@Article{IJNAM-4-74,
author = {L. K. Nielsen, X.-C. Tai, S. I. Aanonsen and M. Espedal},
title = {A Binary Level Set Model for Elliptic Inverse Problems with Discontinuous Coefficients},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2007},
volume = {4},
number = {1},
pages = {74--99},
abstract = {<p style="text-align: justify;">In this paper we propose a variant of a binary level set
approach for solving elliptic problems with piecewise constant
coefficients. The inverse problem is solved by a variational augmented
Lagrangian approach with a total variation regularisation. In the binary
formulation, the sought interfaces between the domains with different
values of the coefficient are represented by discontinuities of the
level set functions. The level set functions shall only take two
discrete values, i.e. 1 and -1, but the minimisation functional is
smooth. Our formulation can, under moderate amount of noise in the
observations, recover rather complicated geometries without requiring
any initial curves of the geometries, only a reasonable guess of the
constant levels is needed. Numerical results show that our
implementation of this formulation has a faster convergence than the
traditional level set formulation used on the same problems.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/852.html}
}