Related papers: Spectral estimation on a sphere in geophysics and …
We present a semi-analytical method to investigate the systematic effects and statistical uncertainties of the calculated angular power spectrum when incomplete spherical maps are used. The computed power spectrum suffers in particular a…
Periodicity analysis of unevenly collected data is a relevant issue in several scientific fields. In astrophysics, for example, we have to find the fundamental period of light or radial velocity curves which are unevenly sampled…
In many cosmological models, the large angular scale anisotropy in the cosmic microwave background is parameterized by a spectral index, $n$, and a quadrupolar amplitude, $Q$. For a Peebles-Harrison-Zel'dovich spectrum, $n=1$. Using data…
Spectral measurements of the 21 cm monopole background have the promise of revealing the bulk energetic properties and ionization state of our universe from z ~ 6-30. Synchrotron foregrounds are orders of magnitude larger than the…
We introduce a new method for performing robust Bayesian estimation of the three-dimensional spatial power spectrum at the Epoch of Reionization (EoR), from interferometric observations. The versatility of this technique allows us to…
The problem of resolving spherical harmonic components from numerical data defined on a rectangular grid has many applications, particularly for the problem of gravitational radiation extraction. A novel method due to Misner improves on…
We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In…
We present the generalized iterative residual fitting (IRF) for the computation of the spherical harmonic transform (SHT) of band-limited signals on the sphere. The proposed method is based on the partitioning of the subspace of…
The use of multitaper estimates for spectral proper orthogonal decomposition (SPOD) is explored. Multitaper and multitaper-Welch estimators that use discrete prolate spheroidal sequences (DPSS) as orthogonal data windows are compared to the…
We describe here an iterative method for jointly estimating the noise power spectrum from a scanning experiment's time-ordered data, together with the maximum-likelihood map. We test the robustness of this method on simulated datasets with…
Quadratic methods with heuristic weighting (e.g. pseudo-C_l or correlation function methods) represent an efficient way to estimate power spectra of the cosmic microwave background (CMB) anisotropies and their polarization. We construct the…
Intensity mapping is a promising technique for surveying the large scale structure of our Universe from $z=0$ to $z \sim 150$, using the brightness temperature field of spectral lines to directly observe previously unexplored portions of…
In this article we establish optimal estimates for the first eigenvalue of Schr\"odinger operators on the d-dimensional unit sphere. These estimates depend on Lebsgue's norms of the potential, or of its inverse, and are equivalent to…
It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
A tomographic method is described to quantify the three-dimensional power-spectrum of the ionospheric electron-density fluctuations based on radio-interferometric observations by a two-dimensional planar array. The method is valid to…
Accurate estimation of the sound field around a rigid sphere necessitates adequate sampling on the sphere, which may not always be possible. To overcome this challenge, this paper proposes a method for sound field estimation based on a…
Polarization induced by cosmological scalar perturbations leads to a typical anisotropy pattern, which can best be analyzed in Fourier domain. This allows one to unambiguously distinguish cosmological signal of polarization from other…
We describe and compare several post-correlation radio frequency interference classification methods. As data sizes of observations grow with new and improved telescopes, the need for completely automated, robust methods for radio frequency…
We propose computationally efficient methods for estimating stationary multivariate spatial and spatial-temporal spectra from incomplete gridded data. The methods are iterative and rely on successive imputation of data and updating of model…