Source separation using N-tree discrete wavelet transform and sparse representation

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400199
• 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: MORIMOTO Akira 大阪教育大学, 教育学部, 教授 (50239688)
• Co-Investigator(Renkei-kenkyūsha): MANDAI Takeshi 大阪電気通信大学, 工学部, 教授 (10181843)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 信号源分離 / ウェーブレット / N 分木離散ウェーブレット変換 / 分数べきヒルベルト変換 / 時間スケール解析 / 双直交ウェーブレット / 画像分離 / スパース表現

Outline of Final Research Achievements

We proposed an N-tree discrete wavelet transform. We implemented the transform and its inversion algorithm with many types of wavelet functions such as biorthogonal wavelets. We designed a preprocessor and a postprocessor of the transform. Using the advantages of N times redundancy, we applied it to digital watermarking to sounds or images. We showed that the transform can be used to solve blind source separation problems of sounds or images. We proposed ideas to estimate the rotation angles of some original image from mixtures of rotated and translated original images.

Free Research Field

応用数学　ウェーブレット解析