Related papers: Sparsity for isotropic spherical random fields
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
In this paper, we review the history, current state-of-art, and physical applications of the spectral theory of two classes of random functions. One class consists of homogeneous and isotropic random fields defined on a Euclidean space and…
We develop criteria for hitting probabilities of anisotropic Gaussian random fields with associated canonical pseudo-metric given by a class of gauge functions. This yields lower and upper bounds in terms of general notions of capacity and…
Random projection is often used to project higher-dimensional vectors onto a lower-dimensional space, while approximately preserving their pairwise distances. It has emerged as a powerful tool in various data processing tasks and has…
Gaussian Markov random fields are used in a large number of disciplines in machine vision and spatial statistics. The models take advantage of sparsity in matrices introduced through the Markov assumptions, and all operations in inference…
The structured sparsity can be leveraged in traditional far-field channels, greatly facilitating efficient sparse channel recovery by compressing the complexity of overheads to the level of the scatterer number. However, when experiencing a…
Provided a random realization of the cosmological model, observations of our cosmic neighborhood now allow us to build simulations of the latter down to the non-linear threshold. The resulting local Universe models are thus accurate up to a…
The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…
Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these…
Explicit and compact expressions describing the reflection and the transmission of a Gaussian beam by anisotropic parallel plates are given. Multiple reflections inside the plate are taken into account as well as arbitrary optical axis…
Non-Gaussianity in the cosmic microwave background and the large-scale structure of galaxies provides an increasingly powerful probe of the universe. I implement an algorithm to generate realisations of fields that possess an arbitrary…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by…
The paper analyses a spectral approach to reconstructing a scalar field on the sphere, given only information about a masked version of the field together with precise information about the (smooth) mask. The theory is developed for a…
We designed and built a novel model of a deployed space telescope which can reliably align its segments to achieve the finest possible resolution. An asymmetric design of both the segment shapes and their pupil locations were tested in…
The statistical translation invariance of cosmological random fields is broken by a finite survey boundary, correlating the observable Fourier modes. Standard methods for generating Gaussian fields either neglect these correlations, or are…
We consider a fast approximation method for a solution of a certain stochastic non-local pseudodifferential equation. This equation defines a Mat\'ern class random field. The approximation method is based on the spectral compactness of the…
We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S^2. Our techniques rely heavily on group representation theory, and specifically on the properties of Wigner matrices and…
The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an…