DocumentCode :
719346
Title :
Accuracy of spike-train Fourier reconstruction for colliding nodes
Author :
Akinshin, Andrey ; Batenkov, Dmitry ; Yomdin, Yosef
Author_Institution :
Dept. of Math., Weizmann Inst. of Sci., Rehovot, Israel
fYear :
2015
fDate :
25-29 May 2015
Firstpage :
617
Lastpage :
621
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 [-N,N] 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 ϵ1/2l-1 the worst case reconstruction error of the cluster nodes is of the same order 1/N ϵ1/2l-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 ϵ1/2l.
Keywords :
Fourier transforms; signal reconstruction; Fourier transform; cluster nodes; colliding nodes; decimation algorithm; reconstruction error; signal reconstruction; spike-train Fourier reconstruction; Accuracy; Fourier transforms; Geometry; Image resolution; Jacobian matrices; Reconstruction algorithms; Signal resolution;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Sampling Theory and Applications (SampTA), 2015 International Conference on
Conference_Location :
Washington, DC
Type :
conf
DOI :
10.1109/SAMPTA.2015.7148965
Filename :
7148965
Link To Document :
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