Wavelets allow researchers to transform and understand data
Because of their wide versatility, wavelets have revolutionized the study of complex wave phenomena in image processing, communication and scientific data streams. "Wavelets have opened the door to many improvements in de-noising, image restoration and image analysis," said Véronique Delouille, an applied mathematician and astrophysicist at the Royal Observatory of Belgium who uses wavelets for analyzing images of the sun. The technique analyzes the signal of a scanned image with wavelets to produce a collection of pixels that is overall much smaller than the original image while still allowing the reconstruction of the image with the original resolution. "There are many kinds of wavelets, and you can squish them, stretch them, you can adapt them to the actual image you are looking at," said Daan Huybrechs, a mathematical engineer at the Catholic University of Leuven in Belgium. The wave patterns in digitized images can differ in many aspects, but wavelets can always be stretched or compressed to match sections of the signal with lower or higher frequencies. One of the best-known wavelet families is the Daubechies mother wavelet, whose members have a self-similar fractal structure, with large asymmetrical peaks mimicking smaller replications of the peaks. Besides their use in analyzing sound signals and in image processing, wavelets are also a tool in basic research.