The linear sampling method revisited

Abstract

This paper is concerned with convergence results for the Linear Sampling method, a method in inverse scattering theory characterizing an unknown obstacle directly through an indicator function computed from the data. Three seperate but related results are shown. Firstly, sufficient conditions are formulated for the choice of the regularization parameter that guarantee that the method converges in the presence of noise for a sampling point inside the obstacle. Secondly, a new, very strong connection to the related Factorization method is proved. Thirdly, for the first time the behaviour of the indicator function for sampling points outside the obstacle is adequately explained. © 2009 Rocky Mountain Mathematics Consortium.