Local super resolution analysis

• Project/Area Number: 22540130
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka Kyoiku University
• Principal Investigator: ASHINO Ryuichi 大阪教育大学, 教育学部, 教授 (80249490)
• Co-Investigator(Kenkyū-buntansha): MANDAI Takeshi 大阪電気通信大学, 工学部, 教授 (10181843) ; MORIMOTO Akira 大阪教育大学, 教育学部, 准教授 (50239688)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 多重解像度解析 / 解析ウェーブレット / スパース表現 / 四元数 / ウェーブレットフレーム / 短時間フーリエ変換 / ウェーブレット変換 / 超解像度 / 時間周波数解析 / ウェーブレット解析 / 圧縮センシング / 信号処理 / 画像解析 / ローカルトモグラフィ

Research Abstract

Wavelet frames in generalized Sobolev spaces were investigated.A wavelet frame design based on the Riesz potential was proposed. The proposed wavelet frame can decomposes functions or data into microlocal components. Quaternion valued Fourier and windowed Fourier transformations were investigated. An uncertainty principle was presented. A design of dictionaries for the sparse representation was proposed and its performances were numerically examined.

Research Products

• [Journal Article] Blind image source separations by wavelet analysis (2012)
  • Author(s): R. Ashino, S. Kataoka, T. Mandai, A. Morimoto
  • Journal Title: Appl. Anal Volume: 94(4) Pages: 617-644
• [Journal Article] Source reduction method using wavelets for the source separation problem (2012)
  • Author(s): A. Morimoto, R. Ashino, T. Mandai
  • Journal Title: IEEE Conference Publications, 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Pages: 346-351
• [Journal Article] Application of the source reduction method with multiwavelets to image separation (2012)
  • Author(s): A. Morimoto, R. Ashino, T. Mandai
  • Journal Title: IEEE Conference Publications, 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Pages: 384-389
• [Journal Article] Two-dimensional quaternion Fourier transform of type II and quaternion wavelet transform (2012)
  • Author(s): B. Mawardi, R. Ashino, R. Vaillancour
  • Journal Title: IEEE Conference Publications, 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Pages: 359-364
• [Journal Article] Blind image source separations by wavelet analysis (2012)
  • Author(s): Ryuichi Ashino, Shusuke Kataoka, Takeshi Mandai, Akira Morimoto
  • Journal Title: Appl. Anal. Volume: 91(4) Issue: 4 Pages: 617-644
  • DOI: 10.1080/00036811.2011.616497
  • Peer Reviewed
• [Journal Article] 連続マルチウェーブレット変換とガウスの消去法を用いた画像分離 (2012)
  • Author(s): 守本晃，芦野隆一，萬代武史
  • Journal Title: 第 40 回可視化シンポジウム講演論文集 Volume: 32(Suppl. No.1) Pages: 197-202
• [Journal Article] Waveform Analysis of 40-Hz Auditory Steady-State Response using Wavelet Analysis (2012)
  • Author(s): Nobuko IKAWA, Akira Morimoto, Ryuichi Ashino
  • Journal Title: IEEE Conference Publications, 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Volume: 1 Pages: 397-402
  • DOI: 10.1109/icwapr.2012.6294814
  • Peer Reviewed
• [Journal Article] Source reduction method using wavelets for the source separation problem (2012)
  • Author(s): Akira Morimoto, Ryuichi Ashino, Takeshi Mandai
  • Journal Title: IEEE Conference Publications, 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Volume: 1 Pages: 346-351
  • DOI: 10.1109/icwapr.2012.6294806
  • Peer Reviewed
• [Journal Article] Application of the source reduction method with multiwavelets to image separation (2012)
  • Author(s): Akira Morimoto, Ryuichi Ashino, Takeshi Mandai
  • Journal Title: IEEE Conference Publications, 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Volume: 1 Pages: 384-389
  • DOI: 10.1109/icwapr.2012.6294812
  • Peer Reviewed
• [Journal Article] Two-dimensional quaternion Fourier transform of type II and quaternion wavelet transform (2012)
  • Author(s): Mawardi Bahri, Ryuichi Ashino, Remi Vaillancourt
  • Journal Title: IEEE Conference Publications, 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Volume: 1 Pages: 359-364
