Multiscale analysis of waveforms using the seislet transform.
Sergey Fomel
Seislet transform is a digital wavelet-like transform tailored
specifically for representing seismic data. In the 1-D case, the seislet
transform breaks the input data into multiple scales similarly to the
digital wavelet transforms but centering at a particular signal
frequency rather than the zero frequency. In the 2-D case, the transform
basis functions are aligned along dipping waveform shapes. In both
cases, the transform is defined with the help of the wavelet lifting
scheme combined with local wave destruction. For multiple interfering
wave components, multiple transforms turn into an overcomplete frame.
When applied to seismic wave recordings, the seislet transform exhibits
superior compression properties, which make it suitable for practical
data analysis tasks such as denoising and data reconstruction.