Journal ArticleDOI
Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients
Tony F. Chan,Xue-Cheng Tai +1 more
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In this paper, a level set approach for elliptic inverse problems with piecewise constant coefficients is proposed, where the geometry of the discontinuity of the coefficient is represented implicitly by level set functions.About:
This article is published in Journal of Computational Physics.The article was published on 2004-01-01. It has received 207 citations till now. The article focuses on the topics: Constant coefficients & Classification of discontinuities.read more
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Nonlinear partial differential equations with applications
TL;DR: In this paper, the authors present a system of equations for evolving pseudomonotone or weakly continuous mappings with set-valued mappings, and a set of auxiliary tools.
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Level set methods for inverse scattering
Oliver Dorn,Dominique Lesselier +1 more
TL;DR: In this paper, the authors give an overview of recent techniques which use a level set representation of shapes for solving inverse scattering problems, including shape sensitivity analysis and topological derivatives, and various techniques for incorporating regularization into the shape inverse problem using level sets.
Journal ArticleDOI
A binary level set model and some applications to Mumford-Shah image segmentation
TL;DR: A PDE-based level set method that needs to minimize a smooth convex functional under a quadratic constraint, and shows numerical results using the method for segmentation of digital images.
Journal ArticleDOI
A survey on level set methods for inverse problems and optimal design
Martin Burger,Stanley Osher +1 more
TL;DR: This paper provides a survey on the recent development in level set methods in inverse problems and optimal design, and provides a review on numerical methods important in this context, and gives an overview of applications treated withlevel set methods.
Journal ArticleDOI
Nonlinear image reconstruction for electrical capacitance tomography using experimental data
TL;DR: In this paper, a regularized Gauss-Newton scheme has been implemented for nonlinear image reconstruction in ECT, where the forward problem has been solved at each iteration using the finite element method and the Jacobian matrix is recalculated using an efficient adjoint field method.
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Journal ArticleDOI
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Stanley Osher,James A. Sethian +1 more
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
Book
Graduate Texts in Mathematics
Rajendra Bhatia,Glen Bredon,Wolfgang Walter,Joseph J. Rotman,M. Ram Murty,Jane Gilman,Peter Walters,Martin Golubitsky,Ioannis Karatzas,Henri Cohen,Raoul Bott,Gaisi Takeuti,Béla Bollobás,John M. Lee,Jiří Matoušek,Saunders Mac Lane,John L. Kelley,B. A. Dubrovin,Tom M. Apostol,John Stillwell,William Arveson +20 more
Journal ArticleDOI
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
Luminita A. Vese,Tony F. Chan +1 more
TL;DR: A new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations, and validated by numerical results for signal and image denoising and segmentation.
Book
Minimal surfaces and functions of bounded variation
TL;DR: In this article, a priori estimation of the gradient of the Bernstein problem is given. But the gradient is not a priorimate of the radius of the singular set, and it is not known whether the gradient can be estimated by direct methods.