On stability of sampling-reconstruction models |
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Authors: | Ernesto Acosta-Reyes Akram Aldroubi Ilya Krishtal |
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Affiliation: | 1. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA 2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115, USA
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Abstract: | A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this paper we prove this result for a large class of sampling models. We define different classes of perturbations and present a way of quantifying the robustness of a model with respect to them. We also use the theory of localized frames to study the dual frame method for recovering the original signal from its samples. |
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