A new non-iterative singular sources method for the reconstruction of piecewise constant media.

Abstract

We describe a novel non-iterative method for the reconstruction of a piecewise constant inhomogeneous medium in acoustic scattering, which we call the ‘singular sources method’. The basic idea of the method is to use the behaviour of the scattered field for singular incident fields (multipoles) to calculate the size of the refractive index n at some point z0 on the boundary of the support of the scatterer and then eliminate this value from the data by subtracting a known piecewise constant background medium. The paper includes the theory for the singular sources method to locate the unknown support of an inhomogeneous medium for a known inhomogeneous background medium. Also, we give a new uniqueness proof for the reconstruction of a piecewise constant medium in two or three dimensions, using techniques that differ from those used to prove previous well-known results.