Description of turbulent dynamics in the interstellar medium: Multifractal microcanonical analysis. II. Sparse filtering of Herschel observation maps and visualization of filamentarystructures at different length scales

We 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.