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関数データ解析的アプローチによる代数的位相アンラップと信号処理問題への応用

Research Project

Project/Area Number 14J00920
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Research Field Perceptual information processing
Research InstitutionTokyo Institute of Technology

Principal Investigator

北原 大地  東京工業大学, 大学院理工学研究科(工学系), 特別研究員(DC1)

Project Period (FY) 2014-04-25 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2016: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2015: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2014: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywords2次元位相アンラップ / スプライン平滑化 / 代数的位相アンラップ / 部分終結式 / 数値安定化 / 代数的連続位相復元法 / 確率密度関数推定 / 凸最適化 / 位相アンラップ / 関数データ解析 / スプライン関数 / 合成開口レーダ
Outline of Annual Research Achievements

2次元の複素信号の観測データから,真の連続位相を推定する問題である「2次元位相アンラップ問題」に対し,研究員らのグループは1. 離散複素信号を表現する連続な複素関数を構成し,2. 代数的位相アンラップを用いて対応する連続位相を厳密に計算する,という2段階の超解像位相アンラップ法を提案している.
今年度は,新たに単位円周上の代数的位相アンラップの数値的不安定性の解消に取り組んだ.単位円周上の位相アンラップは,「フィードバックシステムの安定性解析」や「複素ケプストラム計算」などで必要とされ,代数的位相アンラップを用いれば所望の連続位相が厳密に計算される.しかしながら,実際には多項式除算型の計算による数値的不安定性が原因となり,特に高次の複素多項式に対して,位相アンラップに失敗してしまう問題があった.
代数的位相アンラップの成功のカギは,多項式除算型の計算によって得られる「スツルム列」と呼ばれる関数列の符号判定にかかっている.研究員は新たに「自己反転型多項式除算」を定義し,それにより得られる新たなスツルム列を用いても連続位相が計算可能なことを明らかにした.次に,再定義されたスツルム列の符号が新たに開発した「自己反転型部分終結式」と呼ばれる行列式から判定できることを示した.これにより,多項式除算型の計算を介さずに代数的位相アンラップが実装可能となり,実際に数値実験により代数的位相アンラップが劇的に安定化されることを示した.提案手法は到来方向推定で重要な「MUSICスペクトルのピークサーチ」への応用が期待でき,超解像位相アンラップ法の今後の更なる発展が期待できる.

Research Progress Status

28年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

28年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • Research Products

    (24 results)

All 2017 2016 2015 2014 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results,  Acknowledgement Compliant: 1 results) Presentation (21 results) (of which Int'l Joint Research: 4 results,  Invited: 1 results) Remarks (2 results)

  • [Journal Article] Algebraic Phase Unwrapping Based on Two-Dimensional Spline Smoothing over Triangles2016

    • Author(s)
      Daichi Kitahara, Isao Yamada
    • Journal Title

      IEEE Transactions on Signal Processing

      Volume: 64 Issue: 8 Pages: 2103-2118

    • DOI

      10.1109/tsp.2015.2510986

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Algebraic Phase Unwrapping with Self-Reciprocal Polynomial Algebra2017

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      12th International Conference on Sampling Theory and Applications
    • Place of Presentation
      Tallinn, Estonia
    • Year and Date
      2017-07-03
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Stabilization of Algebraic Phase Unwrapping along the Unit Circle with Self-Reciprocal Subresultant2017

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      2017年電子情報通信学会総合大会
    • Place of Presentation
      名古屋
    • Year and Date
      2017-03-22
    • Related Report
      2016 Annual Research Report
  • [Presentation] A Branch Cut Type Sign Estimator for Single-Frame Fringe Projection Profilometry2016

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      31th IEICE SIP Symposium
    • Place of Presentation
      大阪
    • Year and Date
      2016-11-08
    • Related Report
      2016 Annual Research Report
  • [Presentation] Huber 損失関数を用いたロバストな三重位相差型GPS2016

    • Author(s)
      森和也, 北原大地, 山岸昌夫, 山田功
    • Organizer
      31th IEICE SIP Symposium
    • Place of Presentation
      大阪
    • Year and Date
      2016-11-08
    • Related Report
      2016 Annual Research Report
  • [Presentation] 位相をつなぐ―代数的位相アンラップとその応用2016

    • Author(s)
      山田功, 北原大地
    • Organizer
      2016年電子情報通信学会ソサイエティ大会
    • Place of Presentation
      北海道
    • Year and Date
      2016-09-20
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] A Branch Cut Type Sign Estimator for 3D Measurement from A Single Fringe Pattern2016

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      9th SICE Symposium on Computational Intelligence
    • Place of Presentation
      千葉
    • Year and Date
      2016-07-08
    • Related Report
      2016 Annual Research Report
  • [Presentation] Two-Dimensional Positive Spline Smoothing and Its Application to Probability Density Estimation2016

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      IEEE International Conference on Acoustics, Speech and Signal Processing 2016 (ICASSP'16)
    • Place of Presentation
      Shanghai International Convention Center (Shanghai, China)
    • Year and Date
      2016-03-20
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Stabilization of Adaptive Eigenvector Extraction by Continuation in Nested Orthogonal Complement Structure2016

    • Author(s)
      Kenji Kakimoto, Daichi Kitahara, Masao Yamagishi, and Isao Yamada
    • Organizer
      IEEE International Conference on Acoustics, Speech and Signal Processing 2016 (ICASSP'16)
    • Place of Presentation
      Shanghai International Convention Center (Shanghai, China)
    • Year and Date
      2016-03-20
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Fast Dual Iterative Algorithm for Convexly Constrained Spline Smoothing2016

