Kit Ian KOU, Anna高潔欣
Associate Professor

Phd Students Recruitment Notice!

Publications:

 

Awards

Date AwardedTitle of AwardAwarding Body
06/2024U-level award of “2023/2024” Incentive Scheme for Outstanding Academic StaffUM, Macau, China
06/2018Third Prize of 2018 Macau Natural Science AwardFDCT, Macau, China
08/2017FST Research Excellence AwardFST, UM, Macau. China

 

Teaching

M.Sc. and Ph.D Courses

  • Topics in Analysis; Reading course; Clifford Analysis; Advance in Mathematics; Advanced Engineering Mathematics

B.Sc. Courses

  • Mathematical Analysis I; Mathematical Analysis II; Mathematical Analysis III; Mathematical Analysis IV; Finite Mathematics; Numerical Methods and Computation; Probability and Statistics; Probability; Multivariate Calculus; Ordinary Differential Equations; Complex Analysis; Mathematical Physics Methods; Multivariable Calculus; Partial Differential Equations; Seminar; Fourier and Signal Analysis; Time Series Analysis; Linear Algebra I; Intermediate Calculus; Quantitative Reasoning for Science and Technology; Research in Mathematics

Research

Kit Ian Kou is an accomplished scholar in hypercomplex analysis, mainly focusing on quaternion and Clifford analysis. Here’s an overview of her research work based on the provided search results:

1. Academic Background and Professional Experience:
– Kit Ian Kou holds a Ph.D. in Mathematics from the University of Macau (UM). She has been an Associate Professor in the Department of Mathematics at the University of Macau since August 2013.

2. Research Interests:
– Her research interests span hypercomplex signal analysis, Fourier and linear canonical analysis, quaternion and Clifford analysis, interpolation theories, analytic signal analysis, and high-dimensional data analysis.

3. Published Works:
– Kou has contributed significantly to the field with numerous publications. Some of her notable works include:

4. Research Projects and Grants:
– Kou has been involved in various research projects and has received external grants, indicating the significance and impact of her work in hypercomplex analysis.

5. Expertise in Quaternion Fourier Analysis:
– As indicated by her expertise on OpenReview, Kou is well-versed in quaternion Fourier analysis, a key area within hypercomplex analysis .

6. Contributions to Signal Processing and Image Processing:
– Her work has been applied in signal and color image processing, where low-rank quaternion matrix approximation has been successfully utilized.

Kit Ian Kou’s research is characterized by a deep dive into the theoretical aspects of hypercomplex analysis and their practical applications, particularly in signal and image processing. Her significant impact on the field is underscored by her numerous scholarly publications and the accolades she has garnered through research funding and esteemed academic roles.

Research Projects and Grants

External Grants:

  • Research and commercialization of core computer vision algorithm in the process of lithium battery manufacturing, 06/05/2022-06/05/2024, FDCT/AGJ (PI).
  • Model development of reconstructed iris feature fusion method based on improved BEMD, 04/08/2022-04/03/ 2023, FDCT/AMR, (Co-PI).
  • An intelligent diagnostic system for automatic segmentation and survival prediction of nasopharyngeal carcinoma multimodal
    MRI images, 01/04/2019-31/03/ 2023, GSTIC, (Co-PI).
  • Application of self-defence medical techniques for prevention and early treatment of dementia in the elderly population, 05/01/2020-05/01/2022, FDCT/ASC, (Member).
  • Quaternions method and digital color image processing, 07/01/2019-7/1/2022, FDCT, (PI).
  • Quaternion Linear Canonical Transforms and Applications, 22/07/2016-21/07/2019, FDCT, (PI).
  • Matseav’s theorem for subharmonic functions in half spaces, NSFC, 01/01/2016-31/12/2018, (Co-PI).
  • The related topics about spheroidal wave functions in quaternion analysis, 01/01/2015-31/12/2017, NSFC, (PI).
  • Generalized spheroidal wave functions and applications in Quaternion Analysis, 03/10/2013-02/10/2016, FDCT.
  • Clifford analysis and applications, 05/10/2012-04/10/2014, FDCT, (PI).
  • Research on some problems in high-dimensional space under the framework of Clifford’s algebraic structure, 01/01/2010-1/12/2013, NSFC, (Co-PI)

Internal Grants (Principal Investigator)

  • 16/7/2015-15/7/2018:MYRG2015-00058-FST. The Application of Quaternions to Some Signal Problems, funded by the Research Committee of UM.Principle Investigator.
  • 13/03/2014-12/03/2017：MRG012/KKI/2014/FST.Genearlized pheroidal wave functions and applications in Quaternion Analysis, funded by the Research Committee of UM. Principle Investigator.
  • May 2013-June 2016: MYRG099 (Y1-L2)-FST13-KKI. Fourier Analysis and Applications, funded by the Research Committee of UM. Principle Investigator.
  • January 2013-December 2014: MRG002/KKI/2013/FST. Clifford Analysis and Applications, funded by the Research Committee of UM. Principal Investigator.
  • June 2011-April 2015: MYRG142(Y3-L2)-FST11-KKI. Time-Frequency Analysis and Applications, funded by the Research Committee of UM. Principal Investigator.
  • January 2010-December 2011: RG076/09-10S/11R/KKI/FST. Applied Complex and Harmonic Analysis in Euclidean Space, funded by the Research Committee of UM. Principal Investigator.
  • January 2007 – June 2009: RG070/06-07S/09T/KKI/FST. Hardy Spaces of Monogenic Functions & Applications, funded by the Research Committee of University of Macau. Principal Investigator.
  • January 2005 – December 2006: RG059/05-06S/QT/FST. Paley-Wiener and Shannon Sampling Theorems in Hyper-complex Analysis, funded by the Research Committee of University of Macau. Co-Principal Investigator.
  • January 2003 – December 2005: RG091/04-05S/C117. Clifford Analysis Methods in Harmonic Analysis, funded by the Research Committee of University of Macau. Co-Principal Investigator.
  • January 2002 – December 2002: RG055/01-02S/QT/FST. (a) Monogenic Sinc Function and Applications; (b) Harmonic Analysis on the Unit Spheres in Higher Dimensional Euclidean Space, funded by the Research Committee of University of Macau, Co-Principal Investigator.
  • January 2000 – December 2001: RG024/00-01S/QT/FST. Higher Dimensional Sinc Methods and Applications in Partial Differential Equations, funded by the Research Committee of University of Macau, , two years. Co-Principal Investigator.

