Level set approach to inverse problems

There are several inverse problems where the unknown can be most conveniently parameterized using the level set strategy. Examples are problems involving obstacles in scattering or inverse design problems involving geometry. Our idea is to exploit the versatility of the level set approach as demonstrated in a wide variety of applications (see Sethian's webpage) Here is an examples of how a level set method "captures" the unknown obstacle. The application is in the context of reconstructing a cutout on a screen from diffraction data. The unknown is the letter "F".

Reference material

  1. A level-set approach for inverse problems involving obstacles. Control, Optimization, and Calculus of Variation, 1 (1996). (view)
  2. Reconstruction of a 2-D binary obstacle by controlled evolution of a level-set. (with A. Litman and D. Lesselier), Inverse Problems, 14 (1998), pages 685-706. (view)
  3. Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum. (with S. Osher), J. Comp. Phys. 171 (2001), 272-288. (view)
  4. A topology-preserving level set method for shape optimization. (with O. Alexandrov), submitted. (view)