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Mathematical Analyses on Sampling Theorems in Reproducing Kernel Hilbert Spaces

Research Project

Project/Area Number 24500001
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Fundamental theory of informatics
Research InstitutionHokkaido University

Principal Investigator

TANAKA Akira  北海道大学, 情報科学研究科, 准教授 (20332471)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords標本化定理 / 再生核 / 再生核ヒルベルト空間 / 汎化誤差 / アンサンブルカーネル回帰 / マルチカーネル回帰 / 線形系逆問題
Outline of Final Research Achievements

It is well known that the sampling theorem plays a crucial role in the field of digital signal processing. In this work, we theoretically analyzed the sampling theory for the reproducing kernel Hilbert spaces. The sampling theorem and the separability of a target function space are two sides of the same coin. We proved that a certain continuity of a reproducing kernel corresponding to the target reproducing kernel Hilbert space guarantees the separability of the reproducing kernel Hilbert space. Recently, function estimation by multiple reproducing kernels attracts much attention in this field. We also analyzed the theoretical properties of such problems and revealed the advantages of the so-called ensemble kernel regression scheme which is a combination of the estimated functions by each reproducing kernel.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (24 results)

All 2015 2014 2013 2012

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Acknowledgement Compliant: 1 results) Presentation (20 results)

  • [Journal Article] Analyses on Generalization Error of Ensemble Kernel Regressors2014

    • Author(s)
      Akira Tanaka, Ichigaku Takigawa, Hideyuki Imai, Mineichi Kudo
    • Journal Title

      Lecture Notes in Computer Science, Structural, Syntactical and Statistical Pattern Recognition

      Volume: LNCS 8621 Pages: 273-281

    • DOI

      10.1007/978-3-662-44415-3_28

    • ISBN
      9783662444146, 9783662444153
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Parametric Wiener Filter with Linear Constraints for Unknown Target Signals2014

    • Author(s)
      Akira Tanaka and Hideyuki Imai
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science

      Volume: E97-A Pages: 322-330

    • NAID

      130003385362

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Multi-Frame Image Denoising Based on Minimum Noise Variance Convex Combination with Difference-Based Noise Variance Estimation2013

    • Author(s)
      Akira Tanaka and Katsuya Kohno
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science

      Volume: E96-A Pages: 2066-2070

    • NAID

      130004519169

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Extended Analyses for an Optimal Kernel in a Class of Kernels with an Invariant Metric2012

    • Author(s)
      Akira Tanaka, Ichigaku Takigawa, Hideyuki Imai, and Mineichi Kudo
    • Journal Title

      Lecture Notes in Computer Science, Structural, Syntactical and Statistical Pattern Recognition

      Volume: LNCS 7626 Pages: 345-353

    • DOI

      10.1007/978-3-642-34166-3_38

    • ISBN
      9783642341656, 9783642341663
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Analyses on Empirical Error Minimization in Multiple Kernel Regressors2015

    • Author(s)
      Akira Tanaka
    • Organizer
      2015 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP2015)
    • Place of Presentation
      Convention Center, Brisbane, Australia
    • Year and Date
      2015-04-19 – 2015-04-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] Theoretical Analyses on Ensemble and Multiple Kernel Regressors2014

    • Author(s)
      Akira Tanaka, Ichigaku Takigawa, Hideyuki Imai, Mineichi Kudo
    • Organizer
      The 6th Asian Conference on Machine Learning (ACML2014)
    • Place of Presentation
      Sunrise Hotel, Nha Trang, Vietnum
    • Year and Date
      2014-11-26 – 2014-11-28
    • Related Report
      2014 Annual Research Report
  • [Presentation] マルチカーネル回帰とアンサンブルカーネル回帰の汎化誤差解析2014

    • Author(s)
      田中 章, 瀧川 一学, 今井 英幸, 工藤 峰一
    • Organizer
      第29回信号処理シンポジウム
    • Place of Presentation
      立命館大学朱雀キャンパス, 京都市
    • Year and Date
      2014-11-12 – 2014-11-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] アンサンブルカーネル回帰とマルチカーネル回帰の汎化性能に関する一考察2014

    • Author(s)
      竹林 裕史, 田中 章
    • Organizer
      第29回信号処理シンポジウム
    • Place of Presentation
      立命館大学朱雀キャンパス, 京都市
    • Year and Date
      2014-11-12 – 2014-11-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] ブロックベース線形回帰と非局所的冗長性を利用したデモザイキング2014

    • Author(s)
      河野 克也, 田中 章
    • Organizer
      第29回信号処理シンポジウム
    • Place of Presentation
      立命館大学朱雀キャンパス, 京都市
    • Year and Date
      2014-11-12 – 2014-11-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] 非定常信号選択型独立成分分析によるブラインド信号源分離2014

    • Author(s)
      張 ケン, 田中 章
    • Organizer
      第29回信号処理シンポジウム
    • Place of Presentation
      立命館大学朱雀キャンパス, 京都市
    • Year and Date
      2014-11-12 – 2014-11-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] KLダイバージェンスを用いたNMFアルゴリズムの変数選択に基づく高速化2014

