Mathematical problems in application of multi-dimensional multiwavelet analysis
| Project/Area Number |
17K05298
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 |
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| Co-Investigator(Kenkyū-buntansha) |
萬代 武史 大阪電気通信大学, 共通教育機構, 教授 (10181843)
守本 晃 大阪教育大学, 教育学部, 教授 (50239688)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ウェーブレット解析 / 信号源分離 / フーリエ解析 / マルチウェーブレット解析 / ブラインド信号源分離 / 多次元マルチウェーブレット / 時間周波数解析 / 四元数値関数 / 線型正準変換 / フーリエ変換 / ウェーブレット変換 / 多次元ウェーブレット解析 / 四元数 / 不確定性原理 |
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| Outline of Final Research Achievements |
The uncertainty principles can be regarded as generalization of the uncertainty principles on complex Hilbert space. By applying the linear operators, it is shown that the right-sided quaternion Fourier transform is a unitary operator. The duality property of the right-sided quaternion Fourier transform which enables us to express the alternative form of the Hausdorff-Young inequality associated with the right-sided quaternion Fourier transform is presented.
The image separation problem is considered, where observed images are weighted superpositions of translations and rotations of original images. An algorithm to estimate the number of original images, relative rotation angles, and relative translation parameters for two observed images is proposed. Numerical experiments demonstrate the usefulness of the proposed algorithm.
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| Academic Significance and Societal Importance of the Research Achievements |
カラー画像を四元数値関数の虚部と見なすことにより，人間の視覚情報処理システムを四元数値関数の様々な時間周波数解析を使って解析することができる可能性がある．
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Report
(4 results)
Research Products
(33 results)
