Related papers: Wavelet Moments for Cosmological Parameter Estimat…
Optimal extraction of the non-Gaussian information encoded in the Large-Scale Structure (LSS) of the universe lies at the forefront of modern precision cosmology. We propose achieving this task through the use of the Wavelet Scattering…
We introduce Wavelet Phase Harmonics (WPH) statistics: interpretable low-dimensional statistics that describe 2D non-Gaussian fields. These statistics are built from WPH moments, which were recently introduced in the data science and…
In this article we give an account of a method of smoothing spatial inhomogeneous data sets by using wavelet reconstruction on a regular grid in an auxilliary space onto which the original data is mapped. In a previous paper by the present…
We consider wavelets as a tool to perform a variety of tasks in the context of analyzing cosmic microwave background (CMB) maps. Using Spherical Haar Wavelets we define a position and angular-scale-dependent measure of power that can be…
Focusing on the well motivated aperture mass statistics $\Map$, we study the possibility of constraining cosmological parameters using future space based SNAP class weak lensing missions. Using completely analytical results we construct the…
The thermal state of the intergalactic medium (IGM) contains vital information about the epoch of reionization, one of the most transformative yet poorly understood periods in the young universe. This thermal state is encoded in the…
Degeneracies among parameters of the cosmological model are known to drastically limit the information contained in the matter distribution. In the first paper of this series, we shown that the cosmic web environments; namely the voids,…
We construct the spin flaglet transform, a wavelet transform to analyze spin signals in three dimensions. Spin flaglets can probe signal content localized simultaneously in space and frequency and, moreover, are separable so that their…
Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
In cosmic-ray physics, large field of view experiments are triggered by a number of signals laying on different angular scales: point-like and extended gamma-ray sources, diffuse emissions, as well as large and intermediate scale cosmic-ray…
We suggest a two-dimensional wavelet devised to deduce the large-scale structure of a physical field (e.g., the Galactic magnetic field) from its integrals along straight paths from irregularly spaced data points to a fixed interior point…
We make forecasts for the constraining power of the 1D Wavelet Scattering Transform (WST) when used with a Lyman-$\alpha$ forest cosmology survey. Using mock simulations and a Fisher matrix, we show that there is considerable cosmological…
Large-scale structure (LSS) analysis in galaxy surveys is a powerful cosmological probe but is limited by tracer bias, which can obscure underlying information and weaken parameter constraints. Existing methods either model bias or restrict…
We present a new framework for robust estimation and inference on second-order stationary time series and random fields. This framework is based on the Generalized Method of Wavelet Moments which uses the wavelet variance to achieve…
It is well known that the power spectrum is not able to fully characterize the statistical properties of non-Gaussian density fields. Recently, many different statistics have been proposed to extract information from non-Gaussian…
What do the data, as distinguished from cosmological models, tell us about cosmological parameters that determined the model of the universe? In this paper, we address this question in the context of the WMAP angular power spectra for the…
Wavelet analysis is proposed as a new tool for studying the large-scale structure formation of the universe. To reveal its usefulness, the wavelet decomposition of one-dimensional cosmological density fluctuations is performed. In contrast…
We undertake the first comprehensive and quantitative real-space analysis of the cosmological information content in the environments of the cosmic web (voids, filaments, walls, and nodes) up to non-linear scales, $k = 0.5$ $h$/Mpc. Relying…
We introduce WaveSim, a multi-scale similarity metric for the evaluation of spatial fields in weather and climate applications. WaveSim exploits wavelet transforms to decompose input fields into scale-specific wavelet coefficients. The…