Local and Global Geometry of Prony Systems and Fourier Reconstruction of Piecewise-Smooth Functions

  • D. Batenkov
  • Y. YomdinEmail author
Conference paper
Part of the Abel Symposia book series (ABEL, volume 9)


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 solvability and stable inversion. Of special interest are the so-called “near-singular” situations, such as a collision of two closely spaced nodes. We also discuss the problem of reconstructing piecewise-smooth functions from their Fourier coefficients, which is easily reduced by a well-known method of K. Eckhoff to solving a particular Prony system. As we show in the paper, it turns out that a modification of this highly nonlinear method can reconstruct the jump locations and magnitudes of such functions, as well as the pointwise values between the jumps, with the maximal possible accuracy.


Piecewise Smooth Functions Fourier Reconstruction Multiplicity Vector Finite Divided Difference Rank Strata 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsBen Gurion University of the NegevBeer ShevaIsrael
  2. 2.Department of MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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