Deconvolving COMPTEL gamma-ray data into images presents a major methodolog
ical challenge. We developed a new algorithm called Multiresolution Regular
ized Expectation Maximization (MREM), which explicitly accounts for spatial
correlations in the image by using wavelets (Dixon et al. 1998). We demons
trate that MREM largely suppresses image noise in the reconstruction, showi
ng only significant structures that are present in the data. Application to
1.8 MeV data results in a sky map that is much smoother than the maximum e
ntropy reconstructions presented previously, but it shows the same characte
ristic emission features which have been established earlier.