The Federal Bureau of Investigationuses wavelet transforms to compress digitally scanned fingerprints. NASA's Mars rovers use them to compress images acquired by their 18 cameras. The new JPEG 2000 format is based on wavelet transforms; the smaller files allow one to store images using less memory and to transmit those images faster and more reliably. Researchers also use wavelet transforms to clean signals and images—that is, to reduce unwanted noise and blurring. As illustrated in the figure, some algorithms for processing astronomical images are based on wavelets and wavelet-like transforms.
A wavelet transform, like a Fourier transform, involves integrating a product of a signal and an oscillating function. But unlike the everlasting sines and cosines of Fourier analysis, the oscillating functions in a wavelet transform are usually stretched and translated versions of a single oscillating function of short duration; indeed that localized function is the “wavelet.” This tutorial describes...
