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Multi-wavelet frames and applications to harmonic analysis

Research Project

Project/Area Number 16340035
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

ARAI Hitoshi  The University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院数理科学研究科, 教授 (10175953)

Co-Investigator(Kenkyū-buntansha) NAKAMURA Shu  The University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院数理科学研究科, 教授 (50183520)
YOSHIDA Nakahiro  The University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院数理科学研究科, 教授 (90210707)
KANJIN Yuichi  Kanazawa University, Graduate School of Natural Science & Technology, Professor, 大学院自然科学研究科, 教授 (50091674)
TACHIZAWA Kazuya  Hokkaido University, Faculty of Science, Associate Professor, 大学院理学研究科, 助教授 (80227090)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥8,400,000 (Direct Cost: ¥8,400,000)
Fiscal Year 2006: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2005: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2004: ¥2,800,000 (Direct Cost: ¥2,800,000)
Keywordswavelet / wavelet frame / harmonic analysis / illusion / visual cortex / color vision / perception / systems orthogonal functions / 偏微分方程式 / 視覚 / フレーム / フレームレット / 視覚情報処理 / 画像処理 / 色彩 / マルチプライヤー / 線形代数 / フィルター・バンク / 明暗の錯視 / カフェウェール錯視 / フィルタバンク
Research Abstract

Main themes of this research project are (multi-) wavelet frames and harmonic analysis. The head investigator, Arai, studied wavelet frames and applications to vision science. In particular Arai constructed new wavelet frames which are appropriate to studying vision science (with S. Arai). These wavelet frames will give basis of constructing computational models of human's visual system. In addition, Arai studied also practical applications to image processing. Furthermore he has constructed a computational model of color perception, and gave computer simulation of illusions related color vision. Arai has studied also the mechanism of appearance of visual illusions. In particular, he proposed a new general scheme for discrete wavelet analysis of vision. It is widely believed that visual illusions will provide us a key in order 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 be … More en made. However as for several illusions, their mechanisms are not yet well understood. In this research program Arai obtained nonlinear models of the early vision by using wavelet frames, and investigated mathematical mechanism of appearance of a certain illusion. More specifically, Arai constructed filter banks modeled after the function of the striate cortex in human's brain, and using these systems Arai made several computer simulations which indicate how our visual system produces visual illusions. By his research the mechanisms of several visual illusions can be explained by a mathematical unified way. If an image is inputted to Arai's system and if it outputs an image with illusion, then we can conclude that it is (they are) caused by processing in V1. Kanjin studied harmonic analysis of systems orthogonal functions. For example he proved boundedness of Cesaro operators on Lp and Hp. Nakamura studied local smoothing effect of analytic wave front sets. Yoshida studied sampling problem for stochastic differential equations. Tachizawa studied some weighted function spaces from viewpoint of wavelet theory. Less

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (33 results)

All 2007 2006 2005 2004 Other

All Journal Article (30 results) Book (3 results)

  • [Journal Article] Achromatic and chromatic visual information processing and discrete wavelets2007

    • Author(s)
      Hitoshi Arai
    • Journal Title

      Frontiers of Computational Science (Springer-Verlag)

      Pages: 83-89

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Achromatic and chromatic visual information processing and discrete wavelets2007

    • Author(s)
      Hitoshi Arai
    • Journal Title

      Frontiers of Computational Science Springer-Verlag刊

      Pages: 83-89

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Transplantation operators and Cesaro operators for the Hankel transform2006

    • Author(s)
      Yuichi Kanjin
    • Journal Title

      Studia Math. 171

      Pages: 29-45

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Estimation of parameters for diffusion processes with jumps from discrete observations2006

    • Author(s)
      Y.Shimizu
    • Journal Title

      Stat. Inference Stoch. Process. 9

      Pages: 227-277

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytic smoothing effect for Schroedinger equation with long-range perturbation.2006

    • Author(s)
      A.Martinez
    • Journal Title

      Comm. Pure and Appl. Math. 59

      Pages: 1330-1351

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Wavelets and illusion (Japanese)2006

    • Author(s)
      Hitoshi Arai
    • Journal Title

      Hosodaigaku kyouiku sinkoukai

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Estimation of parameters for diffusion processes with jumps from discrete observations2006

    • Author(s)
      Y.Shimizu, N.Yoshida
    • Journal Title

      Stat. Inference Stoch. Process. 9

      Pages: 227-277

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytic smoothing effect for Schroedinger equation with long-range perturbation.2006

    • Author(s)
      A.Martinez, Shu Nakamura, V.Sordoni
    • Journal Title

      Comm. Pure and Appl. Math. 59

      Pages: 1330-1351

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Estimation of parameters for difuusion processes with jumps from discrete observations2006

    • Author(s)
      Y.Shimizu, N.Yosida
    • Journal Title

      Stat. Inference Stoch. Process 9

      Pages: 227-277

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Analytic smoothing effect for the Schroedinger equations with long-range perturbation2006

    • Author(s)
      A.Martinez, S.Nakamura, V.Sordoni
    • Journal Title

      Comm. Pure and Appl. Math. 59

      Pages: 1330-1351

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A nonlinear model of visual information processing based on discrete maximal wavelets2005

