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Statistical Mechanical Approach for the Theory of Compressed Sensing

Research Project

Project/Area Number 24700007
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Fundamental theory of informatics
Research InstitutionIbaraki University (2013-2015)
Tokyo Institute of Technology (2012)

Principal Investigator

Takeda Koujin  茨城大学, 工学部, 准教授 (70397040)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords圧縮センシング / 統計力学 / 統計物理学 / 高速疎データ再構成 / パラメータ最適化
Outline of Final Research Achievements

In the problem of compressed sensing, a significant algorithm called Approximate Message Passing (AMP) is widely-known, whose computational cost is small and convergence condition has been revealed theoretically. In deriving AMP, an assumption is made on the measurement matrix, which represents the process of signal measurement. In this project, we have attempted to construct generalized algorithm of AMP without such assumption, and have shown that such generalization can be achieved with the aid of formulation for the performance analysis of telecommunication system. We also investigated several topics on data sparsity: For example, we developed a sparse signal recovery algorithm of compressed sensing with less computational cost for spare measurement matrix. We also studied the sparsity-based learning algorithm for deep-learning.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (28 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article (5 results) (of which Peer Reviewed: 2 results,  Acknowledgement Compliant: 2 results) Presentation (14 results) (of which Int'l Joint Research: 2 results,  Invited: 4 results) Book (2 results) Remarks (4 results) Patent(Industrial Property Rights) (3 results)

  • [Journal Article] 情報理論におけるランダム行列理論2014

    • Author(s)
      竹田晃人
    • Journal Title

      日本物理学会誌

      Volume: 69 Pages: 522-530

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] 部分並列干渉除去法の疎信号復元問題への応用2014

    • Author(s)
      竹田晃人,田中利幸
    • Journal Title

      IEICE Technical Report

      Volume: IBISML2014

    • Related Report
      2014 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] Restricted Boltzmann Machineを用いた画像分類のための特徴抽出2014

    • Author(s)
      須田玲輝,竹田晃人
    • Journal Title

      IEICE Technical Report

      Volume: IBISML2014

    • Related Report
      2014 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] Reconstruction algorithm in compressed sensing based on maximum a posteriori estimation2013

    • Author(s)
      Koujin Takeda, Yoshiyuki Kabashima
    • Journal Title

      J. Phys. Conf. Ser.

      Volume: 473 Pages: 12003-12003

    • DOI

      10.1088/1742-6596/473/1/012003

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A study of the universal threshold in the ℓ1 recovery by statistical mechanics2012

    • Author(s)
      Takeda Koujin, Kabashima Yoshiyuki
    • Journal Title

      2012 46th Annual Conference on Information Sciences and Systems (CISS) proceedings (electric journal)

      Volume: IEEE Xplore digital library Pages: 1-6

    • DOI

      10.1109/ciss.2012.6310755

    • Related Report
      2012 Research-status Report
  • [Presentation] 拡張SIR模型におけるネットワーク形状と相転移との関係2016

    • Author(s)
      小林正伸、竹田晃人
    • Organizer
      日本物理学会年次大会
    • Place of Presentation
      仙台市・東北学院大学
    • Year and Date
      2016-03-20
    • Related Report
      2015 Annual Research Report
  • [Presentation] Application of partial parallel interference cancellation to sparse signal recovery2016

    • Author(s)
      Koujin Takeda, Toshiyuki Tanaka
    • Organizer
      国際会議Physics Informed Machine Learning
    • Place of Presentation
      米国・ニューメキシコ州サンタフェ市
    • Year and Date
      2016-01-20
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Application of partial parallel interference cancellation to sparse signal recovery2015

    • Author(s)
      Koujin Takeda, Toshiyuki Tanaka
    • Organizer
      国際会議HD^3-2015
    • Place of Presentation
      京都市・メルバルク京都
    • Year and Date
      2015-12-16
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 多状態拡張したSIRモデルにおける感染爆発のシミュレーション2015

    • Author(s)
      小林正伸、竹田晃人
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      吹田市・関西大学
    • Year and Date
      2015-09-17
    • Related Report
      2015 Annual Research Report
  • [Presentation] 統計力学で圧縮センシングを探る2014

    • Author(s)
      竹田晃人
    • Organizer
      新学術領域研究「スパースモデリングの深化と高次元データ駆動科学の創成」チュートリアル
    • Place of Presentation
      東京工業大学
    • Year and Date
      2014-12-14
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Restricted Boltzmann Machineを用いた画像分類のための特徴抽出2014

    • Author(s)
      須田玲輝,竹田晃人
    • Organizer
      情報論的学習理論と機械学習研究会(IBISML)
    • Place of Presentation
      名古屋大学
    • Year and Date
      2014-11-17 – 2014-11-19
    • Related Report
      2014 Research-status Report
  • [Presentation] 部分並列干渉除去法の疎信号復元問題への応用2014

    • Author(s)
      竹田晃人,田中利幸
    • Organizer
      情報論的学習理論と機械学習研究会(IBISML)
    • Place of Presentation
      名古屋大学
    • Year and Date
      2014-11-17 – 2014-11-19
    • Related Report
      2014 Research-status Report
  • [Presentation] 部分並列干渉除去法を応用した圧縮センシングの疎信号復元アルゴリズム2014

