We present PPMAP, a Bayesian procedure that uses images of dust continuum emission at multiple wavelengths to produce resolution-enhanced image cubes of differential column-density as a function of dust temperature and position. PPMAP is based on the generic point process formalism, whereby the system of interest (in this case, a dusty astrophysical structure such as a filament or prestellar core) is represented by a collection of points in a suitably defined state space. It can be applied to a variety of observational data, such as Herschel images, provided only that the image intensity is delivered by optically thin dust in thermal equilibrium. PPMAP takes full account of the instrumental point spread functions and does not require all images to be degraded to the same resolution. We present the results of testing using simulated data for a prestellar core and a fractal turbulent cloud, and demonstrate its performance with real data from the Hi-GAL survey. Specifically, we analyse observations of a large filamentary structure in the CMa OB1 giant molecular cloud. Histograms of differential column-density indicate that the warm material (T > 13 K) is distributed log-normally, consistent with turbulence, but the column-densities of the cooler material are distributed as a high density tail, consistent with the effects of self-gravity. The results illustrate the potential of PPMAP to aid in distinguishing between different physical components along the line of sight in star-forming clouds, and aid the interpretation of the associated PDFs of column density.
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