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

TL;DR

This paper introduces an advanced sparse filtering and deconvolution method for Herschel observation maps, significantly improving noise reduction and filamentary structure visualization across various molecular clouds.

Contribution

It develops a flexible $l^2$-$l^p$ sparse filtering approach for Herschel data, enhancing noise reduction, deconvolution, and filament detection at multiple scales.

Findings

Enhanced visualization of filamentary structures in Herschel data.

Reduced log-normal behavior in singularity spectra.

Validated deconvolution quality using magneto-hydrodynamic simulations.

Abstract

We present significant improvements to our previous work on noise reduction in {\sl 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 $l^2$-$l^p$, with $p > 0$ variable and apply it to a larger set of molecular clouds using {\sl Herschel} 250 $\mu $m data in order to demonstrate their wide range of application. In the {\sl 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.