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Error Analysis of Frame Reconstruction From Noisy Samples

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3 Author(s)
Aldroubi, A. ; Dept. of Math., Vanderbilt Univ., Nashville, TN ; Leonetti, C. ; Qiyu Sun

This paper addresses the problem of reconstructing a continuous function defined on Rd from a countable collection of samples corrupted by noise. The additive noise is assumed to be i.i.d. with mean zero and variance sigma2. We sample the continuous function / on the uniform lattice (1/m)Zd, and show for large enough m that the variance of the error between the frame reconstruction fepsiv,m from noisy samples of f and the function f satisfy var(fepsiv,m(x) - f(x)) ap(sigma2/md)Cx where Cx is the best constant for every x isin Rd. We also prove a similar result in the case that our data are weighted-average samples of / corrupted by additive noise.

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Signal Processing, IEEE Transactions on  (Volume:56 ,  Issue: 6 )