Approximation theory is a branch of mathematics that strives to understand the fundamental limits in optimally representing different signal types.
Signals here may mean:
- A database of digital audio signal.
- A collection of digital mammograms.
- Solutions of a class of integral equations.
- Triangulated compact surfaces acquired by a oscillatory characteristics.
Researchers typically mathematically model these signals based on their intrinsic smoothness or oscillatory characteristics.
Approximation Theory at Rensselaer
Those studying approximation theory analyze and design various multiresolution techniques that have provable, optimal properties for these models.
Such optimal representations are key ingredients to successful data compression, estimation, and computer-aided geometric design.
Researchers use a range of tools, including:
- Mathematical analysis (Littlewood-Paley theory).
- Fast numerical algorithms.
- Information theory.
- Algebraic and differential geometry.
- Spline and subdivision theory.
- Modern wavelet theory.
- Harmonical analysis.
Projects include the design and analysis of various multiresolution techniques.