This final chapter is about the use of wavelets in astronomy and astrophysics. Wavelets are being applied in many fields of science and technology. We have selected astronomy as an example for several reasons: There are diverse applications within the field, and although they all involve some form of signal or image processing, the techniques vary from one application to another. Astronomy is driven by sophisticated technology for both ground-based and space-based observations, and this technology has led to problems that appear to be well suited to wavelet techniques. Finally, there is widespread popular interest in astronomy and cosmology, an interest that has been kindled by the richness of recent discoveries.

The chapter is based on our interpretation of the literature and on discussions with two groups of astronomers, the one directed by Albert Bijaoui (Observatoire de la C te d'Azur, Nice) and the other led by Andr Lannes (Observatoire Midi-Pyr n es, Toulouse). In his review article on the uses of wavelets in astrophysics [36], Bijaoui discusses a number of problems where wavelet-based techniques are being applied; these include the analysis of solar time series; image compression, detection, and analysis of astronomical sources; and data fusion as well as the study of the large-scale structure of the universe. We have selected three examples that illustrate different problems and techniques. In each case, wavelets are used in complex algorithms that are handcrafted by experts in astronomy to deal with specific problems. Roughly speaking, astronomical applications of wavelets differ from other applications because of the...