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Statistical-mechanical approach for nonconvex compressed sensing and sparse modeling for correlated signals

Research Project

Project/Area Number 17H06758
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Soft computing
Research InstitutionNagoya Institute of Technology

Principal Investigator

Takabe Satoshi  名古屋工業大学, 工学(系)研究科(研究院), 助教 (60804218)

Project Period (FY) 2017-08-25 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords統計力学 / 圧縮センシング / 情報統計力学 / レプリカ法
Outline of Final Research Achievements

The aim of this research project is to extend the application of the sparse modeling that is a well-known strategy to extract a sparse structure from high-dimensional data. In the project, we examined (1) a structure of the solution space of the non-convex lq-norm regularization using statistical mechanics and (2) trainable iterative signal recovery algorithm by deep learning techniques.
As a results, it is showed that correctly solving the lq-norm regularization is typically hard. In addition, we proposed trainable iterative algorithms based on a structure of an existing algorithm whose parameters can be tuned by deep learning techniques. The results show that the proposed algorithm is superior to other algorithms in terms of convergence speed and signal recovery performance.

Academic Significance and Societal Importance of the Research Achievements

本研究課題の遂行により、非凸なスパースモデリングに対する統計力学的描像の深化に貢献した。また、学習可能信号復元アルゴリズムの提案は、従来手法と比較して大きな性能改善を達成しており、非凸なスパースモデリングに対する実用的なアルゴリズム設計の有力なアプローチであることが示された。同時に、研究成果は学習による性能改善の原理の解明等の新たな理論的課題も提示している。
スパースモデリングはビッグデータ解析だけでなく、類似の数理構造が画像解析や無線通信で現れる等応用範囲の広い統計的手法である。今後、それらの分野への統計力学的解析や学習可能アルゴリズムによるアプローチの展開が見込まれる。

Report

(3 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Annual Research Report
  • Research Products

    (24 results)

All 2019 2018 2017

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Open Access: 2 results) Presentation (20 results) (of which Int'l Joint Research: 5 results,  Invited: 1 results)

  • [Journal Article] Trainable ISTA for Sparse Signal Recovery2019

    • Author(s)
      D. Ito, S. Takabe, and T. Wadayama
    • Journal Title

      IEEE Transactions on Signal Processing

      Volume: 67 Issue: 12 Pages: 3113-3125

    • DOI

      10.1109/tsp.2019.2912879

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Fault Tolerance of Random Graphs with respect to Connectivity: Mean-field Approximation for Semi-dense Random Graphs2019

    • Author(s)
      Takabe Satoshi、Takafumi Nakano、Wadayama Tadashi
    • Journal Title

      Physical Review E

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Approximation Theory for Connectivity of Ad Hoc Wireless Networks with Node Faults2019

    • Author(s)
      S. Takabe and T. Wadayama
    • Journal Title

      IEEE Wireless Communications Letters

      Volume: 印刷中 Issue: 4 Pages: 1240-1243

    • DOI

      10.1109/lwc.2019.2912610

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Typical approximation performance for maximum coverage problem2018

    • Author(s)
      Takabe Satoshi、Maehara Takanori、Hukushima Koji
    • Journal Title

      Physical Review E

      Volume: 97 Issue: 2 Pages: 022138-022138

    • DOI

      10.1103/physreve.97.022138

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] ランダム幾何グラフ上の確率的ノード除去モデルの連結性に対する平均場解析2019

    • Author(s)
      高邉賢史,和田山正
    • Organizer
      日本物理学会第74回年次大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 計算-転送方式におけるLDPC符号化変調方式の漸近性能解析2019

    • Author(s)
      高邉賢史,和田山正,林正人
    • Organizer
      第3回情報理論および符号理論とその応用ワークショップ
    • Related Report
      2018 Annual Research Report
  • [Presentation] Trainable ISTA ~ 深層学習を利用した疎信号復元反復アルゴリズム ~2019

    • Author(s)
      高邉賢史,和田山正
    • Organizer
      電子情報通信学会信号処理研究会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 大規模過負荷MIMO通信に適した深層学習を用いた反復検出法2018

