2000 Fiscal Year Final Research Report Summary
Microlocal filtering with multiwavelets
| Project/Area Number |
11640166
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Osaka Kyoiku University |
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Principal Investigator |
ASHINO Ryuichi Faculty of Education, Associate Professor, 教育学部, 助教授 (80249490)
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| Co-Investigator(Kenkyū-buntansha) |
CHODA Hisashi Faculty of Education, Osaka Kyoiku University Professor, 教育学部, 教授 (00030338)
KATAYAMA Yoshikazu Faculty of Education, Osaka Kyoiku University Professor, 教育学部, 教授 (10093395)
TANUMA Kazumi Osaka Kyoiku University, Faculty of Education, Associate Professor, 教育学部, 助教授 (60217156)
NAGASE Michihiro Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70034733)
SUGAHARA Kunio Faculty of Education, Osaka Kyoiku University Professor, 教育学部, 教授 (20093255)
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| Project Period (FY) |
1999 – 2000
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| Keywords | microlocal analysis / multiwavelet / filter / time frequency analysis / wavelet analysis / image processing |
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| Research Abstract |
Hyperfunctions in R^n are intuitively considered as sums of boundary values of holomorphic functions defined in infinitesimal wedges in C^n. Microlocal analysis corresponds the direction of analyticity of hyperfunctions to the direction of exponential decay of their Fourier transforms. Orthonormal multiwavelets, which are a generalization of orthonormal single wavelets, generate a multiresolution analysis by means of several scaling functions. Filtering is one of numerical methods and play central roles in digital image processing. We propose a multiwavelet system adapted to microlocal filtering. The main results are the following.
A rough estimate of the microlocal content of functions or signals is obtained from their multiwavelet expansions.
A fast algorithm for multiwavelet microlocal filtering is presented.
Several numerical examples in digital image processing are considered.
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