Related papers: Sparse Isotropic Regularization for Spherical Harm…
The orthonormal set of Spherical Harmonics provides a natural way of expanding whole sky redshift and peculiar velocity surveys.
The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $\ell_2$ penalties are compared to so-called sparsity promoting $\ell_1$ and $\ell_0$ penalties, and a…
This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel…
We consider the isoperimetric problem in $\mathbb R^n$ with density for the planar case $n=2$. We show that, if the density is ${\rm C}^{0,\alpha}$, then the boundary of any isoperimetric is of class ${\rm C}^{1,\frac \alpha{3-2\alpha}}$.…
Spherical harmonic expansions are well-established tools for estimating magnetic fields from surface measurements and are widely used in applications such as tomographic imaging, geomagnetism, and biomagnetism. Although the mathematical…
In this work, we are interested in the differential geometry of curves in the simply isotropic and pseudo-isotropic 3-spaces, which are examples of Cayley-Klein geometries whose absolute figure is given by a plane at infinity and a…
A methodology to perform topological regularization via information filtering network is introduced. This methodology can be directly applied to covariance selection problem providing an instrument for sparse probabilistic modeling with…
We study generalization in an overparameterized continual linear regression setting, where a model is trained with L2 (isotropic) regularization across a sequence of tasks. We derive a closed-form expression for the expected generalization…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
Pairwise Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. Variables correspond to nodes of a graph, with edges between nodes corresponding to conditional…
Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically,…
Faraday tomography (or rotation measure synthesis) is a procedure to convert linear polarization spectra into the Faraday dispersion function, which provides us with unique information of magneto-ionic media along the line of sight.…
Statistical isotropy (SI) has been one of the simplifying assumptions in cosmological model building. Experiments like WMAP and PLANCK are attempting to test this assumption by searching for specific signals in the Cosmic Microwave…
Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…
The Sphere Covering Inequality was introduced in \cite{GM} (\emph{Invent. Math.}, 2018) as a sharp geometric inequality that provides a lower bound for the total area of two distinct surfaces of Gaussian curvature 1. These surfaces are…
In climate and atmospheric research, many phenomena involve more than one meteorological spatial processes covarying in space. To understand how one process is affected by another, maximum covariance analysis (MCA) is commonly applied.…
For the first time, this paper investigates the phase retrieval problem with the assumption that the phase (of the complex signal) is sparse in contrast to the sparsity assumption on the signal itself as considered in the literature of…