Shape reconstruction of a 2D-elastic penetrable object via the L-curve method

摘要

In this paper we discuss an inversion algorithm which combined with the L-curve criterion for the selection of the regularization parameter, effectively yields shape reconstructions of penetrable obstacles. The required scattered elastic field is generated by either a P or S-incident wave. In particular the improved variant of the linear sampling method (LSM), the so called (F*F)1/4-method is studied for the two dimensional elastic transmission case. For our reconstructions we assume that the far field data are noisy and we employ the L-curve for the selection of the regularization parameter. The location of the vertex of the L-curve yields an appropriate value of the regularization parameter. Furthermore, the L-curve approach does not require a priori knowledge of the noise level, and hence combined with the LSM can be used for real world reconstructions, in which noise in the data is unknown.