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When a signal is recorded that has been physically generated by some scattering process (the interaction of electromagnetic, acoustic or elastic waves with inhomogeneous materials, 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 for equations such as the inhomogeneous Schr¨odinger equation in quantum mechanics and the inhomogeneous Helmholtz equation in electromagnetism 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. The approach is based on applying certain conditions to an exact solution of the inverse scattering problem rather than applying conditions to the forward scattering problem and then inverting the (conditional) result.
Blackledge, J., Hamalainen, T., Joutsensalo, J.: Inverse Scattering Solutions with Applications to Electromagnetic Signal Processing. ISAST Journal of Electronics and Signal Processing, vol: 4, issue: 1, pages: 43-60, 2009.