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A Level-Set Approach for Inverse Problems Involving Obstacles (1996)
| Citations: | 97 - 2 self |
BibTeX
@MISC{Santosa96alevel-set,
author = {Fadil Santosa},
title = {A Level-Set Approach for Inverse Problems Involving Obstacles},
year = {1996}
}
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Abstract
. An approach for solving inverse problems involving obstacles is proposed. The approach uses a level-set method which has been shown to be effective in treating problems of moving boundaries, particularly those that involve topological changes in the geometry. We develop two computational methods based on this idea. One method results in a nonlinear time-dependent partial differential equation for the level-set function whose evolution minimizes the residual in the data fit. The second method is an optimization that generates a sequence of levelset functions that reduces the residual. The methods are illustrated in two applications: a deconvolution problem and a diffraction screen reconstruction problem. Keywords: Inverse problems, level-set method, Hamilton-Jacobi equations, surface evolution, optimization, deconvolution, diffraction. 1. Inverse problems involving obstacles There is a host of inverse problems wherein the desired unknown is a region in IR 2 or IR 3 . ...
Keyphrases
level-set approach inverse problem involving obstacle inverse problem level-set method second method levelset function data fit hamilton-jacobi equation surface evolution nonlinear time-dependent partial differential equation diffraction screen reconstruction problem level-set function method result topological change desired unknown deconvolution problem computational method
