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Wave Phenomena

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Handbook of Mathematical Methods in Imaging

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Abstract

This chapter discusses imaging methods related to wave phenomena, and in particular, inverse problems for the wave equation will be considered. The first part of the chapter explains the boundary control method for determining a wave speed of a medium from the response operator, which models boundary measurements. The second part discusses the scattering relation and travel times, which are different types of boundary data contained in the response operator. The third part gives a brief introduction to curvelets in wave imaging for media with nonsmooth wave speeds. The focus will be on theoretical results and methods.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, PO Box 68 (Gustaf Hällströmin katu 2b), FI-00014, Helsinki, Finland

    Matti Lassas & Mikko Salo

  2. Department of Mathematics, University of Washington, Box 354350, 98195-4350, Seattle, WA, USA

    Gunther Uhlmann

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  1. Matti Lassas
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  2. Mikko Salo
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  3. Gunther Uhlmann
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Correspondence to Matti Lassas .

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

    Otmar Scherzer

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Lassas, M., Salo, M., Uhlmann, G. (2015). Wave Phenomena. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_52

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