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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Discrete Universal Denoiser ： ウィキペディア英語版 Discrete Universal Denoiser In information theory and signal processing, the Discrete Universal Denoiser (DUDE) is a denoising scheme for recovering sequences over a finite alphabet, which have been corrupted by a discrete memoryless channel. The DUDE was proposed in 2005 by Tsachy Weissman, Erik Ordentlich, Gadiel Seroussi, Sergio Verdú and Marcelo J. Weinberger .〔 T. Weissman, E. Ordentlich, G. Seroussi, S. Verdu ́, and M.J. Weinberger. Universal discrete denoising: Known channel. IEEE Transactions on Information Theory,, 51(1):5–28, 2005. 〕 == Overview == The Discrete Universal Denoiser 〔 (DUDE) is a denoising scheme that estimates an unknown signal $x^n=\backslash left(\; x\_1\; \backslash ldots\; x\_n\; \backslash right)$ over a finite alphabet from a noisy version $z^n=\backslash left(\; z\_1\; \backslash ldots\; z\_n\; \backslash right)$. While most denoising schemes in the signal processing and statistics literature deal with signals over an infinite alphabet (notably, real-valued signals), the DUDE addresses the finite alphabet case. The noisy version $z^n$ is assumed to be generated by transmitting $x^n$ through a known discrete memoryless channel. For a fixed ''context length'' parameter $k$, the DUDE counts of the occurrences of all the strings of length $2k+1$ appearing in $z^n$. The estimated value $\backslash hat\_i$ is determined based the two-sided length-$k$ ''context'' $\backslash left(\; z\_,\; \backslash ldots,\; z\_,z\_,\; \backslash ldots,z\_\; \backslash right)$ of $z\_i$, taking into account all the other tokens in $z^n$ with the same context, as well as the known channel matrix and the loss function being used. The idea underlying the DUDE is best illustrated when $x^n$ is a realization of a random vector $X^n$. If the conditional distribution $X\_i\; |\; Z\_,\; \backslash ldots,\; Z\_,\; Z\_,\; \backslash ldots,\; Z\_$, namely the distribution of the noiseless symbol $X\_i$ conditional on its noisy context $\backslash left(\; Z\_,\; \backslash ldots,$ Z_,Z_, \ldots,Z_ \right) was available, the optimal estimator $\backslash hat\_i$ would be the Bayes Response to $X\_i\; |\; Z\_,\; \backslash ldots,\; Z\_,\; Z\_,\; \backslash ldots,\; Z\_$. Fortunately, when the channel matrix is known and non-degenerate, this conditional distribution can be expressed in terms of the conditional distribution $Z\_i\; |\; Z\_,\; \backslash ldots,\; Z\_,\; Z\_,\; \backslash ldots,\; Z\_$, namely the distribution of the noisy symbol $Z\_i$ conditional on its noisy context. This conditional distribution, in turn, can be estimated from an individual observed noisy signal $Z^n$ by virtue of the Law of Large Numbers, provided $n$ is ``large enough''. Applying the DUDE scheme with a context length $k$ to a sequence of length $n$ over a finite alphabet $\backslash mathcal$ requires $O(n)$ operations and space $O\backslash left(\; \backslash min(\; n\; ,\; |\backslash mathcal|^\; )$ \right). Under certain assumptions, the DUDE is a universal scheme in the sense of asymptotically performing as well as an optimal denoiser, which has oracle access to the unknown sequence. More specifically, assume that the denoising performance is measured using a given single-character fidelity criterion, and consider the regime where the sequence length $n$ tends to infinity and the context length $k=k\_n$ tends to infinity “not too fast”. In the stochastic setting, where a doubly infinite sequence noiseless sequence $\backslash mathbf$ is a realization of a stationary process $\backslash mathbf$, the DUDE asymptotically performs, in expectation, as well as the best denoiser, which has oracle access to the source distribution $\backslash mathbf$. In the single-sequence, or “semi-stochastic” setting with a ''fixed'' doubly infinite sequence $\backslash mathbf$, the DUDE asymptotically performs as well as the best “sliding window” denoiser, namely any denoiser that determines $\backslash hat\_i$ from the window $\backslash left(\; z\_,\backslash ldots,z\_\; \backslash right)$, which has oracle access to $\backslash mathbf$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Discrete Universal Denoiser」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.