Modified far field operators in inverse scattering theory

The dual space method for solving the inverse scattering problem reformulates the inverse problem as one in constrained optimization with weighted averages of the far field pattern $u_\infty $ as data. Unfortunately there exists a discrete set of values of the wave number such that the infimum of the cost functional associated with the optimization scheme is not zero. In this paper, the authors show how this difficulty can be removed if instead of $u_\infty ,u_\infty - u_\infty ^0 $ is considered, where $u_\infty ^0 $ is the far field pattern of a surface potential.