@inproceedings{70b5266f521848d6949192db2fe4615e,
title = "Accuracy of spike-train Fourier reconstruction for colliding nodes",
abstract = "We consider a signal reconstruction problem for signals F of the form F(x) = Σdj=1 ajδ(x-xj) from their Fourier transform F(F)(s) = ∫∞-∞ F(x)e-isxdx. We assume F(F)(s) to be known for each s ε [-Ν,Ν] with an absolute error not exceeding ε > 0. We give an absolute lower bound (which is valid with any reconstruction method) for the 'worst case' reconstruction error of F from F(F) for situations where the xj nodes are known to form an I elements cluster contained in an interval of length h << 1. Using 'decimation' algorithm of [6], [7] 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 h of order 1/N 1/2l-1 the worst case reconstruction error of the cluster nodes is of the same order 1/N 1/2l-1, 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 1/N 1/2l.",
author = "Andrey Akinshin and Dmitry Batenkov and Yosef Yomdin",
note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; 11th International Conference on Sampling Theory and Applications, SampTA 2015 ; Conference date: 25-05-2015 Through 29-05-2015",
year = "2015",
month = jul,
day = "2",
doi = "10.1109/SAMPTA.2015.7148965",
language = "الإنجليزيّة",
series = "2015 International Conference on Sampling Theory and Applications, SampTA 2015",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "617--621",
booktitle = "2015 International Conference on Sampling Theory and Applications, SampTA 2015",
address = "الولايات المتّحدة",
}