Abstract: The theory and calculation of scattering and inverse scattering problems has always been an important subject in the field of applied mathematics, and its results have a wide range of applications in the fields of geological prospecting, non-destructive detection, medical imaging, etc. Linear sampling method (LSM) is a very popular non-iterative reconstruction algorithm in inverse scattering problems in recent years, but this method is difficult to generalize to more complex problems such as obstacle inverse scattering in half space.  This paper is associated with the numerical reconstruction algorithm in the inverse Dirichlet obstacle scattering problem from single frequency data. By constructing an auxiliary boundary value problem with an impedance boundary condition, a novel linear sampling method is proposed. Then it is theoretically proved that the method is effective for any given wavenumber in reconstructing the shape and location of the obstacle.

Key words: inverse scattering, Dirichlet obstacle, linear sampling method, single frequency data