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Microlocal filtering with multiwavelets

Research Project

Project/Area Number 11640166
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOsaka Kyoiku University

Principal Investigator

ASHINO Ryuichi  Faculty of Education, Associate Professor, 教育学部, 助教授 (80249490)

Co-Investigator(Kenkyū-buntansha) CHODA Hisashi  Faculty of Education, Osaka Kyoiku University Professor, 教育学部, 教授 (00030338)
KATAYAMA Yoshikazu  Faculty of Education, Osaka Kyoiku University Professor, 教育学部, 教授 (10093395)
TANUMA Kazumi  Osaka Kyoiku University, Faculty of Education, Associate Professor, 教育学部, 助教授 (60217156)
NAGASE Michihiro  Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70034733)
SUGAHARA Kunio  Faculty of Education, Osaka Kyoiku University Professor, 教育学部, 教授 (20093255)
小山 晃  大阪教育大学, 教育学部, 教授 (40116158)
町頭 義朗  大阪教育大学, 教育学部, 講師 (00253584)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2000: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1999: ¥1,600,000 (Direct Cost: ¥1,600,000)
Keywordsmicrolocal analysis / multiwavelet / filter / time frequency analysis / wavelet analysis / image processing / Wavelet / ウェーブレット / Matlab / 正規直交ウェーブレット / 古典的ハーディ空間 / 佐藤の超関数 / 微分方程式ソルバー
Research Abstract

Hyperfunctions in R^n are intuitively considered as sums of boundary values of holomorphic functions defined in infinitesimal wedges in C^n. Microlocal analysis corresponds the direction of analyticity of hyperfunctions to the direction of exponential decay of their Fourier transforms. Orthonormal multiwavelets, which are a generalization of orthonormal single wavelets, generate a multiresolution analysis by means of several scaling functions. Filtering is one of numerical methods and play central roles in digital image processing. We propose a multiwavelet system adapted to microlocal filtering. The main results are the following.
A rough estimate of the microlocal content of functions or signals is obtained from their multiwavelet expansions.
A fast algorithm for multiwavelet microlocal filtering is presented.
Several numerical examples in digital image processing are considered.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (20 results)

All Other

All Publications (20 results)

  • [Publications] R.ASHINO (共著): "Microlocal filtering with multiwavelets"Computers Math.Applic.. 41. 111-133 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] R.ASHINO (共著): "Behind and Beyond the MATLAB ODE Suite"Computers Math.Applic.. 40. 491-512 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 芦野隆一,Remi Vaillancourt: "MATLABによる微分方程式とラプラス変換"共立出版. 260 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 芦野隆一,萬代武史,浅川秀一: "ウェーブレットの基礎(翻訳)"科学技術出版. 527 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] R.ASHINO, C.HEIL, M.NAGASE, and R.VAILLANCOURT: "Microlocal filtering with multiwavelets"Computers Math.Applic.. 41. 111-133 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] R.ASHINO, M.NAGASE, and R.VAILLANCOURT: "Behind and Beyond the MATLAB ODE Suite"Computers Math.Applic.. 40. 491-512 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] R.ASHINO, M.ARAI and A.NAKAOKA: "Restoration of lost samples by oversampling near the Nyquist rate"Japan J.Indust.Appl.Math.. 16, no.1. 123-136 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] R.ASHINO(共著): "Microlocal filtering with multiwavelets"Computers Math.Applic.. 41. 111-133 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] R.ASHINO(共著): "Behind and Beyond the MATLAB ODE Suite"Computers Math.Applic.. 40. 491-512 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] R.ASHINO(共著): "Restoration of lost samples by oversampling near the Nyquist rate"Japan J.Indust.Appl.Math.. 16. 123-136 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] 芦野隆一,Remi Vaillancourt: "MATLABによる微分方程式とラプラス変換"共立出版. 260 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 芦野隆一,萬代武史,浅川秀一: "ウェーブレットの基礎(翻訳)"科学技術出版. 527 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 長瀬道弘,芦野隆一: "微分積分概説"サイエンス社. 238 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] 山本鎮男,曽根彰,芦野隆一,守本晃: "ダイナミカルシステムの数理-応用"共立出版. 245 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] 山本鎮男,曽根彰,芦野隆一,守本晃: "ダイナミカルシステムの数理-基礎"共立出版. 232 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Ryuichi Ashino: "Microlocal filtering with multiwavelets"Computers Math. Applic.. (掲載予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] Ryuichi Ashino: "Behind and Beyond the MATLAB ODE Suite"Computers Math. Applic.. (掲載予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] Ryuichi Ashino: "A condition for constraction of multiwavelets"Proceedings of the Second Congress ISAAC Kluwer Academic Publishers. (掲載予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 芦野 隆一: "ウェーブレットの基礎"科学技術出版. 528 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 長瀬 道弘: "微分積分概説"サイエンス社. 238 (1999)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2021-08-20  

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