Signals are at the heart of many scientific and engineering disciplines,and their representation problem dates back at least to J.Fourier,who proposed the idea of orthogonal series representations. While Fourier series have many attractive properties, their limitations are well known. Probably the most interesting alternative has been provided by wavelets, a simple and computationally efficient way to represent signals and images. As a testimony to their impact, wavelets made it into an international standard, JPEG2000, less than a decade after their discovery. We will discuss the problem of signal representation, approximation, and compression, and contrast classical solutions with new, wavelet based solutions. In particular, we compare classical linear approximation with the more powerful non-linear approximation used with wavelets. We conclude by showing that not all is settled when it comes to the representation of higher dimensional data, where wavelets might be superceded by new, truly multidimensional bases.
 

Convenor: Louis Moresi