An analysis of the accuracy of the linear sampling method for an acoustic inverse obstacle scattering problem

We investigate the accuracy of the linear sampling method for a two-dimensional acoustic inverse obstacle scattering problem with a Dirichlet boundary condition using asymptotic analysis of the so-called indicator function around the boundary of the obstacle. An asymptotic expansion of the limit, as the noise level and the regularization parameter tend to zero, of the indicator function is obtained. The theoretical results show the dependence of the blowup rate of this limit on the geometrical properties of the obstacle. This partly (up to the above limit) explains the dependence of the accuracy of the linear sampling method on the obstacle's geometry. Some numerical results are given to verify the theoretical results