Sharp adaptation for spherical inverse problems with applications to medical imaging
- Authors
- Koo, Ja-Yong; Kim, Peter T.
- Issue Date
- Feb-2008
- Publisher
- ELSEVIER INC
- Keywords
- Deconvolution; Klein-Nishina distribution; Mixtures; Pinsker theory; Spherical harmonics
- Citation
- JOURNAL OF MULTIVARIATE ANALYSIS, v.99, no.2, pp.165 - 190
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF MULTIVARIATE ANALYSIS
- Volume
- 99
- Number
- 2
- Start Page
- 165
- End Page
- 190
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/124170
- DOI
- 10.1016/j.jmva.2006.06.007
- ISSN
- 0047-259X
- Abstract
- This paper examines the estimation of an indirect signal embedded in white noise for the spherical case. It is found that the sharp minimax bound is determined by the degree to which the indirect signal is embedded in the linear operator. Thus, when the linear operator has polynomial decay, recovery of the signal is polynomial, whereas if the linear operator has exponential decay, recovery of the signal is logarithmic. The constants are determined for these classes as well. Adaptive sharp estimation is also carried out. In the polynomial case a blockwise shrinkage estimator is needed while in the exponential case, a straight projection estimator will suffice. The framework of this paper include applications to medical imaging, in particular, to cone beam image reconstruction and to diffusion magnetic resonance imaging. Discussion of these applications are included. (C) 2006 Elsevier Inc. All rights reserved.
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Collections - College of Political Science & Economics > Department of Statistics > 1. Journal Articles
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