scholarly journals A Bayesian level set method for geometric inverse problems

2016 ◽  
Vol 18 (2) ◽  
pp. 181-217 ◽  
Author(s):  
Marco Iglesias ◽  
Yulong Lu ◽  
Andrew Stuart
Keyword(s):  
Inverse Problems ◽  
Level Set Method ◽  
Level Set ◽  
Geometric Inverse Problems

A level set method for inverse problems

2001 ◽  
Vol 17 (5) ◽  
pp. 1327-1355 ◽  
Author(s):  
Martin Burger
Keyword(s):  
Inverse Problems ◽  
Level Set Method ◽  
Level Set

scholarly journals Level set methods for geometric inverse problems in linear elasticity

2004 ◽  
Vol 20 (3) ◽  
pp. 673-696 ◽  
Author(s):  
Hend Ben Ameur ◽  
Martin Burger ◽  
Benjamin Hackl
Keyword(s):  
Inverse Problems ◽  
Level Set ◽  
Linear Elasticity ◽  
Level Set Methods ◽  
Geometric Inverse Problems

scholarly journals On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
A. De Cezaro
Keyword(s):  
Inverse Problems ◽  
Level Set Method ◽  
Level Set ◽  
Regularization Method ◽  
Level Sets ◽  
Approximate Solutions ◽  
Type Method ◽  
Ill Posed ◽  
Level Set Approach ◽  
Level Set Framework

We investigate a level-set-type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem, we propose a Tikhonov-type regularization approach coupled with a level-set framework. We prove the existence of generalized minimizers for the Tikhonov functional. Moreover, we prove convergence and stability for regularized solutions with respect to the noise level, characterizing the level-set approach as a regularization method for inverse problems. We also show the applicability of the proposed level-set method in some interesting inverse problems arising in elliptic PDE models.

Level Set Method Optimized with the Euclidean Distance Transform

2019 ◽  
Author(s):  
Luis Fernando Segalla ◽  
Alexandre Zabot ◽  
Diogo Nardelli Siebert ◽  
Fabiano Wolf
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Euclidean Distance ◽  
Distance Transform ◽  
Euclidean Distance Transform
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