Wavelets could theoretically come to the rescue of the troubled Hubble Space Telescope, by helping scientists enhance the blurred images caused by a flaw in the telescope's light-gathering mirror. Ingrid Daubechies of AT&T Bell Laboratories said wavelets are efficient tools for removing distortion from visual images, though space agency researchers say they plan to use "tried and true" methods at this point.
With wavelets, on the other hand, many differently shaped curves can be fitted to the graphs of complicated phenomena better than Fourier terms, said Ronald Coifman, a professor of mathematics at Yale University who has worked with [Yves Meyer], the French wavelet experts, for a number of years.
The bottom line, said Daubechies, the AT&T Bell Laboratories researchers who has has made important contributions to wavelet theory, is that wavelets allow a more precise analysis or compression of complex information than any previous technique. And, unlike the Fourier transform, wavelets can probe a complex function at different scales of resolution -- high power to capture fine details of how the function is changing (the "trees") or low power to encompass the overall picture (the "forest").