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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 Generalized Wiener filter ： ウィキペディア英語版 Generalized Wiener filter The Wiener filter as originally proposed by Norbert Wiener is a signal processing filter which uses knowledge of the statistical properties of both the signal and the noise to reconstruct an optimal estimate of the signal from a noisy one-dimensional time-ordered data stream. The generalized Wiener filter generalizes the same idea beyond the domain of one-dimensional time-ordered signal processing, with two-dimensional image processing being the most common application. ==Description== Consider a data vector $d$ which is the sum of independent signal and noise vectors $d\; =\; s+n$ with zero mean and covariances $\backslash langle\; s^Ts\backslash rangle=S$ and $\backslash langle\; n^Tn\backslash rangle=N$. The generalized Wiener Filter is the linear operator $G$ which minimizes the expected residual between the estimated signal and the true signal, $e\; =\; \backslash langle(Gd-s)^T(Gd-s)\backslash rangle$. The $G$ that minimizes this is $G\; =\; S(S+N)^$, resulting in the Wiener estimator $\backslash hat\; s\; =\; S(S+N)^d$. In the case of Gaussian distributed signal and noise, this estimator is also the maximum a posteriori estimator. The generalized Wiener filter approaches 1 for signal-dominated parts of the data, and S/N for noise-dominated parts. An often-seen variant expresses the filter in terms of inverse covariances. This is mathematically equivalent, but avoids excessive loss of numerical precision in the presence of high-variance modes. In this formulation, the generalized Wiener filter becomes $G\; =\; (S^+N^)^N^$ using the identity $A^+B^=A^(A+B)B^$. 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「Generalized Wiener filter」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.