General Frame Multiresolution Analysis and Its Wavelet Frame Representation

Mang Ll; Hidemitsu OGAWA; Yukihiko YAMASHITA

General Frame Multiresolution Analysis and Its Wavelet Frame Representation

Mang Ll, Hidemitsu OGAWA, Yukihiko YAMASHITA

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We propose a theory of general frame multiresolution analysis (GFMRA) which generalizes both the theory of multiresolution analysis based on an affine orthonormal basis and the theory of frame multiresolution analysis based on an affine frame to a general frame. We also discuss the problem of perfectly representing a function by using a wavelet frame which is not limited to being of affine type. We call it a "generalized affine wavelet frame." We then characterize the GFMRA and provide the necessary and sufficient conditions for the existence of a generalized affine wavelet frame.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.10 pp.1713-1721

Publication Date: 1996/10/25

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Type of Manuscript: PAPER

Category: Digital Signal Processing

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Mang Ll, Hidemitsu OGAWA, Yukihiko YAMASHITA, "General Frame Multiresolution Analysis and Its Wavelet Frame Representation" in IEICE TRANSACTIONS on Fundamentals, vol. E79-A, no. 10, pp. 1713-1721, October 1996, doi: .
Abstract: We propose a theory of general frame multiresolution analysis (GFMRA) which generalizes both the theory of multiresolution analysis based on an affine orthonormal basis and the theory of frame multiresolution analysis based on an affine frame to a general frame. We also discuss the problem of perfectly representing a function by using a wavelet frame which is not limited to being of affine type. We call it a "generalized affine wavelet frame." We then characterize the GFMRA and provide the necessary and sufficient conditions for the existence of a generalized affine wavelet frame.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e79-a_10_1713/_p

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@ARTICLE{e79-a_10_1713,
author={Mang Ll, Hidemitsu OGAWA, Yukihiko YAMASHITA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={General Frame Multiresolution Analysis and Its Wavelet Frame Representation},
year={1996},
volume={E79-A},
number={10},
pages={1713-1721},
abstract={We propose a theory of general frame multiresolution analysis (GFMRA) which generalizes both the theory of multiresolution analysis based on an affine orthonormal basis and the theory of frame multiresolution analysis based on an affine frame to a general frame. We also discuss the problem of perfectly representing a function by using a wavelet frame which is not limited to being of affine type. We call it a "generalized affine wavelet frame." We then characterize the GFMRA and provide the necessary and sufficient conditions for the existence of a generalized affine wavelet frame.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - General Frame Multiresolution Analysis and Its Wavelet Frame Representation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1713
EP - 1721
AU - Mang Ll
AU - Hidemitsu OGAWA
AU - Yukihiko YAMASHITA
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1996
AB - We propose a theory of general frame multiresolution analysis (GFMRA) which generalizes both the theory of multiresolution analysis based on an affine orthonormal basis and the theory of frame multiresolution analysis based on an affine frame to a general frame. We also discuss the problem of perfectly representing a function by using a wavelet frame which is not limited to being of affine type. We call it a "generalized affine wavelet frame." We then characterize the GFMRA and provide the necessary and sufficient conditions for the existence of a generalized affine wavelet frame.
ER -