Stable soft extrapolation of entire functions
D Batenkov, L Demanet, HN Mhaskar - Inverse Problems, 2018 - iopscience.iop.org
D Batenkov, L Demanet, HN Mhaskar
Inverse Problems, 2018•iopscience.iop.orgSoft extrapolation refers to the problem of recovering a function from its samples, multiplied
by a fast-decaying window and perturbed by an additive noise, over an interval which is
potentially larger than the essential support of the window. To achieve stable recovery one
must use some prior knowledge about the function class, and a core theoretical question is
to provide bounds on the possible amount of extrapolation, depending on the sample
perturbation level and the function prior.
by a fast-decaying window and perturbed by an additive noise, over an interval which is
potentially larger than the essential support of the window. To achieve stable recovery one
must use some prior knowledge about the function class, and a core theoretical question is
to provide bounds on the possible amount of extrapolation, depending on the sample
perturbation level and the function prior.
Abstract
Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which is potentially larger than the essential support of the window. To achieve stable recovery one must use some prior knowledge about the function class, and a core theoretical question is to provide bounds on the possible amount of extrapolation, depending on the sample perturbation level and the function prior.
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