Applications of wavelets to the analysis of cosmic microwave background maps

We consider wavelets as a tool to perform a variety of tasks in the context of analysing cosmic microwave background (CMB) maps. Using spherical Haar wavelets, we define a position and angular-scale-dependent measure of power that can be used to assess the existence of spatial structure. We apply pl anar Daubechies wavelets for the identification and removal of point source s from small sections of sky maps. Our technique can successfully identify virtually all point sources that are above 3 sigma and more than 80 per cen t of those above 1 sigma. We discuss the trade-offs between the levels of c orrect and false detections. We denoise and compress a 100 000-pixel CMB ma p by a factor of similar to 10 in 5 s, achieving a noise reduction of about 35 per cent. In contrast to Wiener filtering, the compression process is m odel-independent and very fast. We discuss the usefulness of wavelets for p ower spectrum and cosmological-parameter estimation. We conclude that at pr esent wavelet functions are most suitable for identifying localized sources .