Image estimation from scattered field data

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Abstract
The purpose of this paper is to reappraise the linearizing methods frequently used to solve inverse scattering problems. We describe inversion algorithms based on the Born and the Rytov approximations and the nature of the distortions obtained in the reconstructions when using them. We present extensions of these methods, namely, the distorted‐wave Born and the distorted‐wave Rytov approximations, which incorporate prior knowledge about part of the scattering structure. A method for inverting scattered field data using these distorted‐wave approximations is described, which retains the computational simplicity of the Born and the Rytov techniques. Some examples of their use with simulated and real data are given. A further extension of our distorted‐wave formalism, which leads to improvements of the reconstructed image, is suggested. This entails a spectral estimation procedure also based on the incorporation of prior knowledge about the scatterer. This spectral estimation procedure can be useful for interpolation of scattered field data as well as resolution enhancement.