June 7, 2007
Over the last dozen years or so, wavelets have appeared as a powerful alternative to the more traditional Fourier representations. In this talk, we first review Fourier and wavelet bases, together with their characteristics. We then address approximation theoretic properties, in particular the interesting behavior of certain simple non-linear approximation schemes for piecewise smooth signals. This leads to applications in denoising and in compression, where wavelets have had a major impact on image coding standards, like JPEG2000. We end by pointing out areas of current research, especially in the area of multidimensional signal representations as well as sampling of sparse signals.
Martin Vetterli (EPFL Switerland)