Regularized quasi-Newton method for inverse scattering problems
The problem is how to extract the properties of the medium from the information contained in the measurements, assuming that the frequency is known and it is constant. The weak scattering case is considered, that is the unknown spatial variations of the medium are assumed to be close to zero. The authors work directly with the Helmholtz differential equation. Compared to usual numerical methods based on the Lippman-Schwinger integral equation this approach is quite different computationally. The iterative algorithm is a regularized quasi-Newton method. The linearized (Born) approximation is the first iteration and further iterations improve the identification by an order of magnitude. A special regularization of the Fréchet derivative's inverse provides a significant improvement in the algorithm's performance. The parameter identification for noisy data is also discussed. The algorithm is tested numerically in the 2D case for scattering from two coaxial cylinders. The mathematical framework covers also the 3D case.
scientific article; zbMATH DE number 474542
scientific article