Advanced search
1 file | 708.87 KB Add to list

On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification

(2013) INVERSE PROBLEMS. 29(11).
Author
Organization
Abstract
We present a new approach to the convexification of the Tikhonov regularization using a continuation method strategy. We embed the original minimization problem into a one-parameter family of minimization problems. Both the penalty term and the minimizer of the Tikhonov functional become dependent on a continuation parameter. In this way we can independently treat two main roles of the regularization term, which are the stabilization of the ill-posed problem and introduction of the a priori knowledge. For zero continuation parameter we solve a relaxed regularization problem, which stabilizes the ill-posed problem in a weaker sense. The problem is recast to the original minimization by the continuation method and so the a priori knowledge is enforced. We apply this approach in the context of topology-to-shape geometry identification, where it allows us to avoid the convergence of gradient-based methods to a local minima. We present illustrative results for magnetic induction tomography which is an example of PDE-constrained inverse problem.
Keywords
SENSITIVITY, OPERATORS, SHAPE OPTIMIZATION, ILL-POSED PROBLEMS, ELLIPTIC INVERSE PROBLEMS, INCORPORATING TOPOLOGICAL DERIVATIVES, LEVEL-SET METHOD, ELECTRICAL-IMPEDANCE TOMOGRAPHY

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 708.87 KB

Citation

Please use this url to cite or link to this publication:

MLA
Melicher, Valdemar, and Vladimír Vrábeľ. “On a Continuation Approach in Tikhonov Regularization and Its Application in Piecewise-constant Parameter Identification.” INVERSE PROBLEMS 29.11 (2013): n. pag. Print.
APA
Melicher, V., & Vrábeľ, V. (2013). On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification. INVERSE PROBLEMS, 29(11).
Chicago author-date
Melicher, Valdemar, and Vladimír Vrábeľ. 2013. “On a Continuation Approach in Tikhonov Regularization and Its Application in Piecewise-constant Parameter Identification.” Inverse Problems 29 (11).
Chicago author-date (all authors)
Melicher, Valdemar, and Vladimír Vrábeľ. 2013. “On a Continuation Approach in Tikhonov Regularization and Its Application in Piecewise-constant Parameter Identification.” Inverse Problems 29 (11).
Vancouver
1.
Melicher V, Vrábeľ V. On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification. INVERSE PROBLEMS. 2013;29(11).
IEEE
[1]
V. Melicher and V. Vrábeľ, “On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification,” INVERSE PROBLEMS, vol. 29, no. 11, 2013.
@article{4157205,
  abstract     = {{We present a new approach to the convexification of the Tikhonov regularization using a continuation method strategy. We embed the original minimization problem into a one-parameter family of minimization problems. Both the penalty term and the minimizer of the Tikhonov functional become dependent on a continuation parameter. In this way we can independently treat two main roles of the regularization term, which are the stabilization of the ill-posed problem and introduction of the a priori knowledge. For zero continuation parameter we solve a relaxed regularization problem, which stabilizes the ill-posed problem in a weaker sense. The problem is recast to the original minimization by the continuation method and so the a priori knowledge is enforced. We apply this approach in the context of topology-to-shape geometry identification, where it allows us to avoid the convergence of gradient-based methods to a local minima. We present illustrative results for magnetic induction tomography which is an example of PDE-constrained inverse problem.}},
  articleno    = {{115008}},
  author       = {{Melicher, Valdemar and Vrábeľ, Vladimír}},
  issn         = {{0266-5611}},
  journal      = {{INVERSE PROBLEMS}},
  keywords     = {{SENSITIVITY,OPERATORS,SHAPE OPTIMIZATION,ILL-POSED PROBLEMS,ELLIPTIC INVERSE PROBLEMS,INCORPORATING TOPOLOGICAL DERIVATIVES,LEVEL-SET METHOD,ELECTRICAL-IMPEDANCE TOMOGRAPHY}},
  language     = {{eng}},
  number       = {{11}},
  pages        = {{22}},
  title        = {{On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification}},
  url          = {{http://dx.doi.org/10.1088/0266-5611/29/11/115008}},
  volume       = {{29}},
  year         = {{2013}},
}

Altmetric
View in Altmetric
Web of Science
Times cited: