THE METHOD OF REGULARIZATION RATIOS APPLIED TO RECONSTRUCTIONS OF ELASTIC RIGID OBSTACLES VIA THE FACTORIZATION METHOD

- Journal title : East Asian mathematical journal
- Volume 32, Issue 1, 2016, pp.129-138
- Publisher : Youngnam Mathematical Society
- DOI : 10.7858/eamj.2016.013

Title & Authors

THE METHOD OF REGULARIZATION RATIOS APPLIED TO RECONSTRUCTIONS OF ELASTIC RIGID OBSTACLES VIA THE FACTORIZATION METHOD

Kim, K.; Leem, K.H.; Pelekanos, G.;

Kim, K.; Leem, K.H.; Pelekanos, G.;

Abstract

In this paper, we propose an efficient regularization technique (The Method of Regularized Ratios) for the reconstruction of the shape of a rigid elastic scatterer from far field measurements. The approach used is based on the factorization method and creates via Picard`s condition ratios, baptized Regularized Ratios, that serve to effectively remove unwanted singular values that may lead to poor reconstructions. This is achieved through the use of a sophisticated algorithm that progressively adjusts an initially set moderate tolerance. In comparison with the well established Tikhonov-Morozov regularization techniques our new algorithm appears to be more computationally efficient as it doesn`t require computation of the regularization parameter for each point in the grid.

Keywords

Regularization;

Language

English

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