56 citations · 196 across the 25 of their papers we have counts for
9 papers · 1 filter
Accuracy of Algebraic Fourier Reconstruction for Shifts of Several Signals
Dmitry Batenkov, Niv Sarig, Yosef Yomdin
We consider the problem of "algebraic reconstruction" of linear combinations of shifts of several known signals from the Fourier samples. Following \cite{Bat.Sar.Y…
Sampling, Metric Entropy and Dimensionality Reduction
D. Batenkov, O. Friedland, Y. Yomdin
Let be a relatively compact subset in a Hilbert space . For a given $\e>0$ let $N(\e,Q)$ be the minimal number of linear measurements, sufficient to reconstruct any $x \in Q…
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…
Decoupling of Fourier Reconstruction System for Shifts of Several Signals
Dmitry Batenkov, Niv Sarig, Yosef Yomdin
We consider the problem of ``algebraic reconstruction'' of linear combinations of shifts of several signals from the Fourier samples. For each we ch…
Moment vanishing of piecewise solutions of linear ODEs
Dmitry Batenkov, Gal Binyamini
We consider the "moment vanishing problem" for a general class of piecewise-analytic functions which satisfy on each continuity interval a linear ODE with polynomial coefficients.…
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…
Taylor Domination, Turán lemma, and Poincaré-Perron Sequences
Dmitry Batenkov, Yosef Yomdin
We consider "Taylor domination" property for an analytic function in the complex disk , which is an inequality of the form \[ |a_{k}|R^{k…
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…