Inverse Scattering Solutions for Side-Band Signals

When a signal is recorded that has been physically generated by some scattering process (the interaction of electromagnetic waves with an inhomogeneous dielectric, for example), the ‘standard model’ for the signal (i.e. information content convolved with a characteristic Impulse Response Function) is usually based on a single scattering approximation. An additive noise term is introduced into the model to take into account a range of non-deterministic factors including multiple scattering that, along with electronic noise and other background noise sources, is assumed to be relatively weak. Thus, the standard model is based on a ‘weak field condition’ and the inverse scattering problem is often reduced to the deconvolution of a signal in the presence of additive noise. Attempts at solving the exact inverse scattering problem which take into account multiple scattering effects often prove to be intractable, particularly with regard to the goal of implementing algorithms that are computationally stable and/or compatible with standard signal analysis methods and Digital Signal Processing ‘toolkits’. This paper provides an approach to solving the multiple scattering problem for narrow side-band systems (typically, electromagnetic signal processing systems) that is compounded in the introduction of a single extra term to the standard model.