Reconstruction of the property profile of a medium from measured data due to an illuminating wave is known as the inverse scattering problem. It arises in many fields of engineering and science, such as non-destructive evaluation, medical diagnosis, and seismology. The signifcance and challenge of the inverse scattering problems have attracted much research activity for decades, yet, it is far from being a resolved issue. Considerable effort is presently under way to find efficient and accurate inversion techniques. This is taking place independently in many disciplines.
The purpose of this review is to summarize the variety of methods in one dimension and in multiple dimensions. The sequence used to organize the review is from one dimensional problems to multiple dimension problems, from approximation methods to exact methods. Electromagnetic and acoustic methods are discussed in parallel.
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