Inverse Obstacle Scattering with Non-Over-Determined Scattering Data

The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering ����(����;����;����), where ����(����;����;����) is the scattering amplitude, ����;���� ���� ����² is the direction of the scattered, incident wave, respectively, ����² is the unit sphere in the ℝ³ and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensio