A note on confidence intervals for deblurred images
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. Bis...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2020-04-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol40/3/art/opuscula_math_4019.pdf |
| _version_ | 1819059383910268928 |
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| author | Michał Biel Zbigniew Szkutnik |
| author_facet | Michał Biel Zbigniew Szkutnik |
| author_sort | Michał Biel |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T14:10:14Z |
| format | Article |
| id | doaj.art-7ca2d29a469d4ed39535ecbb5d17f357 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-21T14:10:14Z |
| publishDate | 2020-04-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-7ca2d29a469d4ed39535ecbb5d17f3572022-12-21T19:01:04ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742020-04-01403361373https://doi.org/10.7494/OpMath.2020.40.3.3614019A note on confidence intervals for deblurred imagesMichał Biel0Zbigniew Szkutnik1https://orcid.org/0000-0002-4607-6268Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, PolandFaculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, PolandWe 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.https://www.opuscula.agh.edu.pl/vol40/3/art/opuscula_math_4019.pdfinverse problemsconfidence intervalsconvolutiondeblurring |
| spellingShingle | Michał Biel Zbigniew Szkutnik A note on confidence intervals for deblurred images Opuscula Mathematica inverse problems confidence intervals convolution deblurring |
| title | A note on confidence intervals for deblurred images |
| title_full | A note on confidence intervals for deblurred images |
| title_fullStr | A note on confidence intervals for deblurred images |
| title_full_unstemmed | A note on confidence intervals for deblurred images |
| title_short | A note on confidence intervals for deblurred images |
| title_sort | note on confidence intervals for deblurred images |
| topic | inverse problems confidence intervals convolution deblurring |
| url | https://www.opuscula.agh.edu.pl/vol40/3/art/opuscula_math_4019.pdf |
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