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Study of harmonic analysis and applications to multidimensional signal processing

Research Project

Project/Area Number 19340029
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 Hotoshi  The University of Tokyo, 大学院・数理科学研究科, 教授 (10175953)

Co-Investigator(Kenkyū-buntansha) KANJIN Yuichi  金沢大学, 理工研究域機械工学系, 教授 (50091674)
HORA Akihito  名古屋大学, 大学院・多元数理科学研究科, 教授 (10212200)
TACHIZAWA Kazuya  北海道大学, 大学院・数学研究院, 准教授 (80227090)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥12,610,000 (Direct Cost: ¥9,700,000、Indirect Cost: ¥2,910,000)
Fiscal Year 2009: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2008: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2007: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Keywords調和解析学 / フレームレット / ウェーブレット / 錯視 / 脳 / 信号処理 / フラクタル / 多次元信号処理 / フレーム / マルチレート信号処理 / 調和解析 / 単純細胞 / V1野 / ウェーブレット・フレーム / 視覚情報処理 / 画像処理
Research Abstract

The main theme of this research project is harmonic analysis and its applications to multidimensional signal processing. I constructed new framelets (with S.Arai). Applying them, we succeeded in the discovery of illusory components in Arai's fractal spiral illusion, and in the removal of illusory components from the illusion (Arai and Arai (1), in press). This result was reported by Kakenhi News (2009, vol.1). Moreover, I obtained some results related to frame operators and multidimensional polyphase matrices.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (36 results)

All 2010 2009 2008 2007 Other

All Journal Article (19 results) (of which Peer Reviewed: 10 results) Presentation (12 results) Book (4 results) Remarks (1 results)

  • [Journal Article] Framelet analysls of some geometrical illusions2010

    • Author(s)
      新井仁之, 新井しのぶ
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 2D tight framelets with orientation selectivity suggested by vision science2009

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

      JSIAM Letters vol. 1

      Pages: 9-12

    • NAID

      130000104498

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] ウェーブレット・フレームとその錯視研究への応用2009

    • Author(s)
      新井仁之
    • Journal Title

      可視化情報学会誌 vol. 29

      Pages: 10-17

    • NAID

      10025308372

    • Related Report
      2009 Final Research Report
  • [Journal Article] 視覚の科学と数学 第6回, 色の知覚と錯視2009

    • Author(s)
      新井仁之
    • Journal Title

      数理科学 vol. 547

      Pages: 75-79

    • Related Report
      2009 Final Research Report
  • [Journal Article] 視覚と錯視の数学的研究2009

    • Author(s)
      新井仁之
    • Journal Title

      応用数理 vol. 19, No. 1

      Pages: 39-41

    • NAID

      110007162491

    • Related Report
      2009 Final Research Report
  • [Journal Article] Paley's inequality of integral transform type2009

    • Author(s)
      Y. Kanjin, K. Sato
    • Journal Title

      Hokkaido Math.J. vol. 38

      Pages: 233-247

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limits of characters of wreath products Sn(T) of a compact group T with the symmetric groups and characters of S∞(T), I, Nagoya Math2009

    • Author(s)
      T. Hirai, E. Hirai, A. Hora
    • Journal Title

      Journal vol. 193

      Pages: 1-93

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] ウェーブレット・フレームとその錯視研究への応用2009

    • Author(s)
      新井仁之
    • Journal Title

      可視化情報学会誌 29

      Pages: 10-17

    • NAID

      10025308372

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 視覚の科学と数学 第5回, 視覚の数理モデルのためのウェーブレット・フレーム2008

    • Author(s)
      新井仁之
    • Journal Title

      数理科学 vol. 546

      Pages: 78-83

    • Related Report
      2009 Final Research Report
  • [Journal Article] 視覚の科学と数学 第4回, 錯視発生のシミュレーション/新しいウェーブレット・フレームの開発2008

    • Author(s)
      新井仁之
    • Journal Title

      数理科学 vol. 545

      Pages: 72-77

    • Related Report
      2009 Final Research Report
  • [Journal Article] 視覚の科学と数学 第3回, 視覚の非線形数理モデルと錯視発生のシミュレーション2008

    • Author(s)
      新井仁之
    • Journal Title

      数理科学 vol. 544

      Pages: 63-68

    • Related Report
      2009 Final Research Report
  • [Journal Article] 視覚の科学と数学 第2回, ウェーブレット・フィルタは脳内に存在するか?2008

    • Author(s)
      新井仁之
    • Journal Title

      数理科学 vol. 543

      Pages: 78-83

    • Related Report
      2009 Final Research Report
  • [Journal Article] 視覚の科学と数学 第1回, 視覚の数理モデルとウェーブレット2008

    • Author(s)
      新井仁之
    • Journal Title

      数理科学 vol. 542

      Pages: 64-69

    • Related Report
      2009 Final Research Report
  • [Journal Article] Wavelet characterizations of weighted Herz spaces2008

    • Author(s)
      M. Izuki, K. Tachizawa
    • Journal Title

      Scientiae Mathematicae Japonicae vol. 67

      Pages: 353-363

    • NAID

      10021089666

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic spectral analysis of growing regular graphs2008

