  We consider Fourier reconstruction problem for signals F, which are linear
combinations of shifted delta-functions. We assume the Fourier transform of F
to be known on the frequency interval [-N,N], with an absolute error not
exceeding e > 0. We give an absolute lower bound (which is valid with any
reconstruction method) for the "worst case" reconstruction error of F in
situations where the nodes (i.e. the positions of the shifted delta-functions
in F) are known to form an l elements cluster of a size h << 1. Using
"decimation" reconstruction algorithm we provide an upper bound for the
reconstruction error, essentially of the same form as the lower one. Roughly,
our main result states that for N*h of order of (2l-1)-st root of e the worst
case reconstruction error of the cluster nodes is of the same order as h, and
hence the inside configuration of the cluster nodes (in the worst case
scenario) cannot be reconstructed at all. On the other hand, decimation
algorithm reconstructs F with the accuracy of order of 2l-st root of e.