    • Author(s)
      竹田晃人,田中利幸
    • Organizer
      日本物理学会
    • Place of Presentation
      中部大学
    • Year and Date
      2014-09-07 – 2014-09-10
    • Related Report
      2014 Research-status Report
  • [Presentation] Reconstruction algorithm in compressed sensing based on maximum a posteriori estimation

    • Author(s)
      Koujin Takeda
    • Organizer
      "Inference, Computation, and Spin Glasses" (ICSG2013)
    • Place of Presentation
      北海道大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 圧縮センシングのL1ノルム復元問題に関する理論

    • Author(s)
      竹田晃人
    • Organizer
      FIT2012 第11回情報科学技術フォーラム
    • Place of Presentation
      法政大学小金井キャンパス
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 平均場近似に基づく圧縮センシングの復元アルゴリズム

    • Author(s)
      竹田晃人・樺島祥介・李斗煥・山田貴之
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      横浜国立大学
    • Related Report
      2012 Research-status Report
  • [Presentation] MAPアルゴリズムを用いたL1ノルム復元に関する考察

    • Author(s)
      竹田晃人・樺島祥介
    • Organizer
      研究会「圧縮センシングとその周辺(3)」
    • Place of Presentation
      広島県立大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 事後確率最大化推定に基づく圧縮センシングのデータ復元アルゴリズム

    • Author(s)
      竹田晃人・樺島祥介
    • Organizer
      研究会IBIS2012 (情報論的学習理論ワークショップ)
    • Place of Presentation
      筑波大学東京校舎
    • Related Report
      2012 Research-status Report
  • [Presentation] 事後確率最大化推定に基づく圧縮センシングのデータ復元アルゴリズム

    • Author(s)
      竹田晃人・樺島祥介
    • Organizer
      研究会SITA2012 (第33回情報理論とその応用シンポジウム)
    • Place of Presentation
      別府湾ロイヤルホテル
    • Related Report
      2012 Research-status Report
  • [Book] 電子情報通信学会技術研究報告 vol.112 No.2792012

    • Author(s)
      竹田晃人・樺島祥介
    • Total Pages
      6
    • Publisher
      事後確率最大化推定に基づく圧縮センシングのデータ復元アルゴリズム
    • Related Report
      2012 Research-status Report
  • [Book] 研究会SITA2012 (第33回情報理論とその応用シンポジウム) 講演録 (電子配布)2012

    • Author(s)
      竹田晃人・樺島祥介
    • Total Pages
      5
    • Publisher
      事後確率最大化推定に基づく圧縮センシングのデータ復元アルゴリズム
    • Related Report
      2012 Research-status Report
  • [Remarks] 竹田晃人のwebページ

    • URL

      http://takeda.ise.ibaraki.ac.jp/takeda/index.html

    • Related Report
      2015 Annual Research Report
  • [Remarks] Takeda's Webpage

    • URL

      http://takeda.ise.ibaraki.ac.jp/takeda/index.html

    • Related Report
      2014 Research-status Report
  • [Remarks] 竹田 晃人の大学サイトでの紹介ページ (茨城大学)

    • URL

      http://info.ibaraki.ac.jp/Profiles/25/0002463/profile.html

    • Related Report
      2013 Research-status Report
  • [Remarks] 研究者「竹田晃人」の研究紹介ページ

    • URL

      http://takeda.ise.ibaraki.ac.jp/takeda/index.html

    • Related Report
      2012 Research-status Report
  • [Patent(Industrial Property Rights)] 信号処理システム及び信号処理方法2012

    • Inventor(s)
      李斗煥・山田貴之・上原一浩・赤羽和徳・竹田晃人・樺島祥介
    • Industrial Property Rights Holder
      日本電信電話株式会社・東京工業大学
    • Industrial Property Rights Type
      特許
    • Filing Date
      2012-06-28
    • Acquisition Date
      2015-06-19
    • Related Report
      2015 Annual Research Report
  • [Patent(Industrial Property Rights)] 復号装置・信号処理システム・復号方法及び信号処理方法2012

    • Inventor(s)
      李斗煥・山田貴之・上原一浩・赤羽和徳・竹田晃人・樺島祥介
    • Industrial Property Rights Holder
      李斗煥・山田貴之・上原一浩・赤羽和徳・竹田晃人・樺島祥介
    • Industrial Property Rights Type
      特許
    • Filing Date
      2012-06-28
    • Related Report
      2012 Research-status Report
  • [Patent(Industrial Property Rights)] 復号装置・信号処理システム・復号方法及び信号処理方法2012

    • Inventor(s)
      李斗煥・山田貴之・上原一浩・赤羽和徳・竹田晃人・樺島祥介
    • Industrial Property Rights Holder
      李斗煥・山田貴之・上原一浩・赤羽和徳・竹田晃人・樺島祥介
    • Industrial Property Rights Type
      特許
    • Filing Date
      2012-06-28
    • Related Report
      2012 Research-status Report

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

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