2012 Fiscal Year Final Research Report
Local super resolution analysis
| Project/Area Number |
22540130
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Osaka Kyoiku University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MANDAI Takeshi 大阪電気通信大学, 工学部, 教授 (10181843)
MORIMOTO Akira 大阪教育大学, 教育学部, 准教授 (50239688)
|
|---|
| Project Period (FY) |
2010 – 2012
|
| Keywords | 多重解像度解析 / 解析ウェーブレット / スパース表現 / 四元数 / ウェーブレットフレーム / 短時間フーリエ変換 / ウェーブレット変換 |
|---|
| Research Abstract |
Wavelet frames in generalized Sobolev spaces were investigated.A wavelet frame design based on the Riesz potential was proposed. The proposed wavelet frame can decomposes functions or data into microlocal components. Quaternion valued Fourier and windowed Fourier transformations were investigated. An uncertainty principle was presented. A design of dictionaries for the sparse representation was proposed and its performances were numerically examined.
|
Research Products
(23 results)
