Adaptive B-Spline Scheme for Solving an Inverse Scattering Problem

Abstract. In this paper, we present an approach to the 2D inverse scattering problem in which the unknown object is well approximated using a small number of adaptively chosen B-spline basis functions. Rather than determining a large collection of pixel values as is commonly done, we estimate directly a much smaller knot sequence associated with a B-spline representation of the object. An iterative scheme is proposed in which, at each stage, we seek to improve our estimate of the object through the insertion and deletion of knots. A specic knot insertion process, based on curvature information, and a specic knot deletion method, based on data tting, are proposed. Given a collection of knots, a non-linear, conjugate-gradient method is employed to determine an estimate of the object. By controlling the degrees of freedom in this manner we are able to forgo an explicit regularization scheme. Finally, using both computer simulated as well as experimental microwave laboratory-controlled data, we demonstrate the ability of our approach to improve upon that obtained from a more standard, pixel-based inverse scheme