Related papers: Prony's method on the sphere
Prony's method is a prototypical eigenvalue analysis based method for the reconstruction of a finitely supported complex measure on the unit circle from its moments up to a certain degree. In this note, we give a generalization of this…
In this paper, we address the problem of reconstruction of support of a measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure…
Prony's method, in its various concrete algorithmic realizations, is concerned with the reconstruction of a sparse exponential sum from integer samples. In several variables, the reconstruction is based on finding the variety for a zero…
The paper gives an extension of Prony's method to the multivariate case which is based on the relationship between polynomial interpolation, normal forms modulo ideals and H--bases.
The parameter reconstruction problem in a sum of Dirac measures from its low frequency trigonometric moments is well understood in the univariate case and has a sharp transition of identifiability with respect to the ratio of the separation…
We study the problem of recovering an atomic measure on the unit 2-sphere $\mathbb{S}^2$ given finitely many moments with respect to spherical harmonics. The analysis relies on the formulation of this problem as an optimization problem on…
The generalized operator-based Prony method is an important tool for describing signals which can be written as finite linear combinations of eigenfunctions of certain linear operators. On the other hand, Bernoulli's algorithm and its…
The paper considers a symbolic approach to Prony's method in several variables and its close connection to multivariate polynomial interpolation. Based on the concept of universal interpolation that can be seen as a weak generalization of…
In this paper we establish accuracy bounds of Prony's method (PM) for recovery of sparse measures from incomplete and noisy frequency measurements, or the so-called problem of super-resolution, when the minimal separation between the points…
This manuscript transfers the main aspects of Prony's method from finitely-supported measures to the classes of signed or non-negative measures supported on algebraic varieties of any dimension. In particular, we show that the Zariski…
Recovering probability measures from moments is a central theme in statistics and optimization. In particular, we focus on the recovery of measures from moments and pseudo-moments, which may come from solving the moment-SOS hierarchy in one…
We propose an algebraic framework generalizing several variants of Prony's method and explaining their relations. This includes Hankel and Toeplitz variants of Prony's method for the decomposition of multivariate exponential sums,…
We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
Complex signed measures of finite total variation are a powerful signal model in many applications. Restricting to the $d$-dimensional torus, finitely supported measures allow for exact recovery if the trigonometric moments up to some order…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
We introduce an interpolation--regression operator for polynomial approximation on the unit sphere $\mathbb{S}^2$ from discrete samples. The approximant is a spherical polynomial of degree $r$ which interpolates the data on a prescribed…
In this paper, we develop a general method to estimate the instantaneous frequencies of the modes making up a multicomponent signal when the former exhibit interference in the time-frequency plane. In particular, studying the representation…
Many reconstruction problems in signal processing require solution of a certain kind of nonlinear systems of algebraic equations, which we call Prony systems. We study these systems from a general perspective, addressing questions of global…