    • Author(s)
      尾崎 大顕, 田中 章
    • Organizer
      第29回信号処理シンポジウム
    • Place of Presentation
      立命館大学朱雀キャンパス, 京都市
    • Year and Date
      2014-11-12 – 2014-11-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] 一般化固有値展開に基づく信号部分空間推定と斜射影を用いたDOA推定2014

    • Author(s)
      安間 悠貴, 田中 章
    • Organizer
      第29回信号処理シンポジウム
    • Place of Presentation
      立命館大学朱雀キャンパス, 京都市
    • Year and Date
      2014-11-12
    • Related Report
      2014 Annual Research Report
  • [Presentation] MUSIC-based DOA Estimation by Oblique Projection Along The Signal Subspace2014

    • Author(s)
      Akira Tanaka and Hideyuki Imai
    • Organizer
      2014 IEEE Workshop on Statistical Signal Processing (SSP2014)
    • Place of Presentation
      Jupiter Hotel, Gold Coast, Australia
    • Year and Date
      2014-06-29 – 2014-07-02
    • Related Report
      2014 Annual Research Report
  • [Presentation] 斜射影を用いたMUSIC法によるDOA推定2014

    • Author(s)
      田中章, 今井英幸
    • Organizer
      日本音響学会2014年春季研究発表会
    • Place of Presentation
      日本大学駿河台キャンパス(東京都千代田区)
    • Related Report
      2013 Research-status Report
  • [Presentation] Performance Improvement of The FFDiag Algorithm Based on Pre-diagonalization by Closed-form Joint Diagonalizers2013

    • Author(s)
      Miho Murota and Akira Tanaka
    • Organizer
      The 15th IASTED International Conference on Signal and Image Processing (SIP 2013)
    • Place of Presentation
      Banff Park Lodge (バンフ、カナダ)
    • Related Report
      2013 Research-status Report
  • [Presentation] Image Inpainting Based on Block-Based Linear Regression and Minimum Variance Convex Combinations2013

    • Author(s)
      Katsuya Kohno and Akira Tanaka
    • Organizer
      The 15th IASTED International Conference on Signal and Image Processing (SIP 2013)
    • Place of Presentation
      Banff Park Lodge(バンフ、カナダ)
    • Related Report
      2013 Research-status Report
  • [Presentation] A Sufficient Condition For Reproducing Kernel Hilbert Spaces Being Separable2013

    • Author(s)
      田中章, 今井英幸, 工藤峰一
    • Organizer
      第28回信号処理シンポジウム
    • Place of Presentation
      海峡メッセ下関(山口県下関市)
    • Related Report
      2013 Research-status Report
  • [Presentation] カーネル回帰を用いたJPEG再適用法によるJPEG画像の画質改善2013

    • Author(s)
      河野克也, 田中章
    • Organizer
      第28回信号処理シンポジウム
    • Place of Presentation
      海峡メッセ下関(山口県下関市)
    • Related Report
      2013 Research-status Report
  • [Presentation] 同時対角化解析解を用いたCVFFDIAGの収束性能改善2013

    • Author(s)
      室田美帆, 田中章
    • Organizer
      第28回信号処理シンポジウム
    • Place of Presentation
      海峡メッセ下関(山口県下関市)
    • Related Report
      2013 Research-status Report
  • [Presentation] KERNEL-INDUCED SAMPLING THEOREM FOR BANDPASS SIGNALS WITH UNIFORM SAMPLING2013

    • Author(s)
      Akira Tanaka
    • Organizer
      2013 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP2013)
    • Place of Presentation
      Vancouver Convention & Exhibition Centre (カナダ)
    • Related Report
      2012 Research-status Report
  • [Presentation] Image Inpainting by Block-Based Linear Regression with Optimal Block Selection2012

    • Author(s)
      Akira Tanaka, Takahiro Ogawa, and Miki Haseyama
    • Organizer
      APSIPA Annual Summit & Conference (APSIPA2012)
    • Place of Presentation
      Loews Hollywood Hotel (米国)
    • Related Report
      2012 Research-status Report
  • [Presentation] Diffusion Noise Suppression by Crystal-Shape Subtraction Array2012

    • Author(s)
      Akira Tanaka and Ryo Takahashi
    • Organizer
      APSIPA Annual Summit & Conference (APSIPA2012)
    • Place of Presentation
      Loews Hollywood Hotel (米国)
    • Related Report
      2012 Research-status Report
  • [Presentation] Performance Improvement of Closed-Form Joint Diagonalizer of Non-Negative Hermitian Matrices2012

    • Author(s)
      Akira Tanaka and Miho Murota
    • Organizer
      APSIPA Annual Summit & Conference (APSIPA2012)
    • Place of Presentation
      Loews Hollywood Hotel (米国)
    • Related Report
      2012 Research-status Report
  • [Presentation] A Novel Criterion for Quality Improvement of JPEG Images Based on Image Database and Re-application of JPEG2012

    • Author(s)
      Katsuya Kohno, Akira Tanaka, and Hideyuki Imai
    • Organizer
      APSIPA Annual Summit & Conference (APSIPA2012)
    • Place of Presentation
      Loews Hollywood Hotel (米国)
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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