Multidimensional multiwavelet analysis and its application to image processing

• Project/Area Number: 25400202
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied 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, 教授 (50239688)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: ウェーブレット解析 / マルチウェーブレット / 画像処理 / 多重解像度解析 / 四元数 / スパース表現 / 多次元マルチウェーブレット / ブランド信号源分離 / 四元数フーリエ解析 / ブラインド信号源分離

Outline of Final Research Achievements

Mathematical basics of blind source separation based on wavelet analysis were studied. Our proposed methods for blind source separation were verified by numerical simulations. Blind source separation algorithms for images based on multidimensional multiwavelet were proposed. Fundamental studies on Fourier analysis and wavelet analysis of quaternion valued functions were investigated. Various theorems on convolution of quaternion valued functions were presented. These convolution theorems are related to filters and linear systems in engineering. An error-correcting code based on compressive sensing was proposed and its validity was demonstrated through numerical experiments.

Research Products

• [Journal Article] A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform (2016)
  • Author(s): Mawardi Bahri and Ryuichi Ashino
  • Journal Title: Abstr. Appl. Anal. Volume: 2016 Pages: 1-11
  • DOI: 10.1155/2016/5874930
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Scaling functions generating fractional Hilbert transforms of a wavelet function (2015)
  • Author(s): Ryuichi Ashino,Takeshi Mandai, Akira Morimoto
  • Journal Title: J. Math. Soc. Japan Volume: 67(3) Pages: 1275-1294
  • NAID: 130005094184
  • Peer Reviewed
• [Journal Article] An Estimation Method of Shift Parameters in Image Separation Problem (2015)
  • Author(s): R. Ashino, T. Mandai, A .Morimoto
  • Journal Title: in Current Trends in Analysis and Its Applications: Proceedings of the 9th ISAAC Congress, Krakow 201, Mityushev, Vladimir, Ruzhansky, Michael V. (Eds.) Volume: 1 Pages: 467-473
  • DOI: 10.1007/978-3-319-12577-0_52
  • ISBN: 9783319125763, 9783319125770
  • Peer Reviewed
• [Journal Article] A phase synchronization model between auditory brainstem response and electroencephalogram using the reconstructed waveform of multi-resolution discrete stationary wavelet analysis (2015)
  • Author(s): N. Ikawa, A. Morimoto, R. Ashino
  • Journal Title: the Proceedings of 2015 International Conference on Wavelet Analysis and Pattern Recognition Volume: 1 Pages: 11-116
  • DOI: 10.1109/icwapr.2015.7295935
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Image separation using N-tree wavelet transforms (2015)
  • Author(s): A. Morimoto, R. Ashino, T. Mandai
  • Journal Title: the Proceedings of 2015 International Conference on Wavelet Analysis and Pattern Recognition Volume: 1 Pages: 93-98
  • DOI: 10.1109/icwapr.2015.7295932
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Convolution and Correlation Theorems for Wigner-Ville Distribution Associated with Linear Canonical Transform (2015)
  • Author(s): M. Bahri, R. Ashino
  • Journal Title: Proceedings of the twelfth International Conference on Information Technology: New Generations Volume: 1 Pages: 341-346
  • DOI: 10.1109/itng.2015.61
  • Peer Reviewed
• [Journal Article] Fractional Hilbert transforms of biorthogonal wavelets (2015)
  • Author(s): Akira Morimoto, Ryuichi Ashino, Kazuma Ikebe, Motoi Tatsumi, and Takeshi Mandai
  • Journal Title: Proceedings of the twelfth International Conference on Information Technology: New Generations Volume: 1 Pages: 347-352
  • DOI: 10.1109/itng.2015.62
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Relationship between quaternion linear canonical and quaternion fourier transforms (2014)
  • Author(s): Mawardi Bahri, Ryuichi Ashino
  • Journal Title: Proceedings of the 2014 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Volume: 1 Pages: 116-120
  • DOI: 10.1109/icwapr.2014.6961301
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The detection of the relation of the stimulus intensity-latency of auditory brainstem response using optimal wavelet analysis (2014)
  • Author(s): Nobuko Ikawa, Akira Morimoto, Ryuichi Ashino
  • Journal Title: Proceedings of the 2014 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Volume: 1 Pages: 127-133
  • DOI: 10.1109/icwapr.2014.6961303
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Filter coefficients of the fractional Hilbert transforms of biorthogonal wavelets (2014)
  • Author(s): Morimoto, A.; Ashino, R.; Ikebe, K.; Mandai, T.; Tatsumi, M.
  • Journal Title: Proceedings of 2014 International Conference on Wavelet Analysis and Pattern Recognition Volume: 1 Pages: 134-139
  • DOI: 10.1109/icwapr.2014.6961304
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] ウェーブレット理論と工学への応用 (2014)
  • Author(s): 芦野隆一
  • Journal Title: 数学 Volume: 66(1) Pages: 90-95
  • NAID: 130006882588
  • Peer Reviewed
• [Journal Article] Convolution and correlation based on discrete quaternion Fourier transform (2013)
  • Author(s): Mawardi Bahri, Ryuichi Ashino, and Remi Vaillancourt
