Related papers: Sampling the X-ray transform on simple surfaces
Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of $n$ functions over a convex…
Folded sampling replaces clipping in analog-to-digital converters by reducing samples modulo a threshold, thereby avoiding saturation artifacts. We study the reconstruction of bandlimited functions from folded samples and show that, for…
We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral…
We consider circles on a translation surface $X$, consisting of points joined to a common center point by a geodesic of length $R$. We show that as $R \to \infty$ these circles distribute to a measure on $X$ which is equivalent to the area.…
Sampling is a pivotal element in the design of metasurfaces, enabling a broad spectrum of applications. Despite its flexibility, sampling can result in reduced efficiency and unintended diffractions, which are more pronounced at high…
In the real world, we often come across soft objects having spatially varying stiffness, such as human palm or a wart on the skin. In this paper, we propose a novel approach to render thin, deformable objects having spatially varying…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
Any finite configuration of curves with minimal intersections on a surface is a configuration of shortest geodesics for some Riemannian metric on the surface. The metric can be chosen to make the lengths of these geodesics equal to the…
We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used…
Both in terrestrial and extraterrestrial environments, the precise and informative model of the ground and the surface ahead is crucial for navigation and obstacle avoidance. The ground surface is not always flat and it may be sloped, bumpy…
We introduce an algorithm for computing geodesics on sampled manifolds that relies on simulation of quantum dynamics on a graph embedding of the sampled data. Our approach exploits classic results in semiclassical analysis and the…
One of the main problems in the studies of large scale galaxy structures concerns the relation of the correlation properties of a certain population of objects with those of a selected subsample of it, when the selection is performed by…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
In this paper, we consider the inverse problem of determining an unknown function defined in three space dimensions from its geodesic X-ray transform. The standard X-ray transform is defined on the Euclidean metric and is given by the…
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…
It is shown that the tessellation of a compact, negatively curved surface induced by a typical long geodesic segment, when properly scaled, looks locally like a Poisson line process. This implies that the global statistics of the…
The 3D Gaussian splatting methods are getting popular. However, they work directly on the signal, leading to a dense representation of the signal. Even with some techniques such as pruning or distillation, the results are still dense. In…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…
We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most $L$ on a compact surface equipped with a Riemannian metric of negative curvature. The proof relies on the…
We propose a method of reduction of experimental noise in single-pixel imaging by expressing the subsets of sampling patterns as linear combinations of vertices of a multidimensional regular simplex. This method may be also directly…