Related papers: Efficient analysis and representation of geophysic…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…
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…
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…
This work presents the construction of a novel spherical wavelet basis designed for incomplete spherical datasets, i.e. datasets which are missing in a particular region of the sphere. The eigenfunctions of the Slepian spatial-spectral…
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…
Inspired by recent interest in geometric deep learning, this work generalises the recently developed Slepian scale-discretised wavelets on the sphere to Riemannian manifolds. Through the sifting convolution, one may define translations and,…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
In this paper, we develop an analytical formulation for the Slepian spatial-spectral concentration problem on the sphere for a limited colatitude-longitude spatial region on the sphere, defined as the Cartesian product of a range of…
Wavelets are widely used in various disciplines to analyse signals both in space and scale. Whilst many fields measure data on manifolds (i.e., the sphere), often data are only observed on a partial region of the manifold. Wavelets are a…
We present spatial-Slepian transform~(SST) for the representation of signals on the sphere to support localized signal analysis. We use well-optimally concentrated Slepian functions, obtained by solving the Slepian spatial-spectral…
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the…
We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of…
In this paper, we develop a new method for the fast and memory-efficient computation of Slepian functions on the sphere. Slepian functions, which arise as the solution of the Slepian concentration problem on the sphere, have desirable…
Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…
Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth's surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the…
We pose and solve the analogue of Slepian's time-frequency concentration problem in the two-dimensional plane, for applications in the natural sciences. We determine an orthogonal family of strictly bandlimited functions that are optimally…
This paper introduces topological Slepians, i.e., a novel class of signals defined over topological spaces (e.g., simplicial complexes) that are maximally concentrated on the topological domain (e.g., over a set of nodes, edges, triangles,…
In the framework of a recently reported linear-scaling method for density-functional-pseudopotential calculations, we investigate the use of localized basis functions for such work. We propose a basis set in which each local orbital is…
We construct spherical vector bases that are bandlimited and spatially concentrated, or, alternatively, spacelimited and spectrally concentrated, suitable for the analysis and representation of real-valued vector fields on the surface of…
We present a simple, robust and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on…