Description of turbulent dynamics in the interstellar medium: Multifractal microcanonical analysis

\nWe present significant improvements to our previous work on noise reduction in Herschel observation maps by defining sparse filtering tools capable of handling, in a unified formalism, a significantly improved noise reduction as well as a deconvolution in order to reduce effects introduced by the limited instrumental response (beam). We implement greater flexibility by allowing a wider choice of parsimonious priors in the noise-reduction process. More precisely, we introduce a sparse filtering and deconvolution approach approach of type l2-lp, with p > 0 variable and apply it to a larger set of molecular clouds using Herschel 250 μm data in order to demonstrate their wide range of application. In the Herschel data, we are able to use this approach to highlight extremely fine filamentary structures and obtain singularity spectra that tend to show a significantly less log-normal behavior and a filamentary nature in the less dense regions. We also use high-resolution adaptive magneto-hydrodynamic simulation data to assess the quality of deconvolution in such a simulated beaming framework.\n