    • Author(s)
      Akihito Hora
    • Journal Title

      Trans.Amer.Math.Soc 360

      Pages: 899-923

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finite discrete, shift-invariant, directional filterbanks for visual information processing, I : Construction2007

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

      Interdisciplinary Information Sciences vol. 13

      Pages: 255-273

    • NAID

      110006541675

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Finite discrete,shift-invariant,directional filterbanks for visual information processing,I:Construction2007

    • Author(s)
      Hitoshi Arai
    • Journal Title

      Interdisciplinary Information Science 13

      Pages: 255-273

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Achromatic and chromatic visual information processing and discrete wavelets(invited paper)2007

    • Author(s)
      Hitoshi Arai
    • Journal Title

      Frontiers of Computational Science(Springer-Verlag)

      Pages: 83-89

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Framelet analysis of some geometrical illusions

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

      Japan Journal of Industrial and Applied Mathematics (印刷中)

    • NAID

      10027314496

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Presentation] かざぐるまフレームレットとその錯視研究への応用2009

    • Author(s)
      新井仁之
    • Organizer
      時間周波数解析の手法と理工学的応用
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-10-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] 方位選択性をもつ2次元フレームレットと視覚科学2009

    • Author(s)
      新井仁之
    • Organizer
      日本応用数理学会2009年度年会
    • Place of Presentation
      於大阪大学
    • Year and Date
      2009-09-30
    • Related Report
      2009 Final Research Report
  • [Presentation] 方位選択性をもつ2 次元フレームレットと視覚科学2009

    • Author(s)
      新井仁之
    • Organizer
      日本応用数理学会2009年度年会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-30
    • Related Report
      2008 Annual Research Report
  • [Presentation] ウェーブレット・フレームの視覚と錯視の研究への応用2009

    • Author(s)
      新井仁之
    • Organizer
      第3回ウェーブレット変換およびその応用に関するワークショップ・講演会 招待講演
    • Place of Presentation
      豊橋技術科学大学
    • Year and Date
      2009-09-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] 数学的方法による錯視の研究2009

    • Author(s)
      新井仁之
    • Organizer
      錯覚ワークショップ-横断的錯覚科学は成立するか?
    • Place of Presentation
      豊橋技術科学大学
    • Year and Date
      2009-09-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] フラクタル螺旋錯視と新しいタイプのウェーブレット・フレーム2009

    • Author(s)
      新井仁之
    • Organizer
      日本視覚学会冬季大会
    • Place of Presentation
      於工学院大学
    • Year and Date
      2009-01-22
    • Related Report
      2009 Final Research Report
  • [Presentation] 視覚と錯視の数学的研究2008

    • Author(s)
      新井仁之
    • Organizer
      日本応用数理学会2008年度年会
    • Place of Presentation
      於東京大学
    • Year and Date
      2008-09-17
    • Related Report
      2009 Final Research Report
  • [Presentation] ウェーブレット・フレームを用いた視知覚の数理モデルと錯視の研究(特別講演)2007

    • Author(s)
      新井 仁之
    • Organizer
      日本応用数理学会
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-09-17
    • Related Report
      2007 Annual Research Report
  • [Presentation] Nonlinear models of visual information processing and applications to visual illusions, DFG-JSPS Conf.2007

    • Author(s)
      Hitoshi Arai
    • Organizer
      Infinite Dimensional Harmonic Analysis
    • Place of Presentation
      Univ. Tokyo (Japan)
    • Year and Date
      2007-09-11
    • Related Report
      2009 Final Research Report
  • [Presentation] A nonlinear model of visual information processing and visual illusions2007

    • Author(s)
      新井 仁之
    • Organizer
      DFG-JSPS Conference on Infinite Dimensional Harmonic Analysis
    • Place of Presentation
      東京大学
    • Year and Date
      2007-09-11
    • Related Report
      2007 Annual Research Report
  • [Presentation] Wavelet characterization of weighted spaces2007

    • Author(s)
      立澤 一哉
    • Organizer
      調和解析と非線形偏微分方程式研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2007-08-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] 移植作用素とチェザロ作用素2007

    • Author(s)
      勘甚 裕一
    • Organizer
      第46回実函数論・函数解析学合同シンポジウム
    • Place of Presentation
      九州大学
    • Year and Date
      2007-07-10
    • Related Report
      2007 Annual Research Report
  • [Book] ウェーブレット2010

    • Author(s)
      新井仁之
    • Publisher
      共立出版
    • Related Report
      2009 Final Research Report
  • [Book] 新・フーリエ解析と関数解析学2010

    • Author(s)
      新井仁之
    • Total Pages
      339
    • Publisher
      培風館(印刷中)
    • Related Report
      2009 Final Research Report
  • [Book] ウェーブレット2010

    • Author(s)
      新井仁之
    • Publisher
      共立出版(463+xi)
    • Related Report
      2009 Annual Research Report
  • [Book] Quantum probaility and spectral analysis of graphs2007

    • Author(s)
      Akihito Hora
    • Total Pages
      3
    • Publisher
      Springer
    • Related Report
      2007 Annual Research Report
  • [Remarks] 新井仁之のホームページ

    • URL

      http://www4.ocn.ne.jp/~arai/

    • Related Report
      2009 Final Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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