Untangling dust emission and CIB anisotropies with the Scattering Transform Statistics

Template-fit approach is often used to separate the Galactic dust emission and the cosmic infrared background (CIB) anisotropies at low $\text{HI}$ column density regions with an underlying assumption that the gas and dust are tightly correlated. However, this method fails in regions where additional Galactic emission within the molecular hydrogen, diffuse ionized gas, and dark gas are present. We develop and test a statistical component separation to extract the dust signal from the contaminated $\textit{Planck}$ $353\,\rm GHz$ observations using the Scattering Covariance (SC) statistics. We first obtain a set CIB maps over $25$ square patches, each with a sky area of $222\,{\rm deg}^{2}$, using the linear correlation of dust and Galactic $21\,\rm cm$ $\text{HI}$ emission valid at low $\text{HI}$ column density regions using the template-fit approach. We then construct, from these $25$ maps, a generative model of CIB using the SC statistics. We finally rely on this contamination model to perform a component separation of dust and CIB in the $\textit{Planck}$ data for different sky regions. Applying our algorithm to the $\textit{Planck}$ $353\,\rm GHz$ observations, we recover a dust map for a test sky region that has more structures as compared to the corrected SFD map at $100\,\mu \rm m$. The differences seen in the map level can be explained by decomposing the recovered $\textit{Planck}$ dust map into two gas phases: dust associated with $N_{\text{HI}}$ and dust associated with $N_{\text{H}_{2}}$. This work provides a clear pathway to map the Galactic interstellar reddening over intermediate and high Galactic latitudes.