Source separation using N-tree discrete wavelet transform and sparse representation

• Project/Area Number: 26400199
• 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: MORIMOTO Akira 大阪教育大学, 教育学部, 教授 (50239688)
• Co-Investigator(Kenkyū-buntansha): 芦野 隆一 大阪教育大学, 教育学部, 教授 (80249490)
• Co-Investigator(Renkei-kenkyūsha): MANDAI Takeshi 大阪電気通信大学, 工学部, 教授 (10181843)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 信号源分離 / ウェーブレット / N 分木離散ウェーブレット変換 / 分数べきヒルベルト変換 / 時間スケール解析 / 双直交ウェーブレット / 画像分離 / スパース表現

Outline of Final Research Achievements

We proposed an N-tree discrete wavelet transform. We implemented the transform and its inversion algorithm with many types of wavelet functions such as biorthogonal wavelets. We designed a preprocessor and a postprocessor of the transform. Using the advantages of N times redundancy, we applied it to digital watermarking to sounds or images. We showed that the transform can be used to solve blind source separation problems of sounds or images. We proposed ideas to estimate the rotation angles of some original image from mixtures of rotated and translated original images.

Research Products

• [Journal Article] Image Source Separation Based on N-tree Discrete Wavelet Transforms (2017)
  • Author(s): R. Ashino, T. Mandai, and A. Morimoto
  • Journal Title: New Trends in Analysis and Interdisciplinary Applications, Selected Contributions of the tenth ISAAC Congress, Macau 2015 Volume: 1 Pages: 579-583
  • DOI: 10.1007/978-3-319-48812-7_75
  • ISBN: 9783319488103, 9783319488127
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A Model of Relationship Between Waveform-Averaging and Slow Auditory Brainstem Response by Using Discrete Stationary Wavelet Analysis (2017)
  • Author(s): N. Ikawa, A. Morimoto, and R. Ashino
  • Journal Title: New Trends in Analysis and Interdisciplinary Applications, Selected Contributions of the 10th ISAAC Congress, Macau 2015 Volume: 1 Pages: 581-587
  • DOI: 10.1007/978-3-319-48812-7_73
  • ISBN: 9783319488103, 9783319488127
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Continuous Multiwavelet Transform for Blind Signal Separation (2017)
  • Author(s): R. Ashino, T. Mandai, and A. Morimoto
  • Journal Title: Pseudo-Differential Operators: Groups, Geometry and Application Volume: 1 Pages: 219-239
  • DOI: 10.1007/978-3-319-47512-7_12
  • ISBN: 9783319475110, 9783319475127
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Optimum wavelet filter estimating peak latencies of auditory brainstem response waveform (2016)
  • Author(s): N. Ikawa, A. Morimoto, and R. Ashino
  • Journal Title: Proceedings of the 2016 International Conference on Wavelet Analysis and Pattern Recognition Volume: 1 Pages: 189-194
  • DOI: 10.1109/icwapr.2016.7731642
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Logarithmic uncertainty principle for quaternion linear canonical transform (2016)
  • Author(s): M. Bahri and R. Ashino
  • Journal Title: Proceedings of the 2016 International Conference on Wavelet Analysis and Pattern Recognition Volume: 1 Pages: 140-145
  • DOI: 10.1109/icwapr.2016.7731634
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [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] 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] Digital audio watermarking method based on wavelet transform (2015)
  • Author(s): Y. Ishida, K. Ikebe, A. Morimoto, M. Tatsumi
  • Journal Title: the Proceedings of 2015 International Conference on Wavelet Analysis and Pattern Recognition Volume: 1 Pages: 87-92
  • DOI: 10.1109/icwapr.2015.7295931
  • 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] 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] Audio Watermarking Based on N-tree Discrete Wavelet Transform (2015)
  • Author(s): A. Morimoto
  • Journal Title: Proceedings of the Seventh International Conference on Information Volume: 1
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Scaling functions generating fractional Hilbert transforms of a wavelet function (2015)
  • Author(s): R. Ashino, T. Mandai, A. Morimoto
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 未定
  • NAID: 130005094184
  • Peer Reviewed
• [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] 私の好きな数学書 (2015)
  • Author(s): 芦野隆一
  • Journal Title: 数学セミナー Volume: 54 Pages: 28-32
• [Journal Article] Multistage blind source separations by wavelet analysis (2014)
  • Author(s): R. Ashino, T. Mandai, A. Morimoto
  • Journal Title: International Journal of Wavelets, Multiresolution and Information Processing Volume: 12 Issue: 04 Pages: 1-25
  • DOI: 10.1142/s0219691314600042
  • Peer Reviewed
• [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] 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] N 分木離散ウェーブレット変換について (2014)
  • Author(s): 守本晃 ，芦野隆一，池邊和馬，辰巳基，萬代武史
  • Journal Title: 数理解析研究所講究録 Volume: 1928 Pages: 1-27
