56 citations · 196 across the 25 of their papers we have counts for
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Algebraic Reconstruction of Piecewise-Smooth Functions of Two Variables from Fourier Data
Michael Levinov, Yosef Yomdin, Dmitry Batenkov
We investigate the problem of reconstructing a 2D piecewise smooth function from its bandlimited Fourier measurements. This is a well known and well studied problem with many real…
On the accuracy of Prony's method for recovery of exponential sums with closely spaced exponents
Rami Katz, Nuha Diab, Dmitry Batenkov
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 supe…
Decimated Prony's Method for Stable Super-resolution
Rami Katz, Nuha Diab, Dmitry Batenkov
We study recovery of amplitudes and nodes of a finite impulse train from noisy frequency samples. This problem is known as super-resolution under sparsity constraints and has numer…
Super-resolution of generalized spikes and spectra of confluent Vandermonde matrices
Dmitry Batenkov, Nuha Diab
We study the problem of super-resolution of a linear combination of Dirac distributions and their derivatives on a one-dimensional circle from noisy Fourier measurements. Following…
Single-exponential bounds for the smallest singular value of Vandermonde matrices in the sub-Rayleigh regime
Dmitry Batenkov, Gil Goldman
Following recent interest by the community, the scaling of the minimal singular value of a Vandermonde matrix with nodes forming clusters on the length scale of Rayleigh distance o…
The spectral properties of Vandermonde matrices with clustered nodes
Dmitry Batenkov, Benedikt Diederichs, Gil Goldman +1
We study rectangular Vandermonde matrices with rows and irregularly spaced nodes on the unit circle, in cases where some of the nodes are "clustered" togethe…
Super-resolution of near-colliding point sources
Dmitry Batenkov, Gil Goldman, Yosef Yomdin
We consider the problem of stable recovery of sparse signals of the form from their spectral measureme…
Conditioning of partial nonuniform Fourier matrices with clustered nodes
Dmitry Batenkov, Laurent Demanet, Gil Goldman +1
We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with arbitrary "off the grid" nodes (equivalently, a rectangular Vandermonde matrix with the…
Stable soft extrapolation of entire functions
Dmitry Batenkov, Laurent Demanet, Hrushikesh N. Mhaskar
Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which…
Accurate solution of near-colliding Prony systems via decimation and homotopy continuation
Dmitry Batenkov
We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding"…
Stability and super-resolution of generalized spike recovery
Dmitry Batenkov
We consider the problem of recovering a linear combination of Dirac delta functions and derivatives from a finite number of Fourier samples corrupted by noise. This is a generalize…
Decimated generalized Prony systems
Dmitry Batenkov
We continue studying robustness of solving algebraic systems of Prony type (also known as the exponential fitting systems), which appear prominently in many areas of mathematics, i…
Algebraic signal sampling, Gibbs phenomenon and Prony-type systems
Dmitry Batenkov, Yosef Yomdin
Systems of Prony type appear in various signal reconstruction problems such as finite rate of innovation, superresolution and Fourier inversion of piecewise smooth functions. We pr…
Geometry and Singularities of the Prony mapping
Dmitry Batenkov, Yosef Yomdin
Prony mapping provides the global solution of the Prony system of equations \[ Σ_{i=1}^{n}A_{i}x_{i}^{k}=m_{k},\ k=0,1,...,2n-1. \] This system appears in numerous theoretical and…
Local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions
Dmitry Batenkov, Yosef Yomdin
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 system…
On the norm of inverses of confluent Vandermonde matrices
Dmitry Batenkov
In this note we present a simple upper bound for the row-wise norm of the inverses of general confluent Vandermonde matrices.
Complete Algebraic Reconstruction of Piecewise-Smooth Functions from Fourier Data
Dmitry Batenkov
In this paper we provide a reconstruction algorithm for piecewise-smooth functions with a-priori known smoothness and number of discontinuities, from their Fourier coefficients, po…