NDLI: Optimal indirect estimation for linear inverse problems with discretely sampled functional data

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Optimal indirect estimation for linear inverse problems with discretely sampled functional data

Content Provider	Scilit
Author	Pricop-Jeckstadt, Mihaela
Copyright Year	2021
Description	Journal: Inverse Problems Optimal mean estimation from noisy independent pathes of a stochastic process that are indirectly observed is an issue of great interest in functional inverse problems. In this paper, minimax rates of convergence for a class of linear inverse problems with correlated noise, general source conditions and various degrees of ill-posedness are proven in a continuous setting, when the pathes are entirely observed, and in a projected framework. The phase transition phenomenon characteristic to the functional data analysis appears also here and the thresholds that separate the sparse and the dense data set scenarios are computed for different smoothness conditions. The common design proves to be a special case of the independent design in view of the interpretation of the sampling properties via s-numbers and the price to pay for the data correlation turns out to be high. Finally. numerical experiments involving Abel’s integral operator illustrate the goodness-of-fit of the Tikhonov estimator in various scenarios reflecting the common and independent design as well as sparse and dense sampling.
Related Links	https://iopscience.iop.org/article/10.1088/1361-6420/ac2d76/pdf
ISSN	02665611
e-ISSN	13616420
DOI	10.1088/1361-6420/ac2d76
Journal	Inverse Problems
Issue Number	12
Volume Number	37
Language	English
Publisher	IOP Publishing
Publisher Date	2021-10-06
Access Restriction	Open
Subject Keyword	Journal: Inverse Problems Interdisciplinary Mathematics Independent Design Inverse Problems Functional Data
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Signal Processing Mathematical Physics Computer Science Applications

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