Characterization and Compression of Turbulent Signals and Images Using Wavelet-Packets

Abstract

The newly introduced Wavelet-Packet transform (Coifman & Meyer 1989, Coifman et al. 1990) allows the decomposition of a signal as a function of the scale, the position and the frequency (or wavelength) optimally. Each Wavelet-Packet coefficient provides insight into the structure of the data locally and at the appropriate scale. We have applied this transform technique to one-dimensional data and two-dimensional images and report on its ability to characterize turbulence data with a few coefficients. We find that, overall, the Wavelet-Packet transform technique performs better than its competitors. That is, significant data compression ratios can be achieved without severely distorting the signal or the image.