Brani Vidakovic and Graduate Student Ben Shi demonstrate pupil diameter measuring system. The resulting data is analyzed using wavelet bootstrapping.
For certain classes of data that may be very expensive or difficult to obtain, a new statistical technique may provide useful information from a single data run by allowing meaningful re-sampling.
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 offer advantages over traditional statistical analysis techniques, including:
Although the beginnings of wavelets can be traced back almost a century, their wide use began only about 15 years ago when new wavelet bases were discovered and their implementation was connected with fast-filtering computational procedures.
"The interest in wavelets is their speed and locality," said Vidakovic. "Locality is the most important, because many natural phenomena are non-stationary and very local. Wavelets are able to economically describe phenomena that are inhomogeneous. For some phenomena, it would be impossible to make sense of the data without wavelets."
Wavelets also help researchers with a major problem of the computer age – large volumes of data mixed with noise. "Their dimension reduction and ability to deal with huge data sets are also strengths of wavelets," he added. "Very nasty data can be de-noised almost in real-time by selecting a few of the important wavelet coefficients that can retain the main trend in the signal."
Many different wavelets exist, and selecting the right ones is a vital part of developing the new technique, Vidakovic said. "Wavelets are not a miracle tool for everything," he warned. "But if the data are amenable to wavelet analysis, then they can be very helpful."
John Toon | EurekAlert!
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