  We consider wavelets as a tool to perform a variety of tasks in the context
of analyzing 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 planar
Daubechies wavelets for the identification and removal of points sources from
small sections of sky maps. Our technique can successfully identify virtually
all point sources which are above 3 sigma and more than 80% of those above 1
sigma. We discuss the trade-offs between the levels of correct and false
detections. We denoise and compress a 100,000 pixel CMB map by a factor of
about 10 in 5 seconds achieving a noise reduction of about 35%. In contrast to
Wiener filtering the compression process is model independent and very fast. We
discuss the usefulness of wavelets for power spectrum and cosmological
parameter estimation. We conclude that at present wavelet functions are most
suitable for identifying localized sources.