PhD Students and Their Dissertation Subjects:

  • Graduated
    1. Cuiming ZOU (2016). Theory and Applications of Spheroidal Wave Quaternionic Signal. (Principle supervisor)
    2. Xiaoxiao HU (2016). Spheroidal Functions in Higher-Dimensional Spaces. (Principle supervisor)
    3. Zhenfeng CAI (2017). Quaternion Differential Equations and Applications. (Principle supervisor)
    4. Dong CHENG (2018). (Principle supervisor) 
    5. Wenshan BI (2021). (Principle supervisor)
    6. Wankai LIU (2019). (Principle supervisor)
    7. Yun HUANG (2020). (Co-Principle supervisor)
    8. Jifei MIAO (2021). (Principle supervisor)
    9. Juan Han (2023). (Principle supervisor)
    10. Liqiao Yang (2023). (Principle supervisor)
  • On going
    1. Yanlin ZHANG (since 8/2021). (Principle supervisor)
    2. Pengling WU (since 8/2022). (Principle supervisor)
    3.  (since 8/2023). (Principle supervisor)

Master Students and Their Dissertation Subjects:

  • Graduated
    1. Yuelin LIU (2009). The linear canonical transform and generalized Hilbert transform with applications in signal processing.
    2. Ruihui XU (2011). Windowed linear canonical transform and its applications.
    3. Jianyu OU (2013). Uncertainty principles for quaternionic linear canonical transform and applications.
    4. Leping LIANG (2013). Paley Wiener theorem under linear canonical transform of slice monogenic functions
    5. Zezhen CAO (2013). Linear canonical transform and applications.
    6. Kaman LEI (2014). A tighter uncertainty principle for hypercomplex signals in the linear canonical transform domains.
    7. Xiaojun LI (2016). Linear canonical transform in time-frequency analysis.
    8. Dong CHENG (2015). The generalized sampling expansions associated with quaternion Fourier transform
    9. Fengyi CHEN (2021). 
    10. Yanlin ZHANG (2024). 
    11. Xiayi ZHOU (2024). 
  • On going
    1. Chengyang LI (2023). 
    2. Unwa HO (2024).
    3. Fandi GAO (2024).
    4. Kaiyin YANG (2024).

Postdoctoral Scholars and Core Research Disciplines

  1. 2010, 2012, 2013: Joao MORAIS (Hyper-complex and Clifford Analysis), University of Aveiro, Portugal.
  2. 2012-2016: Ming Sheng LIU (Complex and Signal Analysis), South China Normal University, Guangzhou, P. R. China.
  3. 2012, 2013, 2014:Yan YANG (Clifford Analysis and Signal Analysis), Sun Yat-Sen University, Guangzhou, P. R. China.
  4. 2013, 2014: Yang LIU (Signal and Control Theory), Zhejiang Normal University, Jinhua, P. R. China.
  5. 2014: Hong LI (Signal and Data Analysis), Huazhong University of Science and Technology. P. R. China.
  6. 2014: Jun Feng XU (Complex and Signal Analysis), Wuyi University, Jiangmen, P. R. China.
  7. 2016: Yonghui XIA (Partial Differential Equations), Zhejiang Normal University, Jinhua, P. R. China.
  8. 2019: Cuiming ZOU (Quaternion Analysis)
  9. 2020: Yulong WANG (Quaternion Analysis)
  10. 2022: Jifei MIAO (Quaternion Analysis)
  11. 2023: Banghua HUANG (Stability Analysis), School of Mathematical Science, Zhejiang Normal University, Jinhua, China.
  12. 2023: Huimin GUAN (Optimization), School of Mathematical Science, Zhejiang Normal University, Jinhua, China.
  13. 2024: Yuanxin ZHAN (Color Image Processing), School of Mathematical Science, Zhejiang Normal University, Jinhua, China.

Professional Affiliations

  • Founding member of the ISAAC interest group on Clifford and Quaternionic analysis since January 2011.
  • Organizer of Computer Graphics International (CGI)
    since 2018, the 10th ENGAGE workshop.
  • External affair – Macao Society of Nuclear Medicine and
    Molecular Imaging (MSNMMI) since 2020.
  • Life Member (ID: 4939) of Clare Hall, A College for Advanced Study at the University of Cambridge, United Kingdom.
  • Fellow – Stanley Ho East Asia College (SHEAC), University of Macau.
  • Member – Centre for Applied Mathematics, University of Macau.

Contact Details

Faculty of Science and Technology
University of Macau, E11
Avenida da Universidade, Taipa,
Macau, China

Room: E11-3067
Telephone: (853) 8822-4472
Fax: (853) 8822-2426
Email: kikou