Related papers: 3D weak lensing with spin wavelets on the ball
We present a framework for analyzing weak gravitational lensing survey data, including lensing and source-density observables, plus spectroscopic redshift calibration data. All two-point observables are predicted in terms of parameters of a…
We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…
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…
Lensing peaks have been proposed as a useful statistic, containing cosmological information from non-Gaussianities that is inaccessible from traditional two-point statistics such as the power spectrum or two-point correlation functions.…
The statistical power of weak lensing measurements is principally driven by the number of high redshift galaxies whose shapes are resolved. Conventional wisdom and physical intuition suggest this is optimised by deep imaging at long (red or…
Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasilinear scales as they relied on…
In this paper, we show that high-dimensional sparse wavelet signals of finite levels can be constructed from their partial Fourier measurements on a deterministic sampling set with cardinality about a multiple of signal sparsity.
Weak gravitational lensing observations probe the spectrum and evolution of density fluctuations and the cosmological parameters which govern them but are currently limited to small fields and subject to selection biases. We show how the…
Sparse representation systems that encode signal architecture have had a profound impact on sampling and compression paradigms. Remarkable examples are multi-scale directional systems, which, similar to our vision system, encode the…
Weak gravitational lensing observations are a key science driver for the NASA Wide Field Infrared Survey Telescope (WFIRST). To validate the performance of the WFIRST infrared detectors, we have performed a laboratory emulation of weak…
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
Gravitational lensing of distant galaxies can be exploited to infer the convergence field as a function of angular position on the sky. The statistics of this field, much like that of the cosmic microwave background (CMB), can be studied to…
Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation…
Gravitational waves (GWs) exhibit wave-optics effects when their wavelength is comparable to the scale of the gravitational lens. This may occur in lensing from galactic subhalos in GWs emitted by binary black-hole mergers, and is gaining…
3D Gaussian Splatting (3DGS) has revolutionized 3D scene reconstruction, which effectively balances rendering quality, efficiency, and speed. However, existing 3DGS approaches usually generate plausible outputs and face significant…
Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…
Sparse-view 3D Gaussian Splatting (3DGS) presents significant challenges in reconstructing high-quality novel views, as it often overfits to the widely-varying high-frequency (HF) details of the sparse training views. While frequency…
This paper presents the first application of 3D cosmic shear to a wide-field weak lensing survey. 3D cosmic shear is a technique that analyses weak lensing in three dimensions using a spherical harmonic approach, and does not bin data in…
We introduce a collection of statistics appropriate for the study of spinorial quantities defined in three dimensions, focussing on applications to cosmological weak gravitational lensing studies in 3D. In particular, we concentrate on…