Related papers: Reconstructing Functions from Random Samples

In this paper we extend results on reconstruction of probabilistic supports of random i.i.d variables to supports of dependent stationary $\mathbb R^d$-valued random variables. All supports are assumed to be compact of positive reach in…

The paper surveys recent progress in understanding geometric, topological and combinatorial properties of large simplicial complexes, focusing mainly on ampleness, connectivity and universality. In the first part of the paper we concentrate…

We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…

We consider the problem of reconstructing a function given its values on a set of points with finite density. We prove that with probability one, the values of an almost periodic function on a random array of points (with finite density)…

Let $\Gamma$ be a closed subset of a complete Riemannian manifold $M$ of dimension $\geq 2$, let $f: M \to N$ be a Lipschitz map to a complete Riemannian manifold $N$, and let $\psi$ be a continuous function which dominates the local…

Image registration is a widespread problem which applies models about image transformation or image similarity to align discrete images of the same scene. Nevertheless, the theoretical limits on its accuracy are not understood even in the…

In this paper, we will study the partial regularity theorem for stationary harmonic maps from a Riemannian manifold into a Lorentzian manifold. For a weakly stationary harmonic map $(u,v)$ from a smooth bounded open domain…

Consider a family of bounded domains $\Omega_{t}$ in the plane (or more generally any Euclidean space) that depend analytically on the parameter $t$, and consider the ordinary Neumann Laplacian $\Delta_{t}$ on each of them. Then we can…

In this work, we construct a proximal average for two prox-bounded functions, which recovers the classical proximal average for two convex functions. The new proximal average transforms continuously in epi-topology from one proximal hull to…

In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean spaces and Heisenberg groups. In addition to…

Let P be a closed triangulated manifold, dim P=n. We consider the group of simplicial 1-chains C_1(P) and the homology group H_1(P). We also use some nonnegative weighting function L on C_1(P). For any homological class from H_1(P) method…

In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to…

We show that every closed, locally homogeneous Riemannian manifold with positive simplicial volume must be homeomorphic to a locally symmetric space of non-compact type.

For a wide family of even kernels $\{\varphi_u, u\in I\}$, we describe discrete sets $\Lambda$ such that every bandlimited signal $f$ can be reconstructed from the space-time samples $\{(f\ast\varphi_u)(\lambda), \lambda\in\Lambda, u\in…

We show that limits of sequences of smooth maps between compact Riemannian manifolds with equi-integrable $W^{1, p}$-Sobolev energy can always be strongly approximated by smooth maps, giving a counterpart of Hang's density result in $W^{1,…

We give a procedure for "reverse engineering" a closed, simply connected, Riemannian manifold with bounded local geometry from a sparse chain complex over $\mathbb{Z}$. Applying this procedure to chain complexes obtained by "lifting"…

We show, as our main theorem, that if a Lipschitz map from a compact Riemannian manifold $M$ to a connected compact Riemannian manifold $N$, where $\dim M \geq \dim N$, has no singular points on $M$ in the sense of F.H. Clarke, then the map…

This article studies the smoothness of conformal mappings between two Riemannian manifolds whose metric tensors have limited regularity. We show that any bi-Lipschitz conformal mapping or $1$-quasiregular mapping between two manifolds with…

The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…

Infinite-dimensional, holomorphic functions have been studied in detail over the last several decades, due to their relevance to parametric differential equations and computational uncertainty quantification. The approximation of such…