  • DOI: 10.1109/icwapr.2012.6294808
  • Peer Reviewed
• [Journal Article] Two-dimensional quaternion wavelet transform (2011)
  • Author(s): B. Mawardi, R. Ashino, R. Vaillancourt
  • Journal Title: Appl. Math. Comput Volume: 218(1) Pages: 10-21
• [Journal Article] Image separation using multiwavelets (2011)
  • Author(s): R. Ashino, S. Kataoka, T. Mandai, A. Morimoto
  • Journal Title: Proceedings of the 2011 International Conference on Wavelet Analysis and Pattern Recognition Pages: 245-250
• [Journal Article] Image separation using monogenic signal of stationary wavelet transform (2011)
  • Author(s): A. Morimoto, R. Ashino, S. Kataoka, T. Mandai
  • Journal Title: Proceedings of the 2011 International Conference on Wavelet Analysis and Pattern Recognition Pages: 239-244
• [Journal Article] Two-dimensional quaternion wavelet transform (2011)
  • Author(s): B.Mawardi, R.Ashino, R.Vaillancourt
  • Journal Title: Appl.Math.Comput. Volume: 218(1) Issue: 1 Pages: 10-21
  • DOI: 10.1016/j.amc.2011.05.030
  • Peer Reviewed
• [Journal Article] Image separation using monogenic signal of stationary wavelet transform (2011)
  • Author(s): A.Morimoto, R.Ashino, S.Kataoka, T.Mandai
  • Journal Title: Proceedings of the 2011 International Conference on Wavelet Analysis and Pattern Recognition, Guilin, 10-13 July, 2011 Pages: 239-244
  • Peer Reviewed
• [Journal Article] Image separation using multiwavelets (2011)
  • Author(s): R.Ashino, S.Kataoka, T.Mandai, A.Morimoto
  • Journal Title: Proceedings of the 2011 International Conference on Wavelet Analysis and Pattern Recognition, Guilin, 10-13 July, 2011 Pages: 245-250
  • Peer Reviewed
• [Journal Article] ICM2010特別企画・ガウス賞業績紹介 メイエ (2011)
  • Author(s): 芦野隆一
  • Journal Title: 数学セミナー,日本評論社 Volume: 50 Pages: 35-39
• [Journal Article] 解析ウェーブレット変換とその応用 (2011)
  • Author(s): 芦野隆一
  • Journal Title: 日本数学会2011年年会予稿集,実関数分科会 Volume: 1 Pages: 10-10
• [Journal Article] Blind source separation of spatio-temporal mixed signals using hase information of analytic wavelet transform (2010)
  • Author(s): R. Ashino, T. Mandai, A. Morimoto
  • Journal Title: Int. J. Wavelets Multiresolut. Inf. Process Volume: vol. 8 Pages: 575-594
• [Journal Article] Image separation using the monogenic wavelet transform (2010)
  • Author(s): A. Morimoto, R. Ashino, T. Mandai
  • Journal Title: Proceedings of the 10th International Symposium on Communications and Information Technologies Pages: 707-712
• [Journal Article] Windowed Fourier transform of twodimensional quaternionic ignals (2010)
  • Author(s): M. Bahri, E. Hitzer, R. Ashino, R. Vaillancourt
  • Journal Title: Appl. Math. Comput Volume: Vol. 216 Pages: 2366-2379
• [Journal Article] Equivalent mean breakdown points for linear codes and compressed sensing by l_1 optimization (2010)
  • Author(s): R. Ashino, R. Vaillancourt
  • Journal Title: Proceedings of the 10th International Symposium on Communications and Information Technologies Pages: 701-706
• [Journal Article] Mean breakdown points for compressed sensing by uniformly distributed matrices (2010)
  • Author(s): R. Ashino, R. Vaillancourt
  • Journal Title: JSIAM Letters Volume: Vol. 2 Pages: 111-114
  • NAID: 130000433683
• [Journal Article] 圧縮センシングの基礎とその研究動向 (2010)
  • Author(s): 芦野隆一
  • Journal Title: システム制御情報学会誌 Volume: 55 Pages: 88-93
  • NAID: 110008514078
• [Journal Article] Blind source separation of spatio-temporal mixed signals using phase information of analytic wavelet transform (2010)
  • Author(s): R.Ashino, T.Mandai, A.Morimoto
  • Journal Title: Int.J.Wavelets Multiresolut.Inf.Process. Volume: 8 Pages: 575-594
  • Peer Reviewed
• [Journal Article] Image separation using the monogenic wavelet transform (2010)
  • Author(s): A.Morimoto, R.Ashino, T.Mandai
  • Journal Title: Proceedings of the 10th International Symposium on Communications and Information Technologies 2010 (ISCIT 2010) Volume: 1 Pages: 707-712
