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Multiple Level Sets for Piecewise Constant Surface Reconstruction in Highly Ill-Posed Problems

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Abstract

This paper considers highly ill-posed surface recovery inverse problems, where the sought surface in 2D or 3D is piecewise constant with several possible level values. These levels may further be potentially unknown. Multiple level set functions are used when there are more than two such levels, and we extend the methods and theory of our previous works to handle such more complex situations. A rather efficient method is developed. Inverse potential problems in two and three space dimensions are solved numerically, demonstrating the method’s capabilities for several both known and unknown level values.

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Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, Vancouver, Canada

    K. van den Doel & U. M. Ascher

  2. Department of Mathematics, Fed. University of St Catarina, Florianopolis, Brazil

    A. Leitão

Authors
  1. K. van den Doel
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  2. U. M. Ascher
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  3. A. Leitão
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Corresponding author

Correspondence to K. van den Doel.

Additional information

K. van den Doel supported in part under NSERC Discovery Grant 84306; U.M. Ascher supported in part under NSERC Discovery Grant 84306; A. Leitão supported in part under CNPq grant 303098/2009-0 and by the Alexander von Humboldt Foundation AvH.

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van den Doel, K., Ascher, U.M. & Leitão, A. Multiple Level Sets for Piecewise Constant Surface Reconstruction in Highly Ill-Posed Problems. J Sci Comput 43, 44–66 (2010). https://doi.org/10.1007/s10915-009-9341-x

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  • DOI: https://doi.org/10.1007/s10915-009-9341-x

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