Wavelet analysis and its application to the blind source separation problem

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540146
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: University of Toyama (2013-2014); Saga University (2011-2012)
• Principal Investigator: FUJITA KEIKO 富山大学, 大学院理工学研究部(理学), 教授 (40274568)
• Co-Investigator(Renkei-kenkyūsha): MORIMOTO Akira 大阪教育大学, 教育学部, 准教授 (50239688)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 逆問題 / 信号源分離

Outline of Final Research Achievements

(1)　A characteristics of our method on the blind source separation problem is to estimate of the number of sources in the first step. To estimate the number of　sources, we transform the signals into the time-frequency domain and consider　the quotient of the transforms of the observed signals. For this method, there　are some problems. We formulated the problems mathematically. A problem is that it will be difficult to separate the sources when the number of sources is large.　For this problem, we clarified the causes by an error evaluation in the theory of mathematics.
(2)　To treat the case that the sources are on the sphere, we considered the Gabor transformation on the sphere. We expressed the Gabor transform of analytic functionals on the sphere as the infinite sum by means of the spherical harmonics (or extended Legendre polynomials) and Bessel functions.

Free Research Field

複素解析