The singular sources method for an inverse problem with mixed boundary conditions

We use the singular sources method to detect the shape of the obstacle in a mixed boundary value problem. The basic idea of the method is based on the singular behavior of the scattered field of the incident point-sources on the boundary of the obstacle. Moreover we take advantage of the scattered field estimate by the backprojection operator. Also we give a uniqueness proof for the shape reconstruction.  2004 Elsevier Inc. All rights reserved