| 研究実績の概要 |
This research project has been focused on inverse problems to estimate the unknown parameters in errors-in-variables (EIV), multiplicative noise and discrete tomography models by combining different types of data. We have achieved a number of new results and published 9 papers in international journals and one book chapter. The applicant has been invited to report the achieved results at several international conferences/symposia. More specifically, we have developed new least-squares (LS)-based estimators to reconstruct multiplicative error models and conducted quality evaluation of lattice
basis reduction for discrete tomography. We found that quality of lattice basis reduction can be directly affected by
the probability distribution of the reduced Gram-Schmidt coefficients. We have proposed bias-corrected weighted LS and
N-calibrated estimators to estimate the unknown parameters in an EIV model. The advantages of these new estimators are
that they can be as good as total LS, but require much less computation. By assuming that data are of different types
and of different accuracy, we have proved for the first time that the variance components in an EIV model cannot be estimable under certain conditions. If they are estimable, they can be unstable. Unless prior subjective information is assumed, we can hardly obtain the correct weighting factors for different types of data. Thus, we have also investigated how EIV can affect the parameter estimation and the determination of weighting factors for different types of data.
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