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Regularization of inverse magnetostatic problems: possibilities and pitfalls

Regularization of inverse magnetostatic problems: possibilities and pitfalls Purpose – Inverse problems are usually ill‐conditioned, requiring the adoption of regularization techniques to obtain reliable results. The choice of the regularization method and of the related parameters represents a critical issue that must be based on the knowledge of reliable additional information on the problem. In the paper some possibilities and pitfalls for the choice of regularization strategy are presented and compared. Design/methodology/approach – Electromagnetic inverse problems (EIP) are usually formulated starting from a direct problem, based on a direct operator , providing the effects (e.g. fields, fluxes) generated by known sources acting through known systems . The direct operators involved in many real world electromagnetic phenomena, due to their compactness, lead to ill posed inverse problems. Inversion procedures pursue the solution regularity through the adoption of various regularization techniques . Improper use of regularizations may unduly constrain the approximated solution and, consequently, cause significant lack of accuracy. Mathematical tools for an effective choice of the regularization technique are not available for every application, and a number of issues are still open. The paper presents a common mathematical model for most of the regularization techniques, discussing their benefits and limitations. Findings – The paper discusses limits, applicability conditions, and impact on the performance of reconstruction procedures, of some relevant characteristics of the inversion algorithms, with particular reference to robustness against noise and inaccuracies in the system parameters. Originality/value – Some criteria for an effective application of regularization are also discussed, showing in particular how proper choices, founded on a careful analysis of the direct problem, may reveal quite effective in improving the solution quality. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

Regularization of inverse magnetostatic problems: possibilities and pitfalls

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Publisher
Emerald Publishing
Copyright
Copyright © 2005 Emerald Group Publishing Limited. All rights reserved.
ISSN
0332-1649
DOI
10.1108/03321640510598102
Publisher site
See Article on Publisher Site

Abstract

Purpose – Inverse problems are usually ill‐conditioned, requiring the adoption of regularization techniques to obtain reliable results. The choice of the regularization method and of the related parameters represents a critical issue that must be based on the knowledge of reliable additional information on the problem. In the paper some possibilities and pitfalls for the choice of regularization strategy are presented and compared. Design/methodology/approach – Electromagnetic inverse problems (EIP) are usually formulated starting from a direct problem, based on a direct operator , providing the effects (e.g. fields, fluxes) generated by known sources acting through known systems . The direct operators involved in many real world electromagnetic phenomena, due to their compactness, lead to ill posed inverse problems. Inversion procedures pursue the solution regularity through the adoption of various regularization techniques . Improper use of regularizations may unduly constrain the approximated solution and, consequently, cause significant lack of accuracy. Mathematical tools for an effective choice of the regularization technique are not available for every application, and a number of issues are still open. The paper presents a common mathematical model for most of the regularization techniques, discussing their benefits and limitations. Findings – The paper discusses limits, applicability conditions, and impact on the performance of reconstruction procedures, of some relevant characteristics of the inversion algorithms, with particular reference to robustness against noise and inaccuracies in the system parameters. Originality/value – Some criteria for an effective application of regularization are also discussed, showing in particular how proper choices, founded on a careful analysis of the direct problem, may reveal quite effective in improving the solution quality.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Sep 1, 2005

Keywords: Magnetism; Optimization techniques

References