  • Acknowledgement Compliant
• [Journal Article] Continuous quaternion Fourier and wavelet transforms (2014)
  • Author(s): M. Bahri, R. Ashino, R. Vaillancourt
  • Journal Title: Int. J. Wavelets Multiresolut. Inf. Process. Volume: 12 Issue: 04 Pages: 1-21
  • DOI: 10.1142/s0219691314600030
  • Peer Reviewed
• [Journal Article] Convolution and correlation theorem for linear canonical transform and properties (2014)
  • Author(s): M. Bahri, R. Ashino
  • Journal Title: INFORMATION-An International Interdisciplinary Journal Volume: 17 Pages: 2509-2522
  • NAID: 40022663635
  • Peer Reviewed
• [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] 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 Pages: 90-95
  • NAID: 130006882588
  • Peer Reviewed
• [Presentation] 画像分離における画像の回転角度の検出について (2017)
  • Author(s): 守本晃・芦野隆一・萬代武史
  • Organizer: 日本応用数理学会 2017 年 研究部会連合発表会
  • Place of Presentation: 電気通信大学
  • Year and Date: 2017-03-07
  • Invited
• [Presentation] ウェーブレット解析に基づいた画像分離について (2016)
  • Author(s): 守本晃・芦野隆一・萬代武史
  • Organizer: 応用数理学会2016年度年会
  • Place of Presentation: 北九州国際会議場, 小倉
  • Year and Date: 2016-09-14
• [Presentation] ウェーブレット解析と画像分離 (2016)
  • Author(s): 守本晃・芦野隆一・萬代武史
  • Organizer: 第44回可視化情報シンポジウム
  • Place of Presentation: 工学院大学
  • Year and Date: 2016-07-19
  • Invited
• [Presentation] Audio Watermarking Based on N-tree Discrete Wavelet Transform (2015)
  • Author(s): Akira Morimoto
  • Organizer: The Seventh International Conference on Information
  • Place of Presentation: Taipei, Taiwan
  • Year and Date: 2015-11-27
  • Int'l Joint Research
• [Presentation] N分木離散ウェーブレット変換を用いた音声信号の電子透かしについて (2015)
  • Author(s): 守本晃，芦野隆一，石田理人，萬代武史
  • Organizer: 応用数理学会2015年度年会
  • Place of Presentation: 金沢大学角間キャンパス
  • Year and Date: 2015-09-11
• [Presentation] Image source separation based on N-tree discrete wavelet transforms (2015)
  • Author(s): Akira Morimoto
  • Organizer: The 10-th International ISAAC Congress
  • Place of Presentation: Macao, China
  • Year and Date: 2015-08-07
  • Int'l Joint Research
• [Presentation] Image separation using N-tree wavelet transforms (2015)
  • Author(s): A. Morimoto, R. Ashino, T. Mandai
  • Organizer: The 2015 International Conference on Wavelet Analysis and Pattern Recognition
  • Place of Presentation: Guangzhou, China
  • Year and Date: 2015-07-13
  • Int'l Joint Research
• [Presentation] Fractional Hilbert transforms of biorthogonal wavelets (2015)
  • Author(s): A. Morimoto, R. Ashino, K. Ikebe, M. Tatsumi, T. Mandai
  • Organizer: 12th International Conference on Information Technology: New Generations
  • Place of Presentation: Las Vegas, Nevada, USA
  • Year and Date: 2015-04-14
  • Int'l Joint Research
• [Presentation] Fractional Hilbert Transforms of Biorthogonal Wavelets (2015)
  • Author(s): A. Morimoto, R. Ashino, K. Ikebe, M. Tatsumi, T. Mandai
  • Organizer: 12th International Conference on Information Technology: New Generations
  • Place of Presentation: 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): M. Bahri, R. Ashino
  • Organizer: 12th International Conference on Information Technology: New Generations
  • Place of Presentation: Las Vegas, Nevada, USA
  • Year and Date: 2015-04-14
• [Presentation] N 分木離散ウェーブレット変換と画像分離法 (2015)
  • Author(s): 守本晃
  • Organizer: 第11回 日本応用数理学会 研究部会連合発表会
  • Place of Presentation: 明治大学中野キャンパス
  • Year and Date: 2015-03-07
• [Presentation] Blind source separation using wavelet analysis (2014)
  • Author(s): R. 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: 2014-11-22
• [Presentation] Filter coefficients of the fractional hilbert transforms of biorthogonal wavelets (2014)
  • Author(s): A. Morimoto
  • Organizer: 2014 International Conference on Wavelet Analysis and Pattern Recognition
  • Place of Presentation: Lanzhou, China
  • Year and Date: 2014-07-15
• [Presentation] Relationship between quaternion linear canonical and quaternion Fourier transforms (2014)
  • Author(s): M. Bahri, R. Ashino
  • Organizer: The 2014 International Conference on Wavelet Analysis and Pattern Recognition
  • Place of Presentation: Lanzhou, China
  • Year and Date: 2014-07-15
• [Book] 応用のためのウェーブレット, シリーズ応用数理 5巻 (2016)
  • Author(s): 山田道夫・萬代武史・芦野隆一
  • Total Pages: 184
  • Publisher: 共立出版
• [Remarks] 守本晃のホームページ
  • URL: https://www.osaka-kyoiku.ac.jp/~morimoto/
• [Remarks] 大阪教育大学教員総覧（守本晃）
  • URL: http://kenkyu-web.bur.osaka-kyoiku.ac.jp/Profiles/2/0000184/profile.html
• [Remarks] 教員総覧 ーー大阪教育大学ーー
  • URL: http://kenkyu-web.bur.osaka-kyoiku.ac.jp/Profiles/2/0000184/profile.html
• [Remarks] 守本晃のホームページ
  • URL: http://www.osaka-kyoiku.ac.jp/~morimoto/
• [Remarks] 大阪教育大学：研究者プロフィール
  • URL: http://kenkyu-web.bur.osaka-kyoiku.ac.jp/Profiles/2/0000184/profile.html
• [Remarks] Morimoto's Home Page
  • URL: http://www.osaka-kyoiku.ac.jp/~morimoto/