  Sub-millimetre dust emission is an important tracer of density N of dense
interstellar clouds. One has to combine surface brightness information at
different spatial resolutions, and specific methods are needed to derive N at a
resolution higher than the lowest resolution of the observations. Some methods
have been discussed in the literature, including a method (in the following,
method B) that constructs the N estimate in stages, where the smallest spatial
scales being derived only use the shortest wavelength maps. We propose simple
model fitting as a flexible way to estimate high-resolution column density
maps. Our goal is to evaluate the accuracy of this procedure and to determine
whether it is a viable alternative for making these maps. The new method
consists of model maps of column density (or intensity at a reference
wavelength) and colour temperature. The model is fitted using Markov chain
Monte Carlo (MCMC) methods, comparing model predictions with observations at
their native resolution. We analyse simulated surface brightness maps and
compare its accuracy with method B and the results that would be obtained using
high-resolution observations without noise. The new method is able to produce
reliable column density estimates at a resolution significantly higher than the
lowest resolution of the input maps. Compared to method B, it is relatively
resilient against the effects of noise. The method is computationally more
demanding, but is feasible even in the analysis of large Herschel maps. The
proposed empirical modelling method E is demonstrated to be a good alternative
for calculating high-resolution column density maps, even with considerable
super-resolution. Both methods E and B include the potential for further
improvements, e.g., in the form of better a priori constraints.
