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How Many Parameters Can One Solve for in Diffuse Tomography?

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Inverse Problems in Wave Propagation

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 90))

Abstract

A lower bound for the number of independent range conditions on Redheffer’s -product is derived in two and three dimensions. In two dimensions this bound is tight. Although the complexity of analysis increases with dimension, the technique of introducing a “slit” should apply to higher dimensions. Therefore, only two and three dimensional systems are considered here.

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References

  1. C. Aitken, Determinants and Matrices, 8th ed., Oliver and Boyd Ltd., Edinburgh, 1954.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at Berkeley, Berkeley, CA, 94720, USA

    F. A. Grünbaum

  2. Institüt für Instr. u. Num. Math, Universität Münster, Einsteinstrasse 62, D-48149, Münster, Germany

    S. K. Patch

  3. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    S. K. Patch

Authors
  1. F. A. Grünbaum
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  2. S. K. Patch
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Editor information

Editors and Affiliations

  1. Domaine de Voluceau, INRIA, B.P. 105, 78153 Le Chesnay, Cedex, France

    Guy Chavent

  2. Department of Mathematics, Iowa State University, Ames, IA, 50011, USA

    Paul Sacks

  3. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    George Papanicolaou

  4. Department of Computer and Applied Mathematics, Rice University, Houston, TX, 77251-1892, USA

    William W. Symes

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© 1997 Springer Science+Business Media New York

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Grünbaum, F.A., Patch, S.K. (1997). How Many Parameters Can One Solve for in Diffuse Tomography?. In: Chavent, G., Sacks, P., Papanicolaou, G., Symes, W.W. (eds) Inverse Problems in Wave Propagation. The IMA Volumes in Mathematics and its Applications, vol 90. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1878-4_10

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  • DOI: https://doi.org/10.1007/978-1-4612-1878-4_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7322-6

  • Online ISBN: 978-1-4612-1878-4

  • eBook Packages: Springer Book Archive

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