Sparse Signal Recovery in a Transform Domain: Theory and Application

The ability to efficiently and sparsely represent seismic data is becoming an increasingly important problem in geophysics. Over the last 30 years many transforms such as wavelets, curvelets, contourlets, surfacelets, shearlets, and many other types ofx-lets have been developed. Such transform were leveraged to resolve this issue. In this work we compare the properties of four of these commonly used transforms, namely the shift-invariant wavelets, complex wavelets, curvelets and surfacelets. We also explore the performance of these transforms for the problem of recovering seismic wavefields from incomplete physical and frequency measurements.