    • Author(s)
      今西真之,高邉賢史,和田山正
    • Organizer
      第41回情報理論とその応用シンポジウム (SITA2018)
    • Related Report
      2018 Annual Research Report
  • [Presentation] Connectivity of Ad Hoc Wireless Networks with Node Faults2018

    • Author(s)
      Takabe Satoshi、Wadayama Tadashi
    • Organizer
      2018 IEEE Global Communications Conference (GLOBECOM)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] k-connectivity of Random Graphs and Random Geometric Graphs in Node Fault Model2018

    • Author(s)
      Takabe Satoshi、Wadayama Tadashi
    • Organizer
      International Symposium on Information Theory and Its Applications (ISITA)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 大規模過負荷 MIMO 通信における深層学習を用いた反復検出法2018

    • Author(s)
      今西真之,高邉賢史,和田山正
    • Organizer
      革新的無線通信技術に関する横断型研究会 (MIKA2018)
    • Related Report
      2018 Annual Research Report
  • [Presentation] 圧縮センシングのための非凸ノルムを用いた学習可能アルゴリズム2018

    • Author(s)
      高邉賢史,和田山正,樺島祥介
    • Organizer
      日本物理学会秋季大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Trainable ISTA for Sparse Signal Recovery2018

    • Author(s)
      Ito Daisuke、Takabe Satoshi、Wadayama Tadashi
    • Organizer
      018 IEEE International Conference on Communications Workshops (ICC Workshops)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 確率的ノード除去に対する連結性の相転移現象:統計力学的解析と確率的解析2018

    • Author(s)
      高邉賢史
    • Organizer
      ネットワーク科学セミナー:つながりと相互作用のランダムネス
    • Related Report
      2017 Annual Research Report
  • [Presentation] Mean-field analysis of network connectivity against stochastic node removals2018

    • Author(s)
      S. Takabe, T. Nakano, and T. Wadayama
    • Organizer
      BIFI International Conference 2018
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Mean-field Analysis of Network Reliability with respect to Connectivity against Stochastic Node Removals2018

    • Author(s)
      S. Takabe, T. Nakano, and T. Wadayama
    • Organizer
      American Physics Society march meeting
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 非凸Lqノルム正則化項をもつ圧縮センシングの統計力学的解析2018

    • Author(s)
      高邉賢史,和田山正,樺島祥介
    • Organizer
      日本物理学会第73回年次大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] ネットワーク上のノード故障時の連結性に関する相転移現象の解析2017

    • Author(s)
      高邉賢史,中野貴文,和田山正
    • Organizer
      情報理論研究会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 確率的ノード故障モデルにおける連結性に関する相転移現象2017

    • Author(s)
      高邉賢史,中野貴文,和田山正
    • Organizer
      ネットワーク科学セミナー2017
    • Related Report
      2017 Annual Research Report
  • [Presentation] ネットワーク上のノード故障時の連結性に関する相転移現象の平均場解析2017

    • Author(s)
      高邉賢史,中野貴文,和田山正
    • Organizer
      日本物理学会2017年秋季大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 確率的ノード故障モデルにおける信頼性と冗長性の確率的解析2017

    • Author(s)
      高邉賢史,和田山正
    • Organizer
      第10回シャノン理論ワークショップ
    • Related Report
      2017 Annual Research Report
  • [Presentation] 組合せ最適化問題に対する近似アルゴリズムの典型性能評価と相転移現象2017

    • Author(s)
      高邉賢史
    • Organizer
      日本オペレーションズ・リサーチ学会「最適化の基盤とフロンティア」研究部会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Probabilistic Analysis of Network Reliability and Robustness in Node Fault Model2017

    • Author(s)
      高邉賢史,和田山正
    • Organizer
      第40回情報理論とその応用シンポジウム
    • Related Report
      2017 Annual Research Report
  • [Presentation] スパース信号復元のためのTrainable ISTA2017

    • Author(s)
      伊藤大輔,高邉賢史,和田山正
    • Organizer
      第40回情報理論とその応用シンポジウム
    • Related Report
      2017 Annual Research Report

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Published: 2017-08-25   Modified: 2020-03-30  

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