Multifrequency inverse problem for the reduced wave equation: Resolution cell and stability

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Abstract
The multifrequency inverse problem associated with the reduced wave equation Δu+k2n2(x)u=0, x ∈ R3 is examined for the case where the data set is sparse. The resolution cell or solution set is examined in detail and is shown to be an infinite-dimensional manifold. The concept of stability is introduced. It is shown that the intrinsic condition of structural stability to the inverse process selects out a preferred set of solutions from the solution set. The structural stability of various iterative schemes used in the inverse process are examined.

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