Asymptotic minimax bounds for stochastic deconvolution over groups
- Authors
- Koo, Ja-Yong; Kim, Peter T.
- Issue Date
- 1월-2008
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Keywords
- fourier analysis on groups; Hellinger distance; irreducible characters; irreducible representations; positive roots; Sobolev class; weights; Weyl' s formula
- Citation
- IEEE TRANSACTIONS ON INFORMATION THEORY, v.54, no.1, pp.289 - 298
- Indexed
- SCIE
SCOPUS
- Journal Title
- IEEE TRANSACTIONS ON INFORMATION THEORY
- Volume
- 54
- Number
- 1
- Start Page
- 289
- End Page
- 298
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/124501
- DOI
- 10.1109/TIT.2007.911263
- ISSN
- 0018-9448
- Abstract
- This paper examines stochastic deconvolution over noncommutative compact Lie groups. This involves Fourier analysis on compact Lie groups as well as convolution products over such groups. An observation process consisting of a known impulse response function convolved with an unknown signal with additive white noise is assumed. Data collected through the observation process then allow us to construct an estimator of the signal. Signal recovery is then assessed through integrated mean squared error for which the main results show that asymptotic minimaxity depends on smoothness properties of the impulse response function. Thus, if the Fourier transform of the impulse response function is bounded polynomially, then the asymptotic minimax signal recovery is polynomial, while if the Fourier transform of the impulse response function is exponentially bounded, then the asymptotic minimax signal recovery is logarithmic. Such investigations have been previously considered in both the engineering and statistics literature with applications in among others, medical imaging, robotics, and polymer science.
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