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UBC Theses and Dissertations

Extracting the hierarchical wavelet coefficients from full-sky maps Abghari, Arefe


Extracting Gaussian information from data is well understood, but characterizing non-Gaussianity is challenging. I describe an approach called the “hierarchical wavelet coefficients” (HWC) method, also known as the “scattering transform”, for analysing full-sky maps and extracting non-Gaussianity information. I introduce a spherical version of the Morlet wavelet and an algorithm using the healpy package to perform the wavelet convolutions. This method is applied to the Sunyaev-Zeldovich and Galactic dust maps constructed from the Planck satellite data to characterize their non-Gaussian features. I propose that in future this method can be used as a test of component-separation methods and robustness of simulations, as well as potentially for cosmological parameter estimation. It can also be used for generating simulated fields with the same statistical features as the real data.

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