Mathematics – Analysis of PDEs
Scientific paper
2010-07-15
SIAM Journal on Imaging Sciences, vol. 4, NO. 2, pp. 618-650, 2011
Mathematics
Analysis of PDEs
Scientific paper
10.1137/100800208
In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results a significantly lower dimensional problem, which bypasses many difficulties with traditional level set methods, such as regularization, re-initialization and use of signed distance function. Moreover, we show that from a computational point of view, low order representation of the problem paves the path for easier use of Newton and quasi-Newton methods. Specifically for the purposes of this paper, we parameterize the level set function in terms of adaptive compactly supported radial basis functions, which used in the proposed manner provides flexibility in presenting a larger class of shapes with fewer terms. Also they provide a "narrow-banding" advantage which can further reduce the number of active unknowns at each step of the evolution. The performance of the proposed approach is examined in three examples of inverse problems, i.e., electrical resistance tomography, X-ray computed tomography and diffuse optical tomography.
Aghasi Alireza
Kilmer Misha
Miller Eric L.
No associations
LandOfFree
Parametric Level Set Methods for Inverse Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Parametric Level Set Methods for Inverse Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Parametric Level Set Methods for Inverse Problems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-598082