  Wavelet functions allow the sparse and efficient representation of a signal
at different scales. Recently the application of wavelets to the denoising of
maps of cosmic microwave background (CMB) fluctuations has been proposed. The
maximum-entropy method (MEM) is also often used for enhancing astronomical
images and has been applied to CMB data. In this paper, we give a systematic
discussion of combining these two approaches by the use of the MEM in wavelet
bases for the denoising and deconvolution of CMB maps and more general images.
Certain types of wavelet transforms, such as the a trous transform, can be
viewed as a multi-channel intrinsic correlation function (ICF). We find that
the wavelet MEM has lower reconstruction residuals than conventional
pixel-basis MEM in the case when the signal-to-noise ratio is low and the point
spread function narrow. Furthermore, the Bayesian evidence for the wavelet MEM
reconstructions is generally higher for a wide range of images.
  From a Bayesian point of view, the wavelet basis thus provides a better model
of the image.
