Applied harmonic analysis including wavelet/framelet methods, Fourier transform methods, sparse approximation and sampling.
Wavelet/framelet methods in image processing, data sciences, deep learning algorithms, functional data analysis, and numerical PDEs.
Scientific computing for Helmholtz equations, elliptic interface problems, Burgers' equations, etc. using finite difference methods and wavelet methods.
Computer aided geometric desgin (CAGD) such as subdivision curves/surfaces, spline approximation, and isogemetric analysis in numerical PDEs.
PhD in Mathematics (09/1994-07/1998),
Department of Math. and Stat. Sciences,
University of Alberta, Canada Ph.D. Thesis:
Subdivision Schemes, Biorthogonal Wavelets and Image Compression,
1998.