Identification of Multilayered Particles from Scattering Data by a Clustering Method

Abstract

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 deterministic 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.

Stable identification of piecewise-constant potentials from fixed-energy phase shifts

“…The HSD method could be described as a variation of a genetic algorithm and a local search with reduction. In [6] two global search algorithms in combination with a special local search method were applied to the identification of piecewise-constant scatterers by acoustic type measurements. The Rinnooy Kan and Timmer's Multilevel Single-Linkage Method in a combination with a special Local Minimization Method has been applied to the identification of piecewise-constant spherically symmetric potentials by their phase shifts in [7].…”

Piecewise constant positive potentials with practically the same fixed energy phase shifts

“…However, since the sought potential may have fewer than M layers, we found that conducting searches in lower-dimensional subspaces of R 2M is essential for the local minimization phase. A variation of the following "reduction" procedure has also been found to be necessary in [6] for the search of small subsurface objects, and in [4] for the identification of multilayered scatterers.…”

“…Such method needs a minimization routine for a one-dimensional minimization of Φ, which we do using a Bisection or a Golden Rule method. See [4] or [5] for a complete description. Now we can describe our Basic Local Minimization Method in R 2M , which is a modification of Powell's minimization method [2].…”

“…The HSD method could be classified as a variation of a genetic algorithm with a local search with reduction. In [4] two global search algorithms in combination with a special local search method were applied to the identification of piecewise-constant scatterers by acoustic type measurements. The global algorithms considered are the Deep's Method, and Rinnooy Kan and Timmer's Multilevel SingleLinkage Method.…”

Identification of Particles in Complex Structures from Scattering Data by an Optimization Method

“…This type of problems arises in many areas of technology and medicine (see [4] and the references therein). We have investigated this type of problem by FEM/BEM techniques [3].…”