On Algebraic Properties of Low Rank Approximations of Prony Systems

Gil Goldman*, Yosef Yomdin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the reconstruction of spike train signals of the form F(x)=∑i=1daiδ(x-xi),from their moments measurements mk(F)=∫xkF(x)dx=∑i=1daixk. When some of the nodes xi near collide the inversion becomes unstable. Given noisy moments measurements, a typical consequence is that reconstruction algorithms estimate the signal F with a signal having fewer nodes, F~. We derive lower bounds for the moments difference between a signal F with d nodes and a signal F~ with strictly less nodes, l. Next we consider the geometry of the non generic case of d nodes signals F, for which there exists an l< d nodes signal F~ , with moments m0(F~)=m0(F),…,mp(F~)=mp(F),p>2l-1.We give a complete description for the case of a general d, l= 1 and p= 2. We give a reference for the case p= 2 l- 1 which can be inferred from earlier work.

Original languageEnglish
Pages (from-to)2799-2811
Number of pages13
JournalComplex Analysis and Operator Theory
Issue number6
StatePublished - 1 Sep 2019
Externally publishedYes


  • Moments inversion
  • Non-linear models
  • Signal acquisition
  • Singularities


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