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Reconstruction of Media Posed as an Optimization Problem

  • P. M. van den Berg
Part of the International Centre for Mechanical Sciences book series (CISM, volume 398)

Abstract

A central problem in target identification, non-destructive testing. medical imaging and numerous other areas of application concerns the determination of the shape. location and constitutive parameters, such as complex index of refraction or local sound speed, of a local inhomogeneity from measurements of the scattered field when a monochromatic wave is incident upon the inhomogeneity. One class of methods of attacking this problem is based on minimizing the discrepancy between the measured data and predicted data as a function of the desired parameters. Although the problem is nonlinear and ill-posed, considerable progress has been made in developing useful algorithms for reconstructing the desired parameters.

In the lectures we discuss, within a unified framework. a number of such algorithms, including Born. extended Born, distorted Born. Newton-Kantorovich, gradient and modified gradient algorithms for index of refraction reconstruction from scattered field data from multiple sources at a single frequency. All of these approaches are based on domain integral representations of the scattered field. Further, it is shown that when a priori information, that the inhomogeneity is highly dissipative, is incorporated into the modified gradient algorithm, it successfully reconstructs the shape and location of impenetrable scatterers. We also present the total variation as one of the many ‘artificial’ constraints that may be used to regularize the reconstructed contrast. Finally, we discuss a new method, the so-called contrast source inversion method, which is extremely efficient and versatile, allowing for the introduction of a priori information, such as positivity constraints, in a simple version.

Keywords

Scattered Field Forward Problem Data Equation Minimum Norm Solution Object Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1999

Authors and Affiliations

  • P. M. van den Berg
    • 1
  1. 1.Delft University of TechnologyDelftThe Netherlands

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