New statistical descriptions related to the so-called Scattering Transform recently obtained attractive results for several astrophysical applications. These statistics share ideas with convolutional neural networks, but do not require to be learned, allowing for very efficient characterization of non-Gaussian processes from a very small amount of data. In this talk, I will introduce these statistical descriptions, and give an overview of the different results they allowed to obtain recently. I will focus on ongoing works on non-Gaussian modeling and component separation directly from observational data, in the scientific context of CMB B-mode detection beyond Galactic foregrounds.
