Accuracy of reconstruction of spike-trains with two near-colliding nodes
Abstract
We consider a signal reconstruction problem for signals F of the form F(x)=Σj=1dajδ(x-xj), from their moments mk(F)=∫ xkF(x)dx. We assume mk(F) to be known for k=0,1,…,N, with an absolute error not exceeding ε > 0. We study the "geometry of error amplification" in reconstruction of F from mk(F), in situations where two neighboring nodes xi and xi+1 near-collide, i.e xi+1-xi=h 1. We show that the error amplification is governed by certain algebraic curves SF,i, in the parameter space of signals F, along which the first three moments m0,m1,m2 remain constant.
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