Abstract

The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.
Practitioners in this field comprise applied physicists, engineers, and technologists, whereas the theory is almost entirely in the domain of abstract mathematics. This gulf between the two, if bridged, can only lead to improvement in the level of scholarship in this highly important discipline. This is the book's primary focus.
The authors explain that inverse problems, unlike direct ones, are mathematical in nature, i.e., inaccessible by direct observation or experimentation: "To extract the hidden sources of the natural and biological phenomena from their manifestations is the leitmotif of inverse problems." Applying such diagnosis to the case of inverse scattering of plane waves from material objects, they discuss such topics as the theory of ill-posed problems, regularization by projections, uniqueness theorems, and algorithms. Roy works for a private firm in Largo, MD. Couchman is with the US Naval Research Laboratory in Washington, DC.Book News, Inc.®, Portland, OR