In this communication we propose to solve the problem of reconstruction from limited data using a statistical regularization method based on a Bayesian information criterion. The minimization of the Bayesian information criterion, which is used here as an objective index to measure the goodness of an estimate, gives the optimum value of the smoothing parameter. By doing so, we could reduce the inversion problem to a simple minimization of a one-variable nonlinear function. The application of such a technique overcomes the nonuniqueness of the solution of the ill-posed problem and all shortcomings of many iterative methods. In the light of simulation and application to real data, we propose a slight modification to the Bayesian information criterion to reconstruct the wave energy distribution at the ionospheric base from the observation of radio wave electromagnetic field on the ground. The achieved results in both the inversion problem and the wave direction finding are very promising and may support other works so far suggested the use of Bayesian methods in the inversion of ill-posed problems to benefit from the valuable information brought by the a priori knowledge.
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Mehrez HIRARI, Masashi HAYAKAWA, "A Bayesian Regularization Approach to Ill-Posed Problems with Application to the Direction Finding of VLF/ELF Radio Waves" in IEICE TRANSACTIONS on Communications,
vol. E79-B, no. 1, pp. 63-69, January 1996, doi: .
Abstract: In this communication we propose to solve the problem of reconstruction from limited data using a statistical regularization method based on a Bayesian information criterion. The minimization of the Bayesian information criterion, which is used here as an objective index to measure the goodness of an estimate, gives the optimum value of the smoothing parameter. By doing so, we could reduce the inversion problem to a simple minimization of a one-variable nonlinear function. The application of such a technique overcomes the nonuniqueness of the solution of the ill-posed problem and all shortcomings of many iterative methods. In the light of simulation and application to real data, we propose a slight modification to the Bayesian information criterion to reconstruct the wave energy distribution at the ionospheric base from the observation of radio wave electromagnetic field on the ground. The achieved results in both the inversion problem and the wave direction finding are very promising and may support other works so far suggested the use of Bayesian methods in the inversion of ill-posed problems to benefit from the valuable information brought by the a priori knowledge.
URL: https://global.ieice.org/en_transactions/communications/10.1587/e79-b_1_63/_p
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@ARTICLE{e79-b_1_63,
author={Mehrez HIRARI, Masashi HAYAKAWA, },
journal={IEICE TRANSACTIONS on Communications},
title={A Bayesian Regularization Approach to Ill-Posed Problems with Application to the Direction Finding of VLF/ELF Radio Waves},
year={1996},
volume={E79-B},
number={1},
pages={63-69},
abstract={In this communication we propose to solve the problem of reconstruction from limited data using a statistical regularization method based on a Bayesian information criterion. The minimization of the Bayesian information criterion, which is used here as an objective index to measure the goodness of an estimate, gives the optimum value of the smoothing parameter. By doing so, we could reduce the inversion problem to a simple minimization of a one-variable nonlinear function. The application of such a technique overcomes the nonuniqueness of the solution of the ill-posed problem and all shortcomings of many iterative methods. In the light of simulation and application to real data, we propose a slight modification to the Bayesian information criterion to reconstruct the wave energy distribution at the ionospheric base from the observation of radio wave electromagnetic field on the ground. The achieved results in both the inversion problem and the wave direction finding are very promising and may support other works so far suggested the use of Bayesian methods in the inversion of ill-posed problems to benefit from the valuable information brought by the a priori knowledge.},
keywords={},
doi={},
ISSN={},
month={January},}
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TY - JOUR
TI - A Bayesian Regularization Approach to Ill-Posed Problems with Application to the Direction Finding of VLF/ELF Radio Waves
T2 - IEICE TRANSACTIONS on Communications
SP - 63
EP - 69
AU - Mehrez HIRARI
AU - Masashi HAYAKAWA
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Communications
SN -
VL - E79-B
IS - 1
JA - IEICE TRANSACTIONS on Communications
Y1 - January 1996
AB - In this communication we propose to solve the problem of reconstruction from limited data using a statistical regularization method based on a Bayesian information criterion. The minimization of the Bayesian information criterion, which is used here as an objective index to measure the goodness of an estimate, gives the optimum value of the smoothing parameter. By doing so, we could reduce the inversion problem to a simple minimization of a one-variable nonlinear function. The application of such a technique overcomes the nonuniqueness of the solution of the ill-posed problem and all shortcomings of many iterative methods. In the light of simulation and application to real data, we propose a slight modification to the Bayesian information criterion to reconstruct the wave energy distribution at the ionospheric base from the observation of radio wave electromagnetic field on the ground. The achieved results in both the inversion problem and the wave direction finding are very promising and may support other works so far suggested the use of Bayesian methods in the inversion of ill-posed problems to benefit from the valuable information brought by the a priori knowledge.
ER -