Interpolatory Estimation of Multi-Dimensional Orthogonal Expansions with Stochastic Coefficients

Takuro KIDA; Somsak SA-NGUANKOTCHAKORN; Kenneth JENKINS

Interpolatory Estimation of Multi-Dimensional Orthogonal Expansions with Stochastic Coefficients

Takuro KIDA, Somsak SA-NGUANKOTCHAKORN, Kenneth JENKINS

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Relating to the problem of suppressing the immanent redundancy contained in an image with out vitiating the quality of the resultant approximation, the interpolation of multi-dimensional signal is widely discussed. The minimization of the approximation error is one of the important problems in this field. In this paper, we establish the optimum interpolatory approximation of multi-dimensional orthogonal expansions. The proposed approximation is superior, in some sense, to all the linear and the nonlinear approximations using a wide class of measures of error and the same generalized moments of these signals. Further, in the fields of information processing, we sometimes consider the orthonormal development of an image each coefficient of which represents the principal featurr of the image. The selection of the orthonormal bases becomes important in this problem. The Fisher's criterion is a powerful tool for this class of problems called declustering. In this paper, we will make some remarks to the problem of optimizing the Fisher's criterion under the condition that the quality of the approximation is maintained.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.5 pp.900-916

Publication Date: 1994/05/25

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Category: Digital Signal Processing

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Takuro KIDA, Somsak SA-NGUANKOTCHAKORN, Kenneth JENKINS, "Interpolatory Estimation of Multi-Dimensional Orthogonal Expansions with Stochastic Coefficients" in IEICE TRANSACTIONS on Fundamentals, vol. E77-A, no. 5, pp. 900-916, May 1994, doi: .
Abstract: Relating to the problem of suppressing the immanent redundancy contained in an image with out vitiating the quality of the resultant approximation, the interpolation of multi-dimensional signal is widely discussed. The minimization of the approximation error is one of the important problems in this field. In this paper, we establish the optimum interpolatory approximation of multi-dimensional orthogonal expansions. The proposed approximation is superior, in some sense, to all the linear and the nonlinear approximations using a wide class of measures of error and the same generalized moments of these signals. Further, in the fields of information processing, we sometimes consider the orthonormal development of an image each coefficient of which represents the principal featurr of the image. The selection of the orthonormal bases becomes important in this problem. The Fisher's criterion is a powerful tool for this class of problems called declustering. In this paper, we will make some remarks to the problem of optimizing the Fisher's criterion under the condition that the quality of the approximation is maintained.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_5_900/_p

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@ARTICLE{e77-a_5_900,
author={Takuro KIDA, Somsak SA-NGUANKOTCHAKORN, Kenneth JENKINS, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Interpolatory Estimation of Multi-Dimensional Orthogonal Expansions with Stochastic Coefficients},
year={1994},
volume={E77-A},
number={5},
pages={900-916},
abstract={Relating to the problem of suppressing the immanent redundancy contained in an image with out vitiating the quality of the resultant approximation, the interpolation of multi-dimensional signal is widely discussed. The minimization of the approximation error is one of the important problems in this field. In this paper, we establish the optimum interpolatory approximation of multi-dimensional orthogonal expansions. The proposed approximation is superior, in some sense, to all the linear and the nonlinear approximations using a wide class of measures of error and the same generalized moments of these signals. Further, in the fields of information processing, we sometimes consider the orthonormal development of an image each coefficient of which represents the principal featurr of the image. The selection of the orthonormal bases becomes important in this problem. The Fisher's criterion is a powerful tool for this class of problems called declustering. In this paper, we will make some remarks to the problem of optimizing the Fisher's criterion under the condition that the quality of the approximation is maintained.},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - Interpolatory Estimation of Multi-Dimensional Orthogonal Expansions with Stochastic Coefficients
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 900
EP - 916
AU - Takuro KIDA
AU - Somsak SA-NGUANKOTCHAKORN
AU - Kenneth JENKINS
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 1994
AB - Relating to the problem of suppressing the immanent redundancy contained in an image with out vitiating the quality of the resultant approximation, the interpolation of multi-dimensional signal is widely discussed. The minimization of the approximation error is one of the important problems in this field. In this paper, we establish the optimum interpolatory approximation of multi-dimensional orthogonal expansions. The proposed approximation is superior, in some sense, to all the linear and the nonlinear approximations using a wide class of measures of error and the same generalized moments of these signals. Further, in the fields of information processing, we sometimes consider the orthonormal development of an image each coefficient of which represents the principal featurr of the image. The selection of the orthonormal bases becomes important in this problem. The Fisher's criterion is a powerful tool for this class of problems called declustering. In this paper, we will make some remarks to the problem of optimizing the Fisher's criterion under the condition that the quality of the approximation is maintained.
ER -