One of the core technical tools of harmonic analysis is to analyse functions by breaking them into simple building blocks.

The Fourier transform is the most famous such decomposition. There the building blocks are the plane waves. However there are other analysis/synthesis systems, for example wavelets. 

In this project we use Fourier Integral Operators to develop analysis/synthesis systems that are well adapted (in the sense that the decomposition is sparse) to deal with wave equation like problems where there is some additional symmetry or dynamical constraints.