    • Author(s)
      Masao Yamagishi, Daichi Kitahara, and Isao Yamada
    • Organizer
      IEEE International Conference on Acoustics, Speech and Signal Processing 2016 (ICASSP'16)
    • Place of Presentation
      Shanghai International Convention Center (Shanghai, China)
    • Year and Date
      2016-03-20
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 2次元スプライン平滑化に基づく代数的連続位相復元法2015

    • Author(s)
      北原大地, 山田功
    • Organizer
      第8回コンピューテーショナル・インテリジェンス研究会
    • Place of Presentation
      県立広島大学広島キャンパス (広島県広島市南区)
    • Year and Date
      2015-12-18
    • Related Report
      2015 Annual Research Report
  • [Presentation] Two-Dimensional Phase Unwrapping Based on Selective Smoothing and Inconsistency Correction2015

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      IEICE SIP Symposium
    • Place of Presentation
      スパリゾートハワイアンズ (福島県いわき市常磐藤原町)
    • Year and Date
      2015-11-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] Positive Quartic and Biquartic C2-Splines and Their Applications to Two-Dimensional Probability Density Estimation2015

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      IEICE SIP Symposium
    • Place of Presentation
      スパリゾートハワイアンズ (福島県いわき市常磐藤原町)
    • Year and Date
      2015-11-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] On A Projection Step by Generalized Orthogonal Complement Matrices for Adaptive Subspace Tracking2015

    • Author(s)
      Kenji Kakimoto, Daichi Kitahara, Masao Yamagishi, and Isao Yamada
    • Organizer
      IEICE SIP Symposium
    • Place of Presentation
      スパリゾートハワイアンズ (福島県いわき市常磐藤原町)
    • Year and Date
      2015-11-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] A VIRTUAL RESAMPLING TECHNIQUE FOR ALGEBRAIC TWO-DIMENSIONAL PHASE UNWRAPPING2015

    • Author(s)
      Daichi Kitahara, Masao Yamagishi, and Isao Yamada
    • Organizer
      IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
    • Place of Presentation
      Brisbane Convention & Exhibition Centre(Brisbane, Australia)
    • Year and Date
      2015-04-19 – 2015-04-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] PROBABILITY DENSITY FUNCTION ESTIMATION BY POSITIVE QUARTIC C2-SPLINE FUNCTIONS2015

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
    • Place of Presentation
      Brisbane Convention & Exhibition Centre(Brisbane, Australia)
    • Year and Date
      2015-04-19 – 2015-04-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] A Smoothness-Aware Phase Unwrapping by Convex Optimization Technique2015

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      リモートセンシングシンポジウム
    • Place of Presentation
      TOKYU REIT 虎ノ門ビル(東京都港区)
    • Year and Date
      2015-03-02
    • Related Report
      2014 Annual Research Report
  • [Presentation] A Preprocessing Using Convex Optimization for Algebraic Two-Dimensional Phase Unwrapping2014

    • Author(s)
      Daichi Kitahara, Masao Yamagishi, and Isao Yamada
    • Organizer
      IEICE SIP Symposium
    • Place of Presentation
      ビナリオ嵯峨嵐山(京都市右京区)
    • Year and Date
      2014-11-12 – 2014-11-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] One-Dimensional Probability Density Function Estimation by Positive Quartic C2-Spline Interpolation and Smoothing2014

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      IEICE SIP Symposium
    • Place of Presentation
      ビナリオ嵯峨嵐山(京都市右京区)
    • Year and Date
      2014-11-12 – 2014-11-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] A fast Gauss-Seidel-like splitting algorithm for convexly constrained spline smoothing2014

    • Author(s)
      Masao Yamagishi, Daichi Kitahara, and Isao Yamada
    • Organizer
      IEICE SIP Symposium
    • Place of Presentation
      ビナリオ嵯峨嵐山(京都市右京区)
    • Year and Date
      2014-11-12 – 2014-11-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] 二次元位相アンラップ問題の難しさと面白さ2014

    • Author(s)
      北原 大地
    • Organizer
      IEICE SIP Symposium(チュートリアル)
    • Place of Presentation
      ビナリオ嵯峨嵐山(京都市右京区)
    • Year and Date
      2014-11-12 – 2014-11-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] Algebraic phase unwrapping over collection of triangles based on two-dimensional spline smoothing2014

    • Author(s)
      Daichi Kitahara and Isao Yamada
    • Organizer
      IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
    • Place of Presentation
      Fortezza dal Basso(Florence, Italy)
    • Year and Date
      2014-05-04 – 2014-05-09
    • Related Report
      2014 Annual Research Report
  • [Remarks] 山田研究室ホームページ

    • URL

      http://www.sp.ce.titech.ac.jp/index.php?%BB%B3%C5%C4%B8%A6%B5%E6%BC%BC

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
  • [Remarks] T2R2(東京工業大学リサーチリポジトリ)

    • URL

      http://t2r2.star.titech.ac.jp/cgi-bin/researcherpublicationlist.cgi?q_researcher_content_number=cb244a21c62c47628229682c0b5dbb85

    • Related Report
      2016 Annual Research Report

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Published: 2015-01-22   Modified: 2024-03-26  

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