Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients

By Tony F. Chan, Xuecheng Tai. 2004

229 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f9065ad7cbbc052c26fa4af7cd032e53dc99db4b

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Citations in the corpus

Nonlinear image reconstruction for electrical capacitance tomography using experimental data (2005, methodology): “TV has also been applied to a general form of the elliptic inverse boundary value problem by [10].”
A method of biological tissues elasticity reconstruction using magnetic resonance elastography measurements (2007, background): “In [16], Chan and Tai have performed a study on the conductivity inverse problem using continuous level set functions (distance functions) in a standard level set formulation.”
Level set methods for inverse scattering (2006, background): “Colour level set An alternative way of describing different phases by more than one level set functions has been introduced in [161] in the framework of image segmentation and further investigated by [16, 37, 36, 62, 106, 157] in the framework of inverse problems.”
An Abstract Framework for Elliptic Inverse Problems: Part 1. An Output Least-Squares Approach (2007, methodology): “The prototypical elliptic inverse problem is to estimate the coefficient q from a measurement of the solution u in the elliptic boundary value problem (BVP) q u f in (1a) u 0 on (1b) A number of papers, such as [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], have examined this problem or variations of it.”
A piecewise constant level set method for elliptic inverse problems (2007, methodology): “For multiple subdomains, one can use multiple level set functions [8].”
A survey on level set methods for inverse problems and optimal design (2005, methodology): “Some authors also tried a direct approach to the computation of derivatives by the level set method, namely by using a variation with respect to the level set function φ in some function space [35, 37, 39, 64, 87].”
A binary level set model and some applications to Mumford-Shah image segmentation (2006, background): “If in , and in can be written as the sum (14) The formula (14) can be generalized to represent functions with more than two constant values by using multiple functions following the essential ideas of the level set formulation used in [4], [26].”
Bayesian inversion for facies detection: An extensible level set framework (2009, methodology): “Unlike the methods mentioned above, the level set method allows for arbitrarily complex zone boundaries that are completely ‘‘data driven.’’ Several researchers have noted the superb performance of the level set method in imaging boolean (i.e., 2 facies) parameter fields when applied to such problem”
Multiple level set methods with applications for identifying piecewise constant functions (2004, methodology): “Applications for identifying the coecient from an elliptic equation are presented in §6 following Chan and Tai [ 7 ].”