Sampling type methods for an inverse waveguide problem

Abstract

We consider the problem of locating a penetrable obstacle in an acoustic waveguide from measurements of pressure waves due to point sources inside the waveguide. More precisely, we assume that we are given the scattered field and its normal derivative for any source point and receiver placed on a pair of surfaces known as the source and the measurement surfaces, respectively. A novel feature of this work is that the obstacle is allowed to touch the boundary of the pipe.  &nbsp We first analyze the associated interior transmission problem. Then, we adapt and analyze the Reciprocity Gap Method (RGM) and the Linear Sampling Method (LSM) to deal with the inverse problem. We also study the relationship between these two methods and provide numerical results.