    • Author(s)
      Hitoshi Arai
    • Journal Title

      Interdisciplinary Information Sciences 11

      Pages: 177-190

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] ウェーブレッド分解で見る,ある種の傾き錯視における類似性2005

    • Author(s)
      新井仁之
    • Journal Title

      VISION, J. Vision Soc. Japan 17

      Pages: 259-265

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A transplantation theorem for the Hankel transform on the Hardy space2005

    • Author(s)
      Yuichi Kanjin
    • Journal Title

      Tohoku Math. J. 57

      Pages: 231-246

    • NAID

      110001232645

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Weighted Sobolev-Lieb-Thirring inequalities.2005

    • Author(s)
      Kazuya Tachizawa
    • Journal Title

      Rev. Mat. Iberoamericana 21

      Pages: 67-85

    • NAID

      120006456909

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Weighted Lp Sobolev-Lieb-Thirring inequalities.2005

    • Author(s)
      Kazuya Tachizawa
    • Journal Title

      Proc. Japan Acad. 81

      Pages: 141-143

    • NAID

      120006459413

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Propagation of the homogeneous wave front set for Schroedinger equations.2005

    • Author(s)
      Shu Nakamaura
    • Journal Title

      Duke Math. J. 126

      Pages: 126-367

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Wavelet bunkai demiru aru syuno katamuki sakusi2005

    • Author(s)
      Hitoshi Arai, Shinobu Arai
    • Journal Title

      VISION, J. Vision Soc. Japan 17

      Pages: 259-265

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Propagation of the homogeneous wave front set for Schroedinger equations.2005

    • Author(s)
      Shu Nakamura
    • Journal Title

      Duke Math. J. 126

      Pages: 349-367

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A nonlinear model of visual information processing based on discrete maximal overlap wavelets2005

    • Author(s)
      新井仁之
    • Journal Title

      Interdisciplinary Information Sciences 11

      Pages: 177-190

    • NAID

      110001717231

    • Related Report
      2005 Annual Research Report
  • [Journal Article] ウェーブレット分解で見る,ある種の傾き錯視における類似性,(研究ノート)2005

    • Author(s)
      新井 仁之
    • Journal Title

      VISION, the Journal of the Vision Society of Japan 17

      Pages: 259-265

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A transplantation theorem for the Hankel tansform on the Hardy space2005

    • Author(s)
      勘甚 裕一
    • Journal Title

      Tohoku Mathematical Journal 57

      Pages: 231-246

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Weighted Lp Sobolev-Lieb-Thirring inequalities2005

    • Author(s)
      立澤 一哉
    • Journal Title

      Proc.Japan Acad.Ser.A Math.Sci. 81

      Pages: 141-143

    • NAID

      120006459413

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Propagation of the homogeneous wave front set for Schr"odinger equations2005

    • Author(s)
      中村 周
    • Journal Title

      Duke Math.J 126

      Pages: 349-367

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Weighted Sobolev-Lieb-Thirring inequalities2005

    • Author(s)
      立澤一哉
    • Journal Title

      Rev.Mat.Iberoamericana 21

      Pages: 67-85

    • NAID

      120006456909

    • Related Report
      2004 Annual Research Report
  • [Journal Article] ウェーブレットと視覚-明暗の錯視をめぐって-2004

    • Author(s)
      新井仁之
    • Journal Title

      数学のたのしみ 2004秋号

      Pages: 78-99

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Hardy's inequality for Jacobi expansions2004

    • Author(s)
      勘甚裕一
    • Journal Title

      Math.Inequal.Appl 17

      Pages: 551-555

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Expansions of the coverage probabilities of prediction region based on a shrinkage estimator.2004

    • Author(s)
      Sakamoto, Y.
    • Journal Title

      Statistics 38

      Pages: 381-390

    • Related Report
      2004 Annual Research Report
  • [Journal Article] ウェーブレット入門2004

    • Author(s)
      新井仁之
    • Journal Title

      数学のたのしみ 2004秋号

      Pages: 14-34

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Achromatic and chromatic visual information processing and discrete wavelets

    • Author(s)
      新井 仁之
    • Journal Title

      The Proceedings of the International Symposium on Frontiers of Computational Science 2005 (Springer)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A transplantation theorem for the Hankel transform on the Hardy

    • Author(s)
      勘甚裕一
    • Journal Title

      Tohoku Math.J. (印刷中)

    • Related Report
      2004 Annual Research Report
  • [Book] ウェーブレットと錯視(ビデオ)2006

    • Author(s)
      新井仁之
    • Total Pages
      45
    • Publisher
      (財)放送大学教育振興会
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Book] ウェーブレットと視覚2006

    • Author(s)
      新井仁之
    • Publisher
      (財)放送大学教育振興会(ビデオ全1巻)
    • Related Report
      2006 Annual Research Report
  • [Book] 線形代数 基礎と応用2006

    • Author(s)
      新井仁之
    • Total Pages
      537
    • Publisher
      日本評論社
    • Related Report
      2005 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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