  • Peer Reviewed
• [Journal Article] Windowed Fourier transform of two-dimensional quaternionic signals (2010)
  • Author(s): M.Bahri, E.Hitzer, R.Ashino, R.Vaillancourt
  • Journal Title: Appl.Math.Comput. Volume: 216 Pages: 2366-2379
  • Peer Reviewed
• [Journal Article] Equivalent mean breakdown points for linear codes and compressed sensing by l_1 optimization (2010)
  • Author(s): R.Ashino. R.Vaillancourt
  • Journal Title: Proceedings of the 10th International Symposium on Communications and Information Technologies 2010 (ISCIT 2010) Volume: 1 Pages: 701-706
  • Peer Reviewed
• [Journal Article] Mean breakdown points for compressed sensing by uniformly distributed matrices (2010)
  • Author(s): R.Ashino. R.Vaillancourt
  • Journal Title: JSIAM Letters Volume: 2 Pages: 111-114
  • NAID: 130000433683
  • Peer Reviewed
• [Presentation] Two-dimensional quaternion wavelet transform (2012)
  • Author(s): R. Ashino
  • Organizer: TAIWAN-JAPAN Joint Conference on PDE and Analysis
  • Place of Presentation: National Taiwan university
  • Year and Date: 2012-12-26
• [Presentation] Image separation by wavelet analysis (2012)
  • Author(s): R. Ashino
  • Organizer: Workshop on Microlocal Methods in Medical Imaging
  • Place of Presentation: Fields Institute, Toronto
  • Year and Date: 2012-09-16
• [Presentation] Two-dimensional quaternion Fourier transform of type II and quaternion wavelet transform (2012)
  • Author(s): B.Mawardi, R. Ashino, R. Vaillancourt
  • Organizer: 2012 International Conference on Wavelet Analysis and Pattern Recognition
  • Place of Presentation: Xian, China
  • Year and Date: 2012-07-17
• [Presentation] 解析ウェーブレット変換とその応用 (2011)
  • Author(s): 芦野隆一
  • Organizer: 日本数学会秋季総合分科会 実函数論分科会 特別講演
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-28
• [Presentation] 解析ウェーブレット変換とその応用 (2011)
  • Author(s): 芦野隆一
  • Organizer: 日本数学会秋季総合分科会実函数論分科会特別講演
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-28
• [Presentation] 解析ウェーブレット変換とその応用 (2011)
  • Author(s): 芦野隆一
  • Organizer: 日本数学会2011年度年会,実関数分科会,特別講演
  • Place of Presentation: 早稲田大学(招待)
  • Year and Date: 2011-03-20
• [Presentation] 定常ウェーブレット変換のモノジェニック信号を用いた画像分離 (2011)
  • Author(s): 守本晃, 芦野隆一, 片岡秀輔, 萬代武史
  • Organizer: 日本応用数理学会 研究部会連合発表会
  • Place of Presentation: 電気通信大学西地区,西9号館,西4号館
  • Year and Date: 2011-03-08
• [Presentation] 聴性誘発脳波を用いた他覚的聴力検査 (2011)
  • Author(s): 井川信子, 守本晃, 芦野隆一
  • Organizer: 日本応用数理学会 研究部会連合発表会
  • Place of Presentation: 電気通信大学西地区,西9号館,西4号館
  • Year and Date: 2011-03-08
• [Presentation] Signal and image source separations by wavelet analysis (2010)
  • Author(s): R. Ashino, S. Kataoka, T. Mandai, A. Morimoto
  • Organizer: International Conference on Inverse Problems
  • Place of Presentation: City University of Hong Kong, Hong Kong
  • Year and Date: 2010-12-15
• [Presentation] Signal and image source separations by wavelet analysis (2010)
  • Author(s): R.Ashino, S.Kataoka, T.Mandai, A.Morimoto
  • Organizer: International Conference on Inverse Problems
  • Place of Presentation: City University of Hong Kong, Hong Kong(招待)
  • Year and Date: 2010-12-15
• [Presentation] Sparse representation and linear codes (2010)
  • Author(s): R.Ashino
  • Organizer: The series of lectures at Banaras Hindu University
  • Place of Presentation: Banaras Hindu University, Varanasi-221005, India
  • Year and Date: 2010-12-04
• [Presentation] Blind image separation using wavelet analysis (2010)
  • Author(s): A.Morimoto
  • Organizer: The series of lectures at Banaras Hindu University
  • Place of Presentation: Banaras Hindu University, Varanasi-221005, India
  • Year and Date: 2010-12-01
• [Presentation] Introduction to wavelet analysis (2010)
  • Author(s): R. Ashino
  • Organizer: The series of lectures at Banaras Hindu University
  • Place of Presentation: Banaras Hindu University, Varanasi-221005, India
