Wavelets: Seeing the Forest and the Trees (Spanish version, 2003)

Summary: This article describes the development of the mathematical modeling technique known as wavelets, which is used in computer imaging and animation as well as by the FBI to encode its large database of fingerprints. In the nineteenth century, mathematicians perfected technique allowing complex periodic and non-periodic functions to be summed as a series of simpler functions. It has trouble reproducing transient signals or signals with abrupt changes, such as the spoken word. Over the course of the twentieth century, scientists worked to get around these limitations. In 1981, Jean Morlet, a geologist analyzing seismic signals, developed a technique that worked better than Fourier transforms. Many researchers followed the original idea with refinements of their own which made wavelet analysis much easier and turned the theory into a practical tool. One prominent application of wavelets has been in digital image compression. Wavelets are central to the new JPEG-2000 digital image standard and the WSQ method that the FBI uses to compress its fingerprint database. They allow us to zoom in on an image without losing resolution, which is common with other techniques.