DMCA
Error analysis of frame reconstruction from noisy samples
| Venue: | λ∈Λ M. ZUHAIR NASHED AND QIYU SUN |
| Citations: | 7 - 2 self |
BibTeX
@INPROCEEDINGS{Aldroubi_erroranalysis,
author = {Akram Aldroubi and Qiyu Sun},
title = {Error analysis of frame reconstruction from noisy samples},
booktitle = {λ∈Λ M. ZUHAIR NASHED AND QIYU SUN},
year = {}
}
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Abstract
Abstract — This paper addresses the problem of reconstructing a continuous function defined on R d from a countable collection of samples corrupted by noise. The additive noise is assumed to be i.i.d. with mean zero and variance σ 2. 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(fε,m(x)−f(x)) ≈ σ2 md Cx where Cx is the best constant for every x ∈ R d. We also prove a similar result in the case that our data are weighted-average samples of f corrupted by additive noise. Index Terms — Sampling, reconstruction from averages, frames. I.