  • Year and Date: 2010-11-30
• [Presentation] Equivalent mean breakdown points for linear codes and compressed sensing by l_1 optimization (2010)
  • Author(s): R.Ashino, R.Vaillancourt
  • Organizer: The 10th International Symposium on Communications and Information Technologies 2010 (ISCIT 2010)
  • Place of Presentation: Meiji University, Tokyo
  • Year and Date: 2010-10-28
• [Presentation] Image separation using the monogenic wavelet transform (2010)
  • Author(s): A.Morimoto, R.Ashino, T.Mandai
  • Organizer: The 10th International Symposium on Communications and Information Technologies 2010 (ISCIT 2010)
  • Place of Presentation: Meiji University, Tokyo
  • Year and Date: 2010-10-28
• [Presentation] Wavelet and signal source separation (2010)
  • Author(s): R. Ashino, T. Mandai, A. Morimoto
  • Organizer: Forum "Math-for-Industry" 2010
  • Place of Presentation: Hilton Fukuoka Sea Hawk, Fukuoka-shi
  • Year and Date: 2010-10-23
• [Presentation] Wavelet and signal source separation (2010)
  • Author(s): R.Ashino, T.Mandai, A.Morimoto
  • Organizer: Forum "Math-for-Industry" 2010
  • Place of Presentation: Hilton Fukuoka Sea Hawk, Fukuoka-shi(招待)
  • Year and Date: 2010-10-23
• [Presentation] 複数の定常離散ウェーブレット変換を用いた画像分離法 (2010)
  • Author(s): 守本晃, 芦野隆一, 片岡秀輔, 萬代武史
  • Organizer: 可視化情報学会全国講演会(鹿児島2010)
  • Place of Presentation: 霧島市国分シビックセンター(霧島市役所内)
  • Year and Date: 2010-10-08
• [Presentation] 複数の定常離散ウェーブレット変換を用いた画像分離アルゴリズム (2010)
  • Author(s): 片岡秀輔, 芦野隆一, 萬代武史, 守本晃
  • Organizer: 可視化情報学会全国講演会(鹿児島2010)
  • Place of Presentation: 霧島市国分シビックセンター(霧島市役所内)
  • Year and Date: 2010-10-08
• [Presentation] 複数の定常離散ウェーブレット変換を用いた画像分離について (2010)
  • Author(s): 守本晃, 芦野隆一, 片岡秀輔, 萬代武史
  • Organizer: 第四回 ウェーブレット変換およびその応用に関するワークショップ
  • Place of Presentation: 豊橋技術科学大学 講義棟A1-101
  • Year and Date: 2010-09-28
• [Presentation] 数学的顕微鏡 (2010)
  • Author(s): 芦野隆一
  • Organizer: 講演会「見方で変わる数学の学び」(第四回関西地区)
  • Place of Presentation: 同志社大学明徳館
  • Year and Date: 2010-07-31
• [Presentation] 圧縮可能測定と線形符号 (2010)
  • Author(s): 芦野隆一, R. Vaillancourt
  • Organizer: 研究集会「偏微分方程式の逆問題解析とその周辺分野に関する研究」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-06-22
• [Presentation] 圧縮可能測定と線形符号 (2010)
  • Author(s): 芦野隆一, R.Vaillancourt
  • Organizer: RIMS研究集会「偏微分方程式の逆問題解析とその周辺分野に関する研究」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-06-22
• [Presentation] Two-dimensional quaternion wavelet transform
  • Author(s): Ryuichi Ashino
  • Organizer: TAIWAN-JAPAN Joint Conference on PDE and Analysis
  • Place of Presentation: National Taiwan university
• [Presentation] Image separation by wavelet analysis
  • Author(s): Ryuichi Ashino
  • Organizer: Workshop on Microlocal Methods in Medical Imaging
  • Place of Presentation: Fields Institute, Toronto
  • Invited
• [Presentation] Two-dimensional quaternion Fourier transform of type II and quaternion wavelet transform
  • Author(s): Mawardi Bahri, Ryuichi Ashino, Remi Vaillancourt
  • Organizer: 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)
  • Place of Presentation: Xian, China
• [Book] INTECH (2011)
  • Author(s): B. Mawardi and R. Ashino
  • Total Pages: 468
  • Publisher: Fourier Transforms -Approach Scientific Principles の 13 章 Two-Dimensional Quaternionic Windowed Fourier Transform
• [Book] Fourier Transforms-Approach Scientific Principlesの13章Two-Dimensional Quaternionic Windowed Fourier Transform (2011)
  • Author(s): B.Mawardi, R.Ashino
  • Total Pages: 468
  • Publisher: INTECH
• [Book] 計算力学理論ハンドブック,7章 数値シミュレーションにおける適応ウェーブレット法 (2010)
  • Author(s): 山田道夫・榊原進・佐々木文夫・芦野隆一
  • Publisher: 朝倉書店
• [Book] 計算力学理論ハンドブック,7章数値シミュレーションにおける適応ウェーブレット法 (2010)
  • Author(s): 山田道夫・榊原進・佐々木文夫・芦野隆一
  • Publisher: 朝倉書店
• [Remarks] Welcome to Ashino's Home Page!
  • URL: http://www.osaka-kyoiku.ac.jp/~ashino/
• [Remarks]
  • URL: http://www.osaka-kyoiku.ac.jp/~ashino/