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22 October 2004 Minimum-phase-based inverse scattering method applied to IPS008
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We discuss an approach to solving the inverse scattering problem using homomorphic filtering and the difficulties that have been experienced in the past in trying to implement it in practice. Solving this problem has important consequences for a number of imaging and remote sensing problems as well as structure-synthesis problems. We show that the problem reduces to one of needing to preprocess the measured data in order that the nonlinear filtering succeeds and gives meaningful recontstructions. We discuss the steps taht have to be taken to achieve this and show that a sufficient condition to obtain a solution is that the data-derived function to be filtered is made close to a minimum phase function. This minimum-phase property is well understood in one dimensional problems but less so in two or higher dimensions. Another significant practical issue is that for inverse scattering problems, in contrast to inverse synthesis problems, only limited noisy data are available from which to compute the structure. These factors are discussed and we note that solving the inverse scattering problem immediately provides a solution to the inverse synthesis problem.
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Michael A. Fiddy, Markus E. Testorf, and Umer Shahid "Minimum-phase-based inverse scattering method applied to IPS008", Proc. SPIE 5562, Image Reconstruction from Incomplete Data III, (22 October 2004);

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