A level set method for inverse problems

By Martin Burger. 2001

190 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1bb8d3fef15da1dc669cad00a375885eb95cfa69

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Citations in the corpus

A piecewise constant level set method for elliptic inverse problems (2007, methodology): “Recently, the level set method, firstly proposed by Osher and Sethian in [25], has been extended and used for this kind of problems in [4, 8, 12, 17, 26, 14, 1, 2, 3].”
Electrical impedance tomography using level set representation and total variational regularization (2005, methodology): “In [5, 7, 6, 18] for some other algorithms in using level set methods for some inverse problems.”
Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients (2004, methodology): “In [3,4,25], the shape derivative is used to get the steepest direction with respect to the entire boundary.”
A survey on level set methods for inverse problems and optimal design (2005, background): “The efficient solution of this linear system for the model problems 1 and 3 has been investigated in Burger [26] using an all-at-once approach [29, 30, 65, 66], which leads to a large, sparse indefinite linear system for the velocity, a linearized state variable and a dual variable.”
Incorporating topological derivatives into level set methods (2004, unknown): “Keywords: Level Set Method, Topology Optimization, Shape Reconstruction, Shape Derivative, Topological Derivative, Hamilton-Jacobi Equations AMS Subject Classification: 65J20, 49Q10, 49L99, 35C44, 35R30.”
Multiple level set methods with applications for identifying piecewise constant functions (2004, background): “The problem given in this section represents such a kind of optimal shape design problems and it is taken from Osher and Santosa [38], see also [ 4 , 5, 42, 32] for some more problems that are similar in nature to what is given below.”