2003 Fiscal Year Final Research Report Summary
Wavelet like basis on manifolds and their applications to harmonic analysis
| Project/Area Number |
14540154
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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 | The University of Tokyo |
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Principal Investigator |
ARAI Hitoshi ARAI,Hitoshi, 大学院・数理科学研究科, 教授 (10175953)
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| Co-Investigator(Kenkyū-buntansha) |
OKADA Masami Tokyo Metropolitan University, Faculty of Sciences, Professor, 理学部, 教授 (00152314)
YAMADA Michio Research Institute of Mathematical Sciences, Professor, 数理解析研究所, 教授 (90166736)
NAKAMURA Shu The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (50183520)
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| Project Period (FY) |
2002 – 2003
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| Keywords | wavelet / multiwavelet / biorthogonal wavelet / BIBO stability / Visual information / visual illusion / Multivariable z transform / system |
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| Research Abstract |
Arai studied analysis by wavelets of mechanism of appearance of visual illusions. It is widely believed that visual illusions will offer a key to understand how our visual system carries out visual information processing. From this reason, over the past 100 years, many studies of visual illusion have been made. However as for several illusions, their mechanisms are not yet well understood. In this research program Arai studied visual illusions by using both maximal overlap multiresolution analysis with respect to a biorthogonal wavelet and new nonlinear processing. Further, Arai has constructed a computational system modeled after the function of the striate cortex in human's brain. By using this system I did several computer simulations which indicate how our visual system produces visual illusions. by these simulations Arai has been able to explain by mathematical language the mechanism of several visual illusions. Furthermore Arai obtained some theorems related BIBO stability of multidimensional digital systems. Professor Yamada studied seismic waves by wavelet method, Prof. Okada studied nonlinear PDE from view point of numerical analysis via wavelet, and Prof. Nakamura obtained some theorems related to discrete Schrodinger operators.
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