Optimal wavelet estimators of the heteroscedastic pointspread effects and Gauss white noises model

The problem of estimating a function's derivative arises in many scientific settings, from medical imaging to astronomy. In this paper, we consider a hard thresholding wavelet approach to certain blind deconvolution problem based on the heteroscedastic data. Motivated by Delaigle & Meister&...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 51; no. 5; pp. 1133 - 1154
Main Authors Wang, Jinru, Shi, Wenhui, Zeng, Xiaochen
Format Journal Article
LanguageEnglish
Published Taylor & Francis 04.03.2022
Subjects
Besov space
convergence
Gauss white noise
pointspread effect
wavelet
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Summary:The problem of estimating a function's derivative arises in many scientific settings, from medical imaging to astronomy. In this paper, we consider a hard thresholding wavelet approach to certain blind deconvolution problem based on the heteroscedastic data. Motivated by Delaigle & Meister's work, the adaptive wavelet estimators are proposed and their asymptotic properties are investigated. It is shown that the derivative estimators for the blind deconvolution model are spatially adaptive and attain the optimal rate of convergence up to a logarithmic factor over a range of Besov classes. Our theorems generalize the results of Cai and Navarro et al. in some sense.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2020.1862874