Related papers: Spatial-Slepian Transform on the Sphere
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…
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…
We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional…
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…
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…
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…
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…
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…
Geographic data is fundamentally local. Disease outbreaks cluster in population centers, ecological patterns emerge along coastlines, and economic activity concentrates within country borders. Machine learning models that encode geographic…
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…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
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…
While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of…
We formulate and solve the Slepian spatial-spectral concentration problem on the three-dimensional ball. Both the standard Fourier-Bessel and also the Fourier-Laguerre spectral domains are considered since the latter exhibits a number of…
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…
Slepian functions provide a solution to the optimization problem of joint time-frequency localization. Here, this concept is extended by using a generalized optimization criterion that favors energy concentration in one interval while…
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…
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,…
For the representation of spin-$s$ band-limited functions on the sphere, we propose a sampling scheme with optimal number of samples equal to the number of degrees of freedom of the function in harmonic space. In comparison to the existing…
We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal…