## Developing mathematical theory to solve problems

Theory and application are two major aspects of research.
I believe that theoretic research should be driven by applications and
applied research should be guided by theory,
and I enjoy doing research in this manner. Especially,
I am interested in
developing mathematical theories and numerical methods to
solve real life problems.
This leads me into the area of wavelet theory and applications.

Wavelet theory and applications are based on two
basic ideas (i)
the ability to choose adaptively and flexibly a `best representation'
of functions from a unified family of representers, and
(ii) non-linear approximation based on multi-level analysis.
This combination allows the formulation of
efficient and robust tools to analyze and process images
from various applications.
In theory, I focus on constructions of good systems
(e.g. redundant
systems, (such as tight frames,) or biorthogonal wavelet systems in, for
example, a pair of dual spaces) and
their (multi-level) approximations and representations of functions in
various spaces.
In applications, I develop algorithms and apply them
to imaging science. In short, I am working in the areas of

- Approximation Theory and Wavelet Theory;

- Time-frequency Analysis;

- Imaging Science.