On stability of sampling-reconstruction models. (English) Zbl 1166.62300
Summary: A useful sampling-reconstruction model should be stable with respect to different kinds of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. 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.
MSC:
| 62B99 | Sufficiency and information |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 46N30 | Applications of functional analysis in probability theory and statistics |
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