A hitchhiker's guide to the galaxy of transform-domain sparsification

The ability to efficiently and sparsely represent seismic data is becoming an increasingly important problem in geophysics. Over the last decade many transforms such as wavelets, curvelets, contourlets, surfacelets, shearlets, and many other types of 'x-lets' have been developed to try to resolve this issue. In this abstract we compare the properties of four of these commonly used transforms, namely the shift-invariant wavelets, complex wavelets, curvelets and surfacelets. We also briefly explore the performance of these transforms for the problem of recovering seismic wavefields from incomplete measurements.