Method. This method, together with a specially designed Reduction Procedure, is capable of finding this type of local minima. In Section 5 Rinnooy Kan and Timmer's Multilevel Single-Linkage Method for global minimization is presented. It is paired with the Local Minimization Method of Section 4, and, finally, gives the tool for the successful