2002 Fiscal Year Final Research Report Summary
Microlocal filtering with multiwavelet frames
| Project/Area Number |
13640171
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Osaka Kyoiku University |
|---|
Principal Investigator |
ASHINO Ryuichi Faculty of Education, Associate Professor, 教育学部, 助教授 (80249490)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MORIMOTO Akira Faculty of Education, Assistant, 教育学部, 助手 (50239688)
CHODA Hisashi Faculty of Education, Professor, 教育学部, 教授 (00030338)
TANUMA Kazumi Gumma University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (60217156)
TAKEUCHI Jiro Science University of Tokyo, Faculty of Industrial Science and Technology, 基礎工学部, 教授 (80082402)
NAGASE Michihiro Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70034733)
|
|---|
| Project Period (FY) |
2001 – 2002
|
| Keywords | microlocal analysis / wavelet frame / multiwavelet / filter / time frequency analysis / wavelet analysis / image processing |
|---|
| Research Abstract |
Our orthonormal multiwavelet bases, which can decompose functions in the Hilbert space L^2(R^n) microlocally, are shown to be a "stepwise" unconditional basis in L^p(R^n) (1<p<∞) and other related spaces. As part of the proof, an elementary proof of the L^p(R^n) version of the sampling theorem with unconditional convergence is given. Finally, an application is given to the expression of some distributions as sums of boundary values of holomorphic functions.
Orthogonal multiwavelets, whose Fourier transforms consist of characteristic functions of squares or sectors of annuli, are constructed in the Fourier domain and are shown to satisfy a multiresolution analysis with several choices of scaling functions. Redundant smooth tight wavelet frames are obtained and these nonorthogonal frame wavelets can be generated by two-scale equations from, a multiresolution analysis. Singularities can be localized in position and direction and the original images can be restored from the scarred images.
|
