  Detecting the cosmic 21-cm signal during the Epoch of Reionisation and Cosmic
Dawn will reveal insights into the properties of the first galaxies and advance
cosmological parameter estimation. Until recently, the primary focus for
astrophysical parameter inference from the 21-cm signal centred on the power
spectrum (PS). However, the cosmic 21-cm signal is highly non-Gaussian
rendering the PS sub-optimal for characterising the cosmic signal. In this
work, we introduce a new technique to analyse the non-Gaussian information in
images of the 21-cm signal called the Wavelet Scattering Transform (WST). This
approach closely mirrors that of convolutional neural networks with the added
advantage of not requiring tuning or training of a neural network. Instead, it
compresses the 2D spatial information into a set of coefficients making it
easier to interpret while also providing a robust statistical description of
the non-Gaussian information contained in the cosmic 21-cm signal. First, we
explore the application of the WST to mock 21-cm images to gain valuable
physical insights by comparing to the known behaviour from the 21-cm PS. Then
we quantitatively explore the WST applied to the 21-cm signal by extracting
astrophysical parameter constraints using Fisher Matrices from a realistic 1000
hr mock observation with the Square Kilometre Array. We find that: (i) the WST
applied only to 2D images can outperform the 3D spherically averaged 21-cm PS,
(ii) the excision of foreground contaminated modes can degrade the constraining
power by a factor of ~1.5-2 with the WST and (iii) higher cadences between the
21-cm images can further improve the constraining power.

Cosmology and Nongalactic Astrophysics