Matrix rank minimization algorithm for control system design

• Project/Area Number: 24760342
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Control engineering
• Research Institution: Kogakuin University
• Principal Investigator: KONISHI Katsumi 工学院大学, 情報工学部, 准教授 (20339138)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 行列ランク最小化 / スパース最適化 / 制御系設計 / システム同定 / 圧縮センシング

Outline of Final Research Achievements

This work dealt an algorithm for the matrix rank minimization problem, which is NP hard in general while it has a lot of applications, and has proposed null space based alternating optimization (NSAO) algorithm and iterative partial matrix shrinkage (IPMS) algorithm. Numerical examples show that both algorithms provide low-rank solutions efficiently and that IPMS algorithm can be applied to huge size problems.

Research Products

• [Journal Article] Block Adaptive Algorithm for Signal Declipping Based on Null Space Alternating Optimization (2015)
  • Author(s): T. Takahashi, K. Konishi and T. Furukawa
  • Journal Title: IEICE Transaction on Information and Systems Volume: E98-D/1 Pages: 206-209
  • NAID: 130004721747
  • Peer Reviewed
• [Journal Article] Iterative Partial Matrix Shrinkage Algorithm for Matrix Rank Minimization (2014)
  • Author(s): Katsumi Konishi, Kazunori Uruma, Tomohiro Takahashi, Toshihiro Furukawa
  • Journal Title: Signal Processing Volume: Vol. 100 Pages: 124-131
  • DOI: 10.1016/j.sigpro.2014.01.014
  • Peer Reviewed
• [Journal Article] 構造化行列のランク最小化に基づく画像修復法 (2013)
  • Author(s): 高橋 智博, 小西 克巳, 古川 利博
  • Journal Title: 電子情報通信学会論文誌 Volume: J96-D/ 7 Pages: 1606-1617
  • NAID: 110009615138
  • Peer Reviewed
• [Journal Article] Reweighted Least Squares Heuristic for SARX System Identification (2013)
  • Author(s): Katsumi Konishi
  • Journal Title: IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Volume: E95-A/ 9 Pages: 1627-1630
  • NAID: 10031142552
  • Peer Reviewed
• [Journal Article] 構造化行列のランク最小化に基づく画像修復法 (2013)
  • Author(s): 高橋智博 小西克巳 古川利博
  • Journal Title: 電子情報通信学会論文誌 Volume: Vol.J96-D/7 Pages: 1-1
  • NAID: 110009615138
  • Peer Reviewed
• [Journal Article] Sequential Matrix Rank Minimization Algorithm for Model Order Identification (2012)
  • Author(s): Katsumi Konishi
  • Journal Title: IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Volume: Vol.E95-A, No. 10 Pages: 1788-1791
  • NAID: 10031142575
  • Peer Reviewed
• [Journal Article] Mixed l0/l1 Norm Minimization Approach to Image Colorization (2012)
  • Author(s): K. Uruma, K Konishi, T. Takahashi and T. Furukawa
  • Journal Title: IEICE TRANSACTIONS on Information and Systems Volume: E95-D/ 8 Pages: 2150-2153
  • Peer Reviewed
• [Presentation] Hankel Structured Matrix Rank Minimization Approach to Signal Declipping (2013)
  • Author(s): T. Takahashi, K. Konishi and T. Furukawa
  • Organizer: European Signal Processing Conference
  • Place of Presentation: モロッコ マラケシュ
• [Presentation] Low-Rank and Sparse Optimization for GPCA with Applications to SARX System Identification (2013)
  • Author(s): K. Konishi
  • Organizer: European Control Conference
  • Place of Presentation: スイス チューリッヒ
• [Presentation] 行列ランク最小化に基づく一般化主成分分析手法とシステム同定への応用 (2013)
  • Author(s): 小西克巳
  • Organizer: 第56回自動制御連合講演会
  • Place of Presentation: 新潟
• [Presentation] Sequential Matrix Rank Minimization Approach to Signal Recovery Based on Subspace System Identification (2012)
  • Author(s): Katsumi Konishi
  • Organizer: IEEE Muti-Conference on Systems and Control
  • Place of Presentation: クロアチア ドブロブニク
• [Presentation] IMAGE COLORIZATION BASED ON THE MIXED L0/L1 NORM MINIMIZATION (2012)
  • Author(s): K. Uruma, K Konishi, T. Takahashi and T. Furukawa
  • Organizer: IEEE International Conference on Image Processing
  • Place of Presentation: アメリカ オーランド
• [Presentation] RANK MINIMIZATION APPROACH TO IMAGE INPAINTING USING NULL SPACE BASED ALTERNATING OPTIMIZATION (2012)
  • Author(s): T. Takahashi, K Konishi and T. Furukawa
  • Organizer: IEEE International Conference on Image Processing
  • Place of Presentation: アメリカ オーランド
• [Presentation] Structured Matrix Rank Minimization Approach to Image Inpainting (2012)
  • Author(s): T. Takahashi, K Konishi and T. Furukawa
  • Organizer: IEEE MWSCAS
  • Place of Presentation: アメリカ ボイシ