| Project/Area Number |
23540135
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka Kyoiku University |
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Principal Investigator |
MORIMOTO Akira 大阪教育大学, 教育学部, 准教授 (50239688)
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| Co-Investigator(Kenkyū-buntansha) |
ASHINO Ryuichi 大阪教育大学, 教育学部, 教授 (80249490)
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| Co-Investigator(Renkei-kenkyūsha) |
MANDAI Takeshi 大阪電気通信大学, 工学部, 教授 (10181843)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | ウェーブレット解析 / 画像分離 / 空間スケール解析 / 連続マルチウェーブレット変換 / 円環分割マルチウェーブレット関数 / ブラインド信号源分離 / 応用数学 / 自己組織化地図 / ガウスの消去法 / 複素相関関数 / N 分木離散ウェーブレット変換 / 瞬時混合モデル / 位置スケール情報 |
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| Research Abstract |
When we observe mixtures of original images, we want to separate original images. This inverse problem is called an image separation problem. This problem appears, analyzing satellite images. In this research, we studied two-dimensional wavelet analysis for an image separation problem.
We proposed a continuous multiwavelet transformation with annular sector multiwavelets, which is the most suitable transformation for solving an image separation problem. When mixtures are superpositions of original images without translations, we can separate ten original images from eleven mixtures, using the proposed transformation and Gaussian elimination. When mixtures are superpositions of original images with translations, we can separate four original images from four mixtures, using complex-valued correlation functions of continuous multiwavelet transforms.
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