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