2015 Fiscal Year Final Research Report
Multidimensional multiwavelet analysis and its application to image processing
| Project/Area Number |
25400202
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Foundations of mathematics/Applied 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, 教授 (50239688)
|
|---|
| Project Period (FY) |
2013-04-01 – 2016-03-31
|
| Keywords | ウェーブレット解析 / マルチウェーブレット / 画像処理 / 多重解像度解析 / 四元数 / スパース表現 |
|---|
| Outline of Final Research Achievements |
Mathematical basics of blind source separation based on wavelet analysis were studied. Our proposed methods for blind source separation were verified by numerical simulations. Blind source separation algorithms for images based on multidimensional multiwavelet were proposed. Fundamental studies on Fourier analysis and wavelet analysis of quaternion valued functions were investigated. Various theorems on convolution of quaternion valued functions were presented. These convolution theorems are related to filters and linear systems in engineering. An error-correcting code based on compressive sensing was proposed and its validity was demonstrated through numerical experiments.
|
| Free Research Field |
数学一般(含確率論・統計数学)
|
