Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
An Augmented Lagrangian Method for Identifying Discontinuous Parameters in Elliptic Systems
SIAM Journal on Control and Optimization
SIAM Journal on Scientific Computing
Journal of Computational Physics
On Effective Methods for Implicit Piecewise Smooth Surface Recovery
SIAM Journal on Scientific Computing
Electrical impedance tomography using level set representation and total variational regularization
Journal of Computational Physics
Energy minimization based segmentation and denoising using a multilayer level set approach
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Piecewise constant level set methods and image segmentation
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
A binary level set model and some applications to Mumford-Shah image segmentation
IEEE Transactions on Image Processing
Design of piezoelectric actuators using a multiphase level set method of piecewise constants
Journal of Computational Physics
Four-Color Theorem and Level Set Methods for Watershed Segmentation
International Journal of Computer Vision
Variational piecewise constant level set methods for shape optimization of a two-density drum
Journal of Computational Physics
Journal of Computational Physics
Applied Numerical Mathematics
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We apply a piecewise constant level set method to elliptic inverse problems. The discontinuity of the coefficients is represented implicitly by a piecewise constant level set function, which allows to use one level set function to represent multiple phases. The inverse problem is solved using a variational penalization method with the total variation regularization of the coefficients. An operator splitting scheme is used to get efficient and robust numerical schemes for solving the obtained problem. Numerical experiments show that the method can recover coefficients with rather complicated geometry of discontinuities under a moderate amount of noise in the observation data.