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Detecting the cosmic 21-cm signal during the Epoch of Reionisation and CosmicDawn will reveal insights into the properties of the first galaxies and advancecosmological parameter estimation. Until recently, the primary focus forastrophysical parameter inference from the 21-cm signal centred on the powerspectrum (PS). However, the cosmic 21-cm signal is highly non-Gaussianrendering the PS sub-optimal for characterising the cosmic signal. In thiswork, we introduce a new technique to analyse the non-Gaussian information inimages of the 21-cm signal called the Wavelet Scattering Transform (WST). Thisapproach closely mirrors that of convolutional neural networks with the addedadvantage of not requiring tuning or training of a neural network. Instead, itcompresses the 2D spatial information into a set of coefficients making iteasier to interpret while also providing a robust statistical description ofthe non-Gaussian information contained in the cosmic 21-cm signal. First, weexplore the application of the WST to mock 21-cm images to gain valuablephysical insights by comparing to the known behaviour from the 21-cm PS. Thenwe quantitatively explore the WST applied to the 21-cm signal by extractingastrophysical parameter constraints using Fisher Matrices from a realistic 1000hr mock observation with the Square Kilometre Array. We find that: (i) the WSTapplied only to 2D images can outperform the 3D spherically averaged 21-cm PS,(ii) the excision of foreground contaminated modes can degrade the constrainingpower by a factor of ~1.5-2 with the WST and (iii) higher cadences between the21-cm images can further improve the constraining power.

Exploring the cosmic 21-cm signal from the Epoch of Reionisation using the Wavelet Scattering Transform