TY  - JOUR
ID  - Biel2020
LB  - Biel2020
AU  - Biel, Michał
AU  - Szkutnik, Zbigniew
TI  - A note on confidence intervals for deblurred images
ST  - A note on confidence intervals for deblurred images
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 3
SP  - 361
EP  - 373
DO  - https://doi.org/10.7494/OpMath.2020.40.3.361
UR  - https://doi.org/10.7494/OpMath.2020.40.3.361
AB  - 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.
KW  - inverse problems
KW  - confidence intervals
KW  - convolution
KW  - deblurring
SN  - 1232-9274
ER  -