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
is to exploit the versatility of the level set approach as demonstrated
in a wide variety of applications (see
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".
A level-set approach for inverse problems
involving obstacles. Control,
Optimization, and Calculus of Variation, 1 (1996).
Reconstruction of a 2-D binary obstacle by controlled evolution of a
(with A. Litman and D. Lesselier),
Inverse Problems, 14 (1998),
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),
A topology-preserving level set method for shape optimization.
(with O. Alexandrov),