Inverse scattering in inhomogeneous background media: II. Multi-frequency case and SVD formulation

The inverse scattering problem formulated and solved within the distorted wave Born approximation (DWBA) in [1] (hereafter referred to as 'part I') is reformulated so as to be applicable to arbitrary (non-point) transmitter and receiver array elements and to frequency-independent (dispersionless) scattering potentials interrogated in a set of scattering experiments employing multiple temporal frequencies. The underlying structure of the pseudo-inverse reconstruction algorithm developed in part I is also revamped by use of the SVD so as to employ an orthonormal basis in the Hilbert space of compactly supported scattering potentials. This basis replaces the linearly dependent set of spanning functions used in part I and results in a more efficient reconstruction algorithm both in terms of CPU execution time as well as required computer storage space. Computer simulations illustrating the performance of the reformulated algorithm are presented.