• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Extension of wavelet transforms and their applications to multidimensional data analysis

Research Project

Project/Area Number 17K12716
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Perceptual information processing
Research InstitutionTokai University

Principal Investigator

Fujinoki Kensuke  東海大学, 理学部, 准教授 (80613629)

Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsウェーブレット / 時間周波数解析 / フレーム / 信号処理 / データ解析 / 画像処理 / 非線形近似 / 画像復元 / 解析学 / 画像
Outline of Final Research Achievements

In this study, wavelet analysis in multiple dimensions was investigated. We proposed a two-dimensional wavelet transform with improved directional selectivity, and confirmed that it is effective for edge detection in image processing. We also worked on the development of a linear transform focusing on data analysis in a more flexible framework, and found the possibility of realizing a design with a high degree of freedom. The relationship between frames and multirate signal processing was examined in terms of a multidimensional multirate lifting scheme.

Academic Significance and Societal Importance of the Research Achievements

画像の特徴量を捉えることは画像処理の主要な目的の一つである。画像処理手法における方位選択性等を改良したことにより、エッジ等の画像の局所的特徴量がより扱いやすくなることが期待されることから意義は大きい。また、フレームとマルチレート信号処理およびリフティングスキームとの関連性を多次元で精査したことで、より柔軟で、よりデータ解析寄りの実用的な線形変換の可能性を見出すことができたことは、今後の展開を考える上で重要な成果であると考えられる。

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (23 results)

All 2020 2019 2018 2017

All Journal Article (8 results) (of which Peer Reviewed: 7 results,  Open Access: 2 results) Presentation (15 results) (of which Int'l Joint Research: 7 results,  Invited: 4 results)

  • [Journal Article] Properties of Haar-Like Four-Point Orthogonal Transforms for Image Processing2020

    • Author(s)
      Kensuke Fujinoki
    • Journal Title

      In: Latifi S. (eds) 17th International Conference on Information Technology - New Generations (ITNG 2020). Advances in Intelligent Systems and Computing

      Volume: - Pages: 233-239

    • DOI

      10.1007/978-3-030-43020-7_31

    • ISBN
      9783030430191, 9783030430207
    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Two-Dimensional Directional Lifting Schemes2019

    • Author(s)
      Kensuke Fujinoki
    • Journal Title

      Analysis, Probability, Applications, and Computation

      Volume: - Pages: 525-531

    • DOI

      10.1007/978-3-030-04459-6_50

    • ISBN
      9783030044589, 9783030044596
    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Nonlinear Approximation of Images with Haar-Like Four-Point Orthogonal Transforms2019

    • Author(s)
      Kensuke Fujinoki
    • Journal Title

      Proceedings of the 16th International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR 2019)

      Volume: - Pages: 110-115

    • DOI

      10.1109/icwapr48189.2019.8946488

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Note on Curvelets and Multiscale Directional Transforms2019

    • Author(s)
      Kensuke Fujinoki
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2102 Pages: 8-31

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Journal Article] Wavelet Constructions with Lifting Scheme2018

    • Author(s)
      藤ノ木 健介
    • Journal Title

      Transactions of the Japan Society for Industrial and Applied Mathematics

      Volume: 28 Issue: 2 Pages: 72-133

    • DOI

      10.11540/jsiamt.28.2_72

    • NAID

      130007410723

    • ISSN
      2424-0982
    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Directional Lifting-based Wavelet Transforms and their Applications2018

    • Author(s)
      Kensuke Fujinoki and Keita Ashizawa
    • Journal Title

      Proceedings of the Ninth International Conference on Information

      Volume: 1 Pages: 47-50

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Generalization of Average Interpolating Wavelets2017

    • Author(s)
      Fujinoki Kensuke
    • Journal Title

      New trends in analysis and interdisciplinary applications, Trends Math. Res. Perspect.

      Volume: 1 Pages: 565-571

    • DOI

      10.1007/978-3-319-48812-7_71

    • ISBN
      9783319488103, 9783319488127
    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] A lapped directional wavelet transform based on B-splines2017

    • Author(s)
      Kensuke Fujinoki and Keita Ahizawa
    • Journal Title

      Proceedings of the 2017 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR 2017)

      Volume: 1 Pages: 43-47

    • DOI

      10.1109/icwapr.2017.8076661

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Presentation] Properties of Haar-Like Four-Point Orthogonal Transforms for Image Processing2020

    • Author(s)
      Kensuke Fujinoki
    • Organizer
      The 17th International Conference on Information Technology - New Generations (ITNG 2020)
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Aspects of Frame Analysis2019

    • Author(s)
      Kensuke Fujinoki
    • Organizer
      2019 RIMS Joint Research, Advanced Innovation powered by Mathematics Platform (AIMaP) “Multidimensional Stockwell Transforms and Time-Frequency Analysis”
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Two-Dimensional Frames for Multidirectional Decompositions2019

    • Author(s)
      Kensuke Fujinoki
    • Organizer
      The 12th International Society for Analysis, its Applications and Computation Congress (ISAAC 2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Nonlinear Approximation of Images with Haar-Like Four-Point Orthogonal Transforms2019

    • Author(s)
      Kensuke Fujinoki
    • Organizer
      The 16th International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR 2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Haar-Like直交変換による非線形画像近似2019

    • Author(s)
      藤ノ木 健介
    • Organizer
      日本応用数理学会2019年度年会
    • Related Report
      2019 Research-status Report
  • [Presentation] On Directional Frames Having Lipschitz Continuous Fourier Transforms2019

    • Author(s)
      橋本紘史,木下保,藤ノ木 健介
    • Organizer
      日本応用数理学会2019年度年会
    • Related Report
      2019 Research-status Report
  • [Presentation] On Parseval Frames for Multidirectional Expansions and a Discretization Scheme of the Inversion of the Radon Transform2019

    • Author(s)
      木下保,藤ノ木 健介
    • Organizer
      日本応用数理学会2019年研究部会連合発表会
    • Related Report
      2018 Research-status Report
  • [Presentation] Directional Lifting-based Wavelet Transforms and their Applications2018

    • Author(s)
      Kensuke Fujinoki and Keita Ashizawa
    • Organizer
      The Ninth International Conference on Information
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 2変数関数の時間周波数解析について2018

    • Author(s)
      藤ノ木 健介
    • Organizer
      釧路高専第8回若手理・工学セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] ウェーブレット入門講義2018

    • Author(s)
      藤ノ木 健介
    • Organizer
      東京都市大学調和解析セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] Two-dimensional time-frequency analysis2018

    • Author(s)
      Kensuke Fujinoki
    • Organizer
      Harmonic Analysis Forum at Tokyo City University
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Multi-lapped directional wavelet transforms and their applications to image analysis2017

    • Author(s)
      Kensuke Fujinoki
    • Organizer
      2017 RIMS Joint Research, Advanced Innovation powered by Mathematics Platform (AIMaP), Signal analysis and time-frequency analysis
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A two-dimensional lapped directional wavelet transform with directional lifting2017

    • Author(s)
      Kensuke Fujinoki
    • Organizer
      The 11th International Society for Analysis, its Applications and Computation Congress (ISAAC 2017)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] A lapped directional wavelet transform based on B-splines2017

    • Author(s)
      Kensuke Fujinoki and Keita Ahizawa
    • Organizer
      The 2017 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR 2017)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] ウェーブレット解析と多次元信号処理2017

    • Author(s)
      藤ノ木健介
    • Organizer
      第45回可視化情報シンポジウム
    • Related Report
      2017 Research-status Report
    • Invited

URL: 

Published: 2017-04-28   Modified: 2022-01-27  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi