An Alternative to Tikhonov Regularization for Linear Sampling Methods

The problem of determining the shape of an obstacle from far-field measurements is considered. It is well known that linear sampling methods have been widely used for shape reconstructions obtained via the singular system of an ill conditioned discretized far-field operator. For our reconstructions we assume that the far-field data are noisy and we employ a novel regularization method that does not require determination of a regularization parameter.