Inverse obstacle scattering using reduced data
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The classical result of Schiffer in acoustic scattering is that a knowledge of the far field pattern for all observation directions and all incident directions at a fixed wave number k uniquely determines the sound-soft scattering obstacle D. This is widely believed to be far greater information than is required for uniqueness, and more recent results have been obtained that considerably weaken the amount of data needed, provided certain restrictions are placed on the scatterer. Most of this work has concentrated on reducing the number of incident waves required for a unique determination. This paper takes another approach and seeks to determine sufficient information to recover the obstacle from measurements of the far field at isolated points. Our approach will be constructive and some numerical reconstructions will be presented.
SIAM JOURNAL ON APPLIED MATHEMATICS
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