Related papers: Fast Convolution on the Sphere
We present a case study describing efforts to optimise and modernise "Modal", the simulation and analysis pipeline used by the Planck satellite experiment for constraining general non-Gaussian models of the early universe via the bispectrum…
M\"obius transformations play an important role in both geometry and spherical image processing - they are the group of conformal automorphisms of 2D surfaces and the spherical equivalent of homographies. Here we present a novel,…
A new method for estimating the angular power spectrum C_l from cosmic microwave background (CMB) maps is presented, which has the following desirable properties: (1) It is unbeatable in the sense that no other method can measure C_l with…
We propose a simple method for uniform sampling of points on the surface of a hypersphere in arbitrarily many dimensions. By avoiding the evaluation of computationally expensive functions like logarithms, sines, cosines, or higher order…
The confrontation of the Cosmic Microwave Background (CMB) theoretical angular power spectrum with available data often requires the calculation of large numbers of power spectra. The standard practice is to use a fast code to compute the…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
Most of the calculations in standard sphere decoders are redundant, in the sense that they either calculate quantities that are never used or calculate some quantities more than once. A new method, which is applicable to lattices as well as…
We present an augmented version of our dual messenger algorithm for spin field reconstruction on the sphere, while accounting for highly non-trivial and realistic noise models such as modulated correlated noise. We also describe an…
In radio astronomy obtaining a high dynamic range in synthesis imaging of wide fields requires a correction for time and direction-dependent effects. Applying direction-dependent correction can be done by either partitioning the image in…
An improved method for subtracting contaminants from Cosmic Microwave Background (CMB) sky maps is presented, and used to estimate how well future experiments will be able to recover the primordial CMB fluctuations. We find that the naive…
We present a method for the computation of the variance of cosmic microwave background (CMB) temperature maps on azimuthally symmetric patches using a fast convolution approach. As an example of the application of the method, we show…
We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The…
We present a simple approximation that can speed up the computation of the mode-coupling matrices, which are usually the bottleneck for computing unbiased angular power spectra, as well as their associated covariance matrices, of the cosmic…
It is well known that our motion with respect to the cosmic microwave background (CMB) rest frame introduces a large dipolar CMB anisotropy, with an amplitude ~beta=v/c~10^{-3}. In addition it should lead to a small breaking of statistical…
We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating…
One of the main goals of modern observational cosmology is to map the large scale structure of the Universe. A potentially powerful approach for doing this would be to exploit three-dimensional spectral maps, i.e. the specific intensity of…
This work describes a new version of the Fast Multipole Method for summing pairwise particle interactions that arise from discretizing integral transforms and convolutions on the sphere. The kernel approximations use barycentric Lagrange…
Important problems across multiple disciplines involve computations on the semiring $(\times, \max)$ (or its equivalents, the negated version $(\times, \min)$), the log-transformed version $(+, \max)$, or the negated log-transformed version…
We present a new method for calculating CMB anisotropies in a non-flat Friedmann universe, relying on a very stable algorithm for the calculation of hyperspherical Bessel functions, that can be pushed to arbitrary precision levels. We also…
We have developed a fast, accurate and generally applicable method for inferring the power spectrum and its uncertainties from maps of the cosmic microwave background (CMB) in the presence of inhomogeneous and correlated noise. For maps…