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We consider a signal reconstruction problem for signals F of the form F(x) = Sigma(d)(j=1) a(j)delta (x-xj) , from their moments m(k) (F) = integral x(k) F(x)dx. We assume m(k) (F) to be known for k = 0,1,...., N, with an absolute error not exceeding epsilon > 0.We study the "geometry of error amplification" in reconstruction of F from m(k) (F), in situations where two neighboring nodes x(i) and x(i+1) near-collide, i.e x(i+1) - x(i) = h << 1.We show that the error amplification is governed by certain algebraic curves S (F,i,) in the parameter space of signals F, along which the first three moments m(0), m(1), m(2) remain constant.


Akinshin, Andrey;  Goldman, Gil;  Golubyatnikov, Vladimir;  Yomdin, Yosef

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