Sparse Signal Recovery in a Transform Domain

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.

Autorentext

Evgeniy Lebed, M.Sc., received Bachelor of Science in Applied
Mathematics from Simon Fraser University and Master of Science
in Mathematics from University of British Columbia. He is
currently completing Ph.D. in Engineering.

Klappentext

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.