  • Journal Title: INFORMATION Volume: 16(11) Pages: 7837-7848
  • Peer Reviewed
• [Journal Article] Convolution theorems for quaternion Fourier transform: properties and applications (2013)
  • Author(s): Mawardi Bahri, Ryuichi Ashino, and Remi Vaillancourt
  • Journal Title: Abstr. Appl. Anal. Volume: 162769 Pages: 1-10
  • DOI: 10.1155/2013/162769
  • Peer Reviewed
• [Journal Article] Correlation theorems for type II quaternion Fourier transform (2013)
  • Author(s): Mawardi Bahri, Ryuichi Ashino
  • Journal Title: IEEE Conference Publications, 2013 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Volume: 1 Pages: 136-141
  • DOI: 10.1109/icwapr.2013.6599305
  • Peer Reviewed
• [Journal Article] An application of wavelet analysis to procedure of averaging waveform of 40-Hz auditory steady-state response (2013)
  • Author(s): Nobuko Ikawa, Akira Morimoto, Ryuichi Ashino
  • Journal Title: IEEE Conference Publications, 2013 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Volume: 1 Pages: 79-84
  • DOI: 10.1109/icwapr.2013.6599296
  • Peer Reviewed
• [Journal Article] Phase transitions in error correcting and compressed sensing by $\ell_1$ linear programming (2013)
  • Author(s): Ryuichi Ashino, Remi Vaillancourt
  • Journal Title: Int. J. Wavelets Multiresolut. Inf. Process. Volume: 11 Issue: 04 Pages: 1-16
  • DOI: 10.1142/s0219691313600047
  • Peer Reviewed
• [Presentation] General quaternionic Fourier transform convolution theorem (2015)
  • Author(s): Mawardi Bahri and Ryuichi Ashino
  • Organizer: The Seventh International Conference on Information
  • Place of Presentation: National Taiwan University, Taipei, Taiwan
  • Year and Date: 2015-11-25
  • Int'l Joint Research
• [Presentation] A blind separation method based on multiwavelet analysis (2015)
  • Author(s): Ryuichi Ashino
  • Organizer: The International Congress on Industrial and Applied Mathematics
  • Place of Presentation: China National Convention Center, Beijing, China
  • Year and Date: 2015-08-10
  • Int'l Joint Research / Invited
• [Presentation] Convolution and correlation theorems for continuous reduced biquaternion wavelet (2015)
  • Author(s): Mawardi Bahri and Ryuichi Ashino
  • Organizer: The 2015 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)
  • Place of Presentation: Guangzhou, China
  • Year and Date: 2015-07-12
  • Int'l Joint Research
• [Presentation] Multiwavelet analysis and its application to signal processing (2015)
  • Author(s): Ryuichi Ashino
  • Organizer: RIMS 研究集会 調和解析と非線形偏微分方程式
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2015-07-06
  • Int'l Joint Research / Invited
• [Presentation] Convolution and Correlation Theorems for Wigner-Ville Distribution Associated with Linear Canonical Transform (2015)
  • Author(s): Mawardi Bahri, Ryuichi Ashino
  • Organizer: the The twelfth International Conference on Information Technology: New Generations
  • Place of Presentation: The Flamingo Hotel, Las Vegas, Nevada, USA
  • Year and Date: 2015-04-14
• [Presentation] Convolution and Correlation Theorems for Wigner-Ville Distribution Associated with Linear Canonical Transform (2015)
  • Author(s): Mawardi Bahri and Ryuichi Ashino
  • Organizer: The twelfth International Conference on Information Technology: New Generations
  • Place of Presentation: Las Vegas, Nevada, USA
  • Year and Date: 2015-04-13
  • Int'l Joint Research
• [Presentation] Blind source separation using wavelet analysis (2014)
  • Author(s): Ryuichi Ashino
  • Organizer: 2014 A3 Foresight Program Conference on Modeling and Computation of Applied Inverse Problems
  • Place of Presentation: International Convention Center, Jeju, Korea
  • Year and Date: 2014-11-20 – 2014-11-23
  • Invited
• [Presentation] Relationship between quaternion linear canonical and quaternion Fourier transforms (2014)
  • Author(s): Mawardi Bahri, Ryuichi Ashino
  • Organizer: The 2014 International Conference on Wavelet Analysis and Pattern Recognition
  • Place of Presentation: Crowne Plaza Lanzhou, Lanzhou, China
  • Year and Date: 2014-07-13 – 2014-07-16
• [Presentation] スパース表現と圧縮センシング
  • Author(s): 芦野隆一
  • Organizer: 地球流体現象の疎構造 科学技術試験研究委託事業「数学協働プロジェクト」 スタディグループ
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] Correlation theorems for type II quaternion Fourier transform
  • Author(s): Mawardi Bahri, Ryuichi Ashino
  • Organizer: 2013 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)
  • Place of Presentation: Tianjin, China
• [Presentation] Blind separation by wavelet analysis
  • Author(s): Ryuichi Ashino
  • Organizer: Invited lecture at Faculty of Mathematics and Computer Science, Hubei University
  • Place of Presentation: Hubei University, Wuhan, China
  • Invited
• [Presentation] Two-dimensional quaternion wavelet transform
  • Author(s): Ryuichi Ashino
  • Organizer: The sixth international conference on information
  • Place of Presentation: Tokyo
• [Book] 応用のためのウェーブレット (2016)
  • Author(s): 山田道夫・萬代武史・芦野隆一
  • Total Pages: 184
  • Publisher: 共立出版
• [Book] 応用数理ハンドブック，項目「ウェーブレット解析の発展」 (2013)
  • Author(s): 芦野隆一
  • Total Pages: 2
  • Publisher: 朝倉書店