Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Weakly differentiable functions
Weakly differentiable functions
The augmented lagrangian method for parameter estimation in elliptic systems
SIAM Journal on Control and Optimization
The determination of a coefficient in an elliptic equation from average flux data
Journal of Computational and Applied Mathematics
Sequential and Parallel Splitting Methods for Bilinear Control Problems in Hilbert Spaces
SIAM Journal on Numerical Analysis
An Augmented Lagrangian Method for Identifying Discontinuous Parameters in Elliptic Systems
SIAM Journal on Control and Optimization
Electrical Impedance Tomography
SIAM Review
A PDE-based fast local level set method
Journal of Computational Physics
Basis Norm Rescaling for Nonlinear Parameter Estimation
SIAM Journal on Scientific Computing
Journal of Computational Physics
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Existence for Shape Optimization Problems in Arbitrary Dimension
SIAM Journal on Control and Optimization
SIAM Journal on Scientific Computing
On level set regularization for highly ill-posed distributed parameter estimation problems
Journal of Computational Physics
A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data
Journal of Computational Physics
Image Segmentation Using Some Piecewise Constant Level Set Methods with MBO Type of Projection
International Journal of Computer Vision
A piecewise constant level set method for elliptic inverse problems
Applied Numerical Mathematics
Journal of Computational Physics
Four-Color Theorem and Level Set Methods for Watershed Segmentation
International Journal of Computer Vision
On Level-Set Type Methods for Recovering Piecewise Constant Solutions of Ill-Posed Problems
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Electrical impedance tomography using level set representation and total variational regularization
Journal of Computational Physics
High performance computing for the level-set reconstruction algorithm
Journal of Parallel and Distributed Computing
A multi-phase level set framework for source reconstruction in bioluminescence tomography
Journal of Computational Physics
Variational piecewise constant level set methods for shape optimization of a two-density drum
Journal of Computational Physics
Level set method for the inverse elliptic problem in nonlinear electromagnetism
Journal of Computational Physics
Journal of Mathematical Imaging and Vision
A shape prior constraint for implicit active contours
Pattern Recognition Letters
Parametric Level Set Methods for Inverse Problems
SIAM Journal on Imaging Sciences
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
Hi-index | 31.48 |
We propose a level set approach for elliptic inverse problems with piecewise constant coefficients. The geometry of the discontinuity of the coefficient is represented implicitly by level set functions. The inverse problem is solved using a variational augmented Lagrangian formulation with total variation regularization of the coefficient. The corresponding Euler-Lagrange equation gives the evolution equation for the level set functions and the constant values of the coefficients. We use a multiple level set representation which allows the coefficient to have multiple constant regions. Knowledge of the exact number of regions is not required, only an upper bound is needed. Numerical experiments show that the method can recover coefficients with rather complicated geometries of discontinuities under moderate amount of noise in the observation data. The method is also robust with respect to the initial guess for the geometry of the coefficient discontinuities.