Since the hardback edition of this book was put together wavelets have continued to flourish both in mathematics and in applications in ever more diverse branches of science and engineering. A standard library electronic alert system now easily produces more than fourteen hundred references to papers per year, developing or using wavelet techniques. These are published in a very broad array of journals. Here we can point to only a few of the recently developed methods, in particular as they have been used in physics.

In recent years many variations on the wavelet theme have appeared. One tries to go ‘beyond wavelets’. In this context there is a whole family of new animals in the wavelet zoo. Its members carry names like bandelets, beamlets, chirplets, contourlets, curvelets, fresnelets, ridgelets … These are new bases or frames of functions, customized to handle 2D or 3D data processing better. In [23] for example, it is explained how ridgelets and curvelets can be used in astrophysics. It turns out that noise filtering, contrast enhancement and morphological component analysis of galaxy images are performed much better by a skilful combination of the new transforms than by mere wavelet transforms. More examples can be found on the ‘curvelet homepage’ [24], maintained by J.L. Starck.

It seems that the applications of the discrete wavelet transform (DWT) far outnumber those of the continuous wavelet transform (CWT), although the latter started the modern development of wavelet theory in the early eighties.