  The interstellar medium (ISM) is a complex non-linear system governed by
gravity and magneto-hydrodynamics, as well as radiative, thermodynamical, and
chemical processes. Our understanding of it mostly progresses through
observations and numerical simulations, and a quantitative comparison between
these two approaches requires a generic and comprehensive statistical
description. The goal of this paper is to build such a description, with the
purpose to permit an efficient comparison independent of any specific prior or
model. We start from the Wavelet Scattering Transform (WST), a low-variance
statistical description of non-Gaussian processes, developed in data science,
that encodes long-range interactions through a hierarchical multiscale approach
based on the Wavelet transform. We perform a reduction of the WST through a fit
of its angular dependencies, allowing to gather most of the information it
contains into a few components whose physical meanings are identified, and that
describe, e.g., isotropic and anisotropic behaviours. The result of this paper
is the Reduced Wavelet Scattering Transform (RWST), a statistical description
with a small number of coefficients that characterizes complex structures
arising from non-linear phenomena, free from any specific prior. The RWST
coefficients encode moments of order up to four, have reduced variances, and
quantify the couplings between scales. To show the efficiency and generality of
this description, we apply it successfully to three kinds of processes:
fractional Brownian motions, MHD simulations, and Herschel observations in a
molecular cloud. With fewer than 100 coefficients when probing 6 scales and 8
angles on 256*256 maps, we were able with the RWST to perform quantitative
comparisons, to infer relevant physical properties, and to produce realistic
synthetic fields.
