Harmonic Analysis and Computational Mathematics

Advances in communication, sensing, and computational power have led to an explosion of data. The size and varied formats for these datasets challenge existing techniques for transmission, storage, querying, display, and numerical manipulation. It is thus vital to develop efficient and robust data representations that lend themselves to scientific analysis and computation.

Harmonic analysis studies the decomposition of signals and data as the superposition of basic waves. This provides an efficient framework for compact representation of data, signals and operators using multiscale and other decompositions.

Computational mathematics is the application of computer methods for analyzing and manipulating data. This involves developing and implementing new algorithms based on efficient signal representations.

TOPICS OF RECENT AND CURRENT INTEREST INCLUDE

  • Generalized wavelet systems, such as brushlets, curvelets, wavelet packets, and Gabor systems
  • Function spaces and approximation with redundant systems
  • Pseudodifferential operators
  • Time-frequency analysis
  • Signal analysis/synthesis
  • Machine learning