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Wavelet analysis and its application to the blind source separation problem

Research Project

Project/Area Number 23540146
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionUniversity 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
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (12 results)

All 2015 2014 2013 2012 2011 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 2 results) Presentation (7 results)

  • [Journal Article] Gabor transform of analytic functional on the sphere2015

    • Author(s)
      K.Fujita
    • Journal Title

      Current Trends in Analysis and its Applications, Proceedings of the 9th ISAAC Congress, Krakow 2013, Springer.

      Volume: なし Pages: 451-458

    • DOI

      10.1007/978-3-319-12577-0_50

    • ISBN
      9783319125763, 9783319125770
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Gabor transformation on the circle2014

    • Author(s)
      K.Fujita
    • Journal Title

      Proceedings of the 2014 International Conference on Wavelet Analysis and Pattern Recognition

      Volume: なし Pages: 122-126

    • DOI

      10.1109/icwapr.2014.6961302

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Gabor transformation on the sphere2013

    • Author(s)
      Keiko Fujita
    • Journal Title

      Proceedings of the he Sixth International Conference on Information

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Remarks on a method to estimate the number of sources on blind source separation2012

    • Author(s)
      K.Fujita
    • Journal Title

      Proc. of the 2012 International Conference on Wavelet Analysis and Pattern Recognition

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] On Blind Source Separation Problrm in Time-Frequency Space2012

    • Author(s)
      K.Fujita
    • Journal Title

      Progress in analysis, Proceedings of the 8th Congress of the ISAAC

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Gabor transformation on the circle2014

    • Author(s)
      K.Fujita
    • Organizer
      International Conference on Wavelet Analysis and Pattern Recognition
    • Place of Presentation
      Crowne Plaza Lanzhou, China
    • Year and Date
      2014-07-15
    • Related Report
      2014 Annual Research Report
  • [Presentation] An application of a quotient function in the time-frequency space2011

    • Author(s)
      Keiko Fujita
    • Organizer
      Conference on several complex variables
    • Place of Presentation
      Jagiellonian University
    • Related Report
      2011 Research-status Report
  • [Presentation] On blind source separation problem in time-frequency space2011

    • Author(s)
      Keiko Fujita
    • Organizer
      The 8th ISAAC Congress
    • Place of Presentation
      Peoples' Friendship University of Russia
    • Related Report
      2011 Research-status Report
  • [Presentation] Gabor transformation on the sphere

    • Author(s)
      Keiko Fujita
    • Organizer
      The Sixth International Conference on Information
    • Place of Presentation
      Hotel Arcadia Ichigaya, Tokyo, Japan
    • Related Report
      2013 Research-status Report
  • [Presentation] Gabor transform of analytic functional on the sphere

    • Author(s)
      Keiko Fujita
    • Organizer
      ISAAC 2013
    • Place of Presentation
      Pedagogical University, Krakow, Poland
    • Related Report
      2013 Research-status Report
  • [Presentation] Remarks on a method to estimate the number of sources in blind source separation

    • Author(s)
      Keiko Fujita
    • Organizer
      International Conference on Wavelet Analysis and Pattern Recognition 2012
    • Place of Presentation
      Xian, Shaanxi, China
    • Related Report
      2012 Research-status Report
  • [Presentation] Complex Analysis related to the blind source separation problem

    • Author(s)
      Keiko Fujita
    • Organizer
      Geometric Complex Analysis Tokyo 2012
    • Place of Presentation
      University of Tokyo
    • Related Report
      2012 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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