Reconstruction of Media Posed as an Optimization Problem

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.

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