The technique, known as "wavelet bootstrapping" or "wavestrapping," has applications in the geophysical sciences, bioinformatics, medical imaging, nanotechnology and other areas. It can also be useful for rapidly obtaining information from small data sets in such applications as medical diagnostics.
Wavelets are mathematical functions that have become increasingly important to researchers because of their ability to analyze data sets that are difficult to understand using traditional techniques such as Fast Fourier Transform. For instance, signals within noisy data recorded in the time domain can become more meaningful when analyzed in the wavelet domain.
Wavestrapping was pioneered by University of Washington researchers, who applied wavelet transforms to an established statistical re-sampling technique known as bootstrapping, which is used to extract additional information from single data runs. The marriage of bootstrapping and wavelets offers a new tool for the analysis of data sets that would otherwise be difficult to study because of correlation and time-dependency issues.
"The new thing here is re-sampling, but not in the time domain, which would be nearly impossible because of the strong dependence of data or correlation of data," said Brani Vidakovic, associate professor at the Georgia Institute of Technology's School of Industrial and Systems Engineering. "By transferring the data to the wavelet domain, applying re-sampling methods and then returning the re-sampled data as variants in the time domain, you can then proceed as if you had a data ensemble rather than a single run."
Vidakovic will discuss his research on validating wavelet bootstrapping strategies and assessing their variability bounds at the annual meeting
Contact: John Toon
Georgia Institute of Technology Research News