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Sonic Imaging

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Handbook of Mathematical Methods in Imaging

Abstract

This paper deals with the inverse problem of the wave equation, which is of relevance in fields such as ultrasound tomography, seismic imaging, and nondestructive testing. We study the linearized problem by Fourier analysis, and we describe an iterative reconstruction method for the fully nonlinear problem in the time domain. We discuss practical problems such as the spectral incompleteness in reflection imaging and finding a good initial approximation. We demonstrate by numerical reconstructions from synthetic data what can be achieved.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Münster, Einsteinstrasse 62, 48149, Münster, Germany

    Frank Natterer

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  1. Frank Natterer
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Correspondence to Frank Natterer .

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  1. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

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Natterer, F. (2015). Sonic Imaging. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_37

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