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2012 Fiscal Year Final Research Report

Local super resolution analysis

Research Project

  • PDF
Project/Area Number 22540130
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionOsaka Kyoiku University

Principal Investigator

ASHINO Ryuichi  大阪教育大学, 教育学部, 教授 (80249490)

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)

All 2012 2011 2010

All Journal Article (13 results) Presentation (8 results) Book (2 results)

  • [Journal Article] Blind image source separations by wavelet analysis2012

    • Author(s)
      R. Ashino, S. Kataoka, T. Mandai, A. Morimoto
    • Journal Title

      Appl. Anal

      Volume: 94(4) Pages: 617-644

  • [Journal Article] Source reduction method using wavelets for the source separation problem2012

    • Author(s)
      A. Morimoto, R. Ashino, T. Mandai
    • Journal Title

      IEEE Conference Publications, 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)

      Pages: 346-351

  • [Journal Article] Application of the source reduction method with multiwavelets to image separation2012

    • Author(s)
      A. Morimoto, R. Ashino, T. Mandai
    • Journal Title

      IEEE Conference Publications, 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)

      Pages: 384-389

  • [Journal Article] Two-dimensional quaternion Fourier transform of type II and quaternion wavelet transform2012

    • Author(s)
      B. Mawardi, R. Ashino, R. Vaillancour
    • Journal Title

      IEEE Conference Publications, 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)

      Pages: 359-364

  • [Journal Article] Two-dimensional quaternion wavelet transform2011

    • Author(s)
      B. Mawardi, R. Ashino, R. Vaillancourt
    • Journal Title

      Appl. Math. Comput

      Volume: 218(1) Pages: 10-21

  • [Journal Article] Image separation using multiwavelets2011

    • Author(s)
      R. Ashino, S. Kataoka, T. Mandai, A. Morimoto
    • Journal Title

      Proceedings of the 2011 International Conference on Wavelet Analysis and Pattern Recognition

      Pages: 245-250

  • [Journal Article] Image separation using monogenic signal of stationary wavelet transform2011

    • Author(s)
      A. Morimoto, R. Ashino, S. Kataoka, T. Mandai
    • Journal Title

      Proceedings of the 2011 International Conference on Wavelet Analysis and Pattern Recognition

      Pages: 239-244

  • [Journal Article] Blind source separation of spatio-temporal mixed signals using hase information of analytic wavelet transform2010

    • Author(s)
      R. Ashino, T. Mandai, A. Morimoto
    • Journal Title

      Int. J. Wavelets Multiresolut. Inf. Process

      Volume: vol. 8 Pages: 575-594

  • [Journal Article] Image separation using the monogenic wavelet transform2010

    • Author(s)
      A. Morimoto, R. Ashino, T. Mandai
    • Journal Title

      Proceedings of the 10th International Symposium on Communications and Information Technologies

      Pages: 707-712

  • [Journal Article] Windowed Fourier transform of twodimensional quaternionic ignals2010

    • Author(s)
      M. Bahri, E. Hitzer, R. Ashino, R. Vaillancourt
    • Journal Title

      Appl. Math. Comput

      Volume: Vol. 216 Pages: 2366-2379

  • [Journal Article] Equivalent mean breakdown points for linear codes and compressed sensing by l_1 optimization2010

    • Author(s)
      R. Ashino, R. Vaillancourt
    • Journal Title

      Proceedings of the 10th International Symposium on Communications and Information Technologies

      Pages: 701-706

  • [Journal Article] Mean breakdown points for compressed sensing by uniformly distributed matrices2010

    • Author(s)
      R. Ashino, R. Vaillancourt
    • Journal Title

      JSIAM Letters

      Volume: Vol. 2 Pages: 111-114

  • [Journal Article] 圧縮センシングの基礎とその研究動向2010

    • Author(s)
      芦野隆一
    • Journal Title

      システム制御情報学会誌

      Volume: 55 Pages: 88-93

  • [Presentation] Two-dimensional quaternion wavelet transform2012

    • Author(s)
      R. Ashino
    • Organizer
      TAIWAN-JAPAN Joint Conference on PDE and Analysis
    • Place of Presentation
      National Taiwan university
    • Year and Date
      2012-12-26
  • [Presentation] Image separation by wavelet analysis2012

    • Author(s)
      R. Ashino
    • Organizer
      Workshop on Microlocal Methods in Medical Imaging
    • Place of Presentation
      Fields Institute, Toronto
    • Year and Date
      2012-09-16
  • [Presentation] Two-dimensional quaternion Fourier transform of type II and quaternion wavelet transform2012

    • Author(s)
      B.Mawardi, R. Ashino, R. Vaillancourt
    • Organizer
      2012 International Conference on Wavelet Analysis and Pattern Recognition
    • Place of Presentation
      Xian, China
    • Year and Date
      2012-07-17
  • [Presentation] 解析ウェーブレット変換とその応用2011

    • Author(s)
      芦野隆一
    • Organizer
      日本数学会秋季総合分科会 実函数論分科会 特別講演
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-28
  • [Presentation] Signal and image source separations by wavelet analysis2010

    • Author(s)
      R. Ashino, S. Kataoka, T. Mandai, A. Morimoto
    • Organizer
      International Conference on Inverse Problems
    • Place of Presentation
      City University of Hong Kong, Hong Kong
    • Year and Date
      2010-12-15
  • [Presentation] Introduction to wavelet analysis2010

    • Author(s)
      R. Ashino
    • Organizer
      The series of lectures at Banaras Hindu University
    • Place of Presentation
      Banaras Hindu University, Varanasi-221005, India
    • Year and Date
      2010-11-30
  • [Presentation] Wavelet and signal source separation2010

    • Author(s)
      R. Ashino, T. Mandai, A. Morimoto
    • Organizer
      Forum "Math-for-Industry" 2010
    • Place of Presentation
      Hilton Fukuoka Sea Hawk, Fukuoka-shi
    • Year and Date
      2010-10-23
  • [Presentation] 圧縮可能測定と線形符号2010

    • Author(s)
      芦野隆一, R. Vaillancourt
    • Organizer
      研究集会「偏微分方程式の逆問題解析とその周辺分野に関する研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-06-22
  • [Book] INTECH2011

    • Author(s)
      B. Mawardi and R. Ashino
    • Total Pages
      468
    • Publisher
      Fourier Transforms -Approach Scientific Principles の 13 章 Two-Dimensional Quaternionic Windowed Fourier Transform
  • [Book] 計算力学理論ハンドブック,7章 数値シミュレーションにおける適応ウェーブレット法2010

    • Author(s)
      山田道夫・榊原進・佐々木文夫・芦野隆一
    • Total Pages
      146-189
    • Publisher
      朝倉書店

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Published: 2014-08-29  

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