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Wavelet like basis on manifolds and their applications to harmonic analysis

Research Project

Project/Area Number 14540154
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionThe University of Tokyo

Principal Investigator

ARAI Hitoshi  ARAI,Hitoshi, 大学院・数理科学研究科, 教授 (10175953)

Co-Investigator(Kenkyū-buntansha) OKADA Masami  Tokyo Metropolitan University, Faculty of Sciences, Professor, 理学部, 教授 (00152314)
YAMADA Michio  Research Institute of Mathematical Sciences, Professor, 数理解析研究所, 教授 (90166736)
NAKAMURA Shu  The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (50183520)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 2003: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2002: ¥2,100,000 (Direct Cost: ¥2,100,000)
Keywordswavelet / multiwavelet / biorthogonal wavelet / BIBO stability / Visual information / visual illusion / Multivariable z transform / system / 視覚情報処理 / コイフレット / 多重解像度解析
Research Abstract

Arai studied analysis by wavelets of mechanism of appearance of visual illusions. It is widely believed that visual illusions will offer a key to understand how our visual system carries out visual information processing. From this reason, over the past 100 years, many studies of visual illusion have been made. However as for several illusions, their mechanisms are not yet well understood. In this research program Arai studied visual illusions by using both maximal overlap multiresolution analysis with respect to a biorthogonal wavelet and new nonlinear processing. Further, Arai has constructed a computational system modeled after the function of the striate cortex in human's brain. By using this system I did several computer simulations which indicate how our visual system produces visual illusions. by these simulations Arai has been able to explain by mathematical language the mechanism of several visual illusions. Furthermore Arai obtained some theorems related BIBO stability of multidimensional digital systems. Professor Yamada studied seismic waves by wavelet method, Prof. Okada studied nonlinear PDE from view point of numerical analysis via wavelet, and Prof. Nakamura obtained some theorems related to discrete Schrodinger operators.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (22 results)

All Other

All Publications (22 results)

  • [Publications] 新井仁之: "視覚情報処理とウェーブレット"数理解析研究所構研録. (発行予定)(印刷中). (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Maeda, M.Okada: "Hamilton formulation of energy conservative variational equations by wavelet expansions"J.Functional Analysis. (発行予定). (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ueno, M.Okada: "A wavelet collocation method for evolution equations with energy conservation properties"Bull.Si.Math.. 127. 180-205 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Nakamura: "Resonance expansion of propagations in the presense of pocential barrier"J.Functional Analysis. 205. 180-205 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] F.Klopp, S.Nakamura: "Anderson localization for 2D discrete Schrodinger operators with random magnetic fields"Ann.H.Poincare'. 4. 795-811 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 新井 仁之: "フーリエ解析学"朝倉書店. 277 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Arai Hitoshi: "Visual information processing and wavelets"RIMS kokyuroku. 2004(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Maeda, M.Okada: "Hamilton formulation of energy conservative variational equations by wavelet expansions"J.Functional Analysis. 2004(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ueno, M.Okada: "A wavelet collection method for evolution equations with energy conservation properties"Bull.Si.Math.. 127. 180-205 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Nakamura: "Resonance expansion of propagations in the presense of pocential barrier"J.Functional Analysis. 205. 180-205 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] F.Klopp, S.Nakamura: "Anderson localization for 2D discrete Scrodinger operators with random magnetic fields"Ann.H.Poincare'. 4. 795-811 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 新井仁之: "視覚情報処理とウェーブレット"数理解析研究所講究録. to appear.

    • Related Report
      2003 Annual Research Report
  • [Publications] 玉置哲男: "実地震波の波形を利用した人工地震波の作成"日本地震工学論文集. 3. 1-12 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Maeda: "Hamiltonian Formulation of energy conservative variational equations by wavelet expansion"J.Functional Analysis. to appear.

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Ueno: "A wavelet collocation method for evolution equations with energy conservation properties"Bull.Sci.Math.. 127. 569-583 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Nakamura: "Resonance expansions of propagations in the presence of potential barriers"J.Funct.Analysis. 205. 180-205 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] F.Klopp: "Anderson localization for 2D discrete Schrodinger operators with random magnetic fields"Ann.H.Poincare. 4. 795-811 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 新井仁之: "フーリエ解析学"朝倉書店. 277 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Taniguchi: "Flow pattern formation in a two dimensional flow on the rotating hemisphere bounded by the meodional line"Theo. and Appl.Mech.. 51. 217-223 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Ueno: "Quasi-norms for a double sequence"Interdisciplinary. 8. 157-166 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Maeda: "Hamilton Formulation of energy conservative variational equations by wavelet expansion"J.Funct.Anal.. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] 新井 仁之: "フーリエ解析学"朝倉書店(予定)(印刷中). 300

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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