Publication & Preprints and AMS MathSciNet

Research Interests:

• Time--scale-frequency Analysis: wavelets, framelets, Gabor frames, multifractals.
• Application of wavelets and framelets to signal denoising and image compression.
• Multiresolution and wavelets in computer graphics and CAGD.
• Biorthogonal wavelets in general domains and their applications to ODEs and PDEs.
• Sampling theory and sigma-delta modulation.
• Learning theory and its applications
• Any interesting pure and applied mathematical problems.

Grants:

• NSERC Research Grant, April 2009---March 2014.
• NSERC Research Grant, April 2004---March 2009.
• Canada Fundation for Innovation (CFI) infrastructure fund (with Michael Li and Samuel Shen) to establish an Information Research Laboratory.
• NSERC Research Grant, April 2000---March 2004.
• University of Alberta start-up fund, July 2000--April 2002.

Editorships:

• Applied and Computational Harmonic Analysis
• Numerical Mathematics: Theory, Method and Applications
• International Journal of Applied Mathematics and Applications

Graduate and Undergraduate Students

• Xiaosheng Zhuang, Ph.D. candidate in mathematics, September 2005--present.
• Xinghua Deng, Ph.D. in mathematics, September 2001 -- July 2006.
  Co-supervised with Professor Robert Moody at the Department of Mathematics, University of Victoria.
  PhD Thesis: Diffraction and its Relationship to Dynamical Systems.
  
• Mengzhe Wang, Ph.D. candidate in mathematics, December 2003 -- January 2005.
• Robert Liao, M.Sc. in applied mathematics, January 2003 -- June 2004.
  M.Sc. Thesis: New interplatory subdivision schemes in computer graphics, 2004.
• Stephen Wasylishen, NSERC summer undergraduate student, April 2003--August 2003.
• Qun Mo, Ph.D. in mathematics, November 2000 -- August 2003.
  PhD Thesis: Compactly supported symemtric MRA wavelet frames, 2003.
  Currently, an associate professor at Department of Mathematics, Zhejiang University, China.
• Paul Shelley, M.Sc. in computing sciences, December 2000 -- August 2001.
  Co-supervised with Professor Xiaobo Li at the Department of Computing Sciences.
  MSc Thesis: New techniques in wavelet image compression, 2001.

Postdoctoral Fellows and Research Associates

• Dr. Soon Geol Kwon, Visiting professor from Korea, February 2004--February 2005.
• Dr. Sang Soo Park, KOSEF postdoctoral fellow, October 2003 -- September 2004.
• Dr. Wen Chen, PIMS postdoctoral fellow, September 2001 -- August 2003.
  Co-sponsor with Professor Rong-Qing Jia.
  Currently, a full professor at Department of Electronical Engineering, Shanghai Jiaotong University, China.

Current Plenary Talks