Title: Describe and model without learning using wavelet scattering-like statistics: an application to Galactic dust emission
In Cosmology, the emission of interstellar dust is a main obstacle to the search for primordial B-modes in the cosmic microwave background. The complexity of the physics of the interstellar medium makes the statistical characterization of this emission a major challenge. To account for the non-Gaussian statistics of its spatial distribution, we need statistical descriptors that accurately quantify couplings across scales. In this talk, I employ the wavelet scattering transform (WST) and the wavelet phase harmonics (WPH) to derive multiscale representations of dust maps that allow me to describe and model the non-Gaussian properties of dust emission based on a very small amount of data. WST representations can be simplified by leveraging regularity in the data. The outcome of this, called “reduced” WST, provides a very low-dimensional statistical description of dust maps, quantifying their properties in terms of isotropic and anisotropic contributions. Then, I show how the RWST, and similarly the WPH, may define realistic generative statistical models of this data. Finally, when noise becomes prominent in the data and contaminates these representations, I propose a strategy designed to recover the non-Gaussian properties of the noise-free emission.
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