We present a new algorithm, called Multiresolution Regularized Expectation Maximization (MREM), for the reconstruction of gamma-ray intensity maps from COMPTEL data. The algorithm is based on the iterative Richardson-Lucy scheme to which we added a wavelet thresholding step in order to eliminate image-noise in the reconstruction. The wavelet thresholding explicitly accounts for spatial correlations in the data, and adapts the angular resolution locally, depending on the significance of the signal in the data. We compare the performance of MREM to that of the maximum entropy and the Richardson-Lucy algorithms by means of Monte-Carlo simulations of COMPTEL 1.809 MeV gamma-ray line observations. The simulations demonstrate that the maximum entropy and Richardson-Lucy algorithms provide virtually identical reconstructions which are heavily disturbed by image noise. MREM largely suppresses this noise in the reconstructions, showing only the significant structures that are present in the data. Application of MREM to COMPTEL 1.8 MeV gamma-ray line data results in a 1.809 MeV sky map that is much smoother than the maximum entropy or Richardson-Lucy reconstructions presented previously. The essential features of this map are (1) an asymmetric galactic ridge emission reaching from l=45 deg to l=240 deg, (2) a bright localised emission feature in the Cygnus region around (l,b)=(80 deg,0 deg), (3) two emission spots at l=317 deg and l=332 deg situated in the galactic plane, and (4) an extended emission region around (l,b)=(160 deg, 0 deg). Comparison of the MREM map to the simulated reconstructions demonstrates that the 1.809 MeV emission is confined to the galactic plane.
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