Title

Error Analysis Of Frame Reconstruction From Noisy Samples

Keywords

Frames; Reconstruction from averages; Sampling

Abstract

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 σ2. We sample the continuous function f on the uniform lattice (1/m)Zd, and show for large enough m that the variance of the error between the frame reconstruction fε,m from noisy samples of f and the function f satisfy var(fepsi;,m(x)-f(x))≈(σ2/md) Cx where Cx is the best constant for every χ ∈ Rd. We also prove a similar result in the case that our data are weighted-average samples of f corrupted by additive noise. © 2008 IEEE.

Publication Date

6-1-2008

Publication Title

IEEE Transactions on Signal Processing

Volume

56

Issue

6

Number of Pages

2311-2325

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/TSP.2007.913138

Socpus ID

44849143942 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/44849143942

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