A note on confidence intervals for deblurred images

• Autorzy: Biel Michał , Szkutnik Zbigniew

Identyfikatory

DOI

10.7494/OpMath.2020.40.3.361

• Języki publikacji: EN

Abstrakty

EN

We consider pointwise asymptotic confidence intervals for images that are blurred and observed in additive white noise. This amounts to solving a stochastic inverse problem with a convolution operator. Under suitably modified assumptions, we fill some apparent gaps in the proofs published in [N. Bissantz, M. Birke, Asymptotic normality and confidence intervals for inverse regression models with convolution-type operators, J. Multivariate Anal. 100 (2009), 2364-2375]. In particular, this leads to modified bootstrap confidence intervals with much better finite-sample behaviour than the original ones, the validity of which is, in our opinion, questionable. Some simulation results that support our claims and illustrate the behaviour of the confidence intervals are also presented.

Słowa kluczowe

EN

inverse problems; confidence intervals; convolution; deblurring

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2020
• Tom: Vol. 40, no. 3
• Strony: 361--–373
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Biel Michał

• Faculty of Applied Mathematics AGH University of Science and Technology AL Mickiewicza 30, 30-059 Krakow, Poland

autor

Szkutnik Zbigniew

• Faculty of Applied Mathematics AGH University of Science and Technology AL Mickiewicza 30, 30-059 Krakow, Poland

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).