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

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.

• Content Type Journal Article
• DOI 10.1007/s10915-009-9341-x
• Authors
  
  
  • K. van den Doel, University of British Columbia Department of Computer Science Vancouver Canada
  • U. M. Ascher, University of British Columbia Department of Computer Science Vancouver Canada
  • A. Leitão, Fed. University of St Catarina Department of Mathematics Florianopolis Brazil
  
  

• Journal Journal of Scientific Computing
• Online ISSN 1573-7691
• Print ISSN 0885-7474

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Original source : http://www.springerlink.com/content/b025305881571v...