The Optimum Approximation of Muliti-Dimensional Signals Using Parallel Wavelet Filter Banks
Summary :
A systematic theory of the optimum sub-band interpolation using parallel wavelet filter banks presented with respect to a family of n-dimensional signals which are not necessarily band-limited. It is assumed that the Fourier spectrums of these signals have weighted L2 norms smaller than a given positive number. In this paper, we establish a theory that the presented optimum interpolation functions satisfy the generalized discrete orthogonality and minimize the wide variety of measures of error simultaneously. In the following discussion, we assume initially that the corresponding approximation formula uses the infinite number of interpolation functions having limited supports and functional forms different from each other. However, it should be noted that the resultant optimum interpolation functions can be realized as the parallel shift of the finite number of space-limited functions. Some remarks to the problem of distinction of images is presented relating to the generalized discrete orthogonality and the reciprocal property for the proposed approximation.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.10 pp.1830-1848
- Publication Date
- 1993/10/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Parallel/Multidimensional Signal Processing
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Takuro KIDA, "The Optimum Approximation of Muliti-Dimensional Signals Using Parallel Wavelet Filter Banks" in IEICE TRANSACTIONS on Fundamentals,
vol. E76-A, no. 10, pp. 1830-1848, October 1993, doi: .
Abstract: A systematic theory of the optimum sub-band interpolation using parallel wavelet filter banks presented with respect to a family of n-dimensional signals which are not necessarily band-limited. It is assumed that the Fourier spectrums of these signals have weighted L2 norms smaller than a given positive number. In this paper, we establish a theory that the presented optimum interpolation functions satisfy the generalized discrete orthogonality and minimize the wide variety of measures of error simultaneously. In the following discussion, we assume initially that the corresponding approximation formula uses the infinite number of interpolation functions having limited supports and functional forms different from each other. However, it should be noted that the resultant optimum interpolation functions can be realized as the parallel shift of the finite number of space-limited functions. Some remarks to the problem of distinction of images is presented relating to the generalized discrete orthogonality and the reciprocal property for the proposed approximation.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e76-a_10_1830/_p
Copy
@ARTICLE{e76-a_10_1830,
author={Takuro KIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Optimum Approximation of Muliti-Dimensional Signals Using Parallel Wavelet Filter Banks},
year={1993},
volume={E76-A},
number={10},
pages={1830-1848},
abstract={A systematic theory of the optimum sub-band interpolation using parallel wavelet filter banks presented with respect to a family of n-dimensional signals which are not necessarily band-limited. It is assumed that the Fourier spectrums of these signals have weighted L2 norms smaller than a given positive number. In this paper, we establish a theory that the presented optimum interpolation functions satisfy the generalized discrete orthogonality and minimize the wide variety of measures of error simultaneously. In the following discussion, we assume initially that the corresponding approximation formula uses the infinite number of interpolation functions having limited supports and functional forms different from each other. However, it should be noted that the resultant optimum interpolation functions can be realized as the parallel shift of the finite number of space-limited functions. Some remarks to the problem of distinction of images is presented relating to the generalized discrete orthogonality and the reciprocal property for the proposed approximation.},
keywords={},
doi={},
ISSN={},
month={October},}
Copy
TY - JOUR
TI - The Optimum Approximation of Muliti-Dimensional Signals Using Parallel Wavelet Filter Banks
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1830
EP - 1848
AU - Takuro KIDA
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1993
AB - A systematic theory of the optimum sub-band interpolation using parallel wavelet filter banks presented with respect to a family of n-dimensional signals which are not necessarily band-limited. It is assumed that the Fourier spectrums of these signals have weighted L2 norms smaller than a given positive number. In this paper, we establish a theory that the presented optimum interpolation functions satisfy the generalized discrete orthogonality and minimize the wide variety of measures of error simultaneously. In the following discussion, we assume initially that the corresponding approximation formula uses the infinite number of interpolation functions having limited supports and functional forms different from each other. However, it should be noted that the resultant optimum interpolation functions can be realized as the parallel shift of the finite number of space-limited functions. Some remarks to the problem of distinction of images is presented relating to the generalized discrete orthogonality and the reciprocal property for the proposed approximation.
ER -
English
