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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 Matching pursuit ： ウィキペディア英語版 Matching pursuit Matching pursuit is a type of sparse approximation which involves finding the "best matching" projections of multidimensional data onto an over-complete dictionary $D$. The basic idea is to represent a signal $f$ from Hilbert space $H$ as a weighted sum of functions $g\_$ (called atoms) taken from $D$: : $f(t)\; =\; \backslash sum\_^\; a\_n\; g\_(t)$ where $n$ indexes the atoms that have been chosen, and $a\_n$ a weighting factor (an amplitude) for each atom. Given a fixed dictionary, matching pursuit will first find the one atom that has the biggest inner product with the signal, then subtract the contribution due to that atom, and repeat the process until the signal is satisfactorily decomposed. For comparison, consider the Fourier series representation of a signal - this can be described in the terms given above, where the dictionary is built from sinusoidal basis functions (the smallest possible complete dictionary). The main disadvantage of Fourier analysis in signal processing is that it extracts only global features of signals and does not adapt to analysed signals $f$. By taking an extremely redundant dictionary we can look in it for functions that best match a signal $f$. Finding a representation where most of the coefficients in the sum are close to 0 (sparse representation) is desirable for signal coding and compression. == The algorithm == Searching over an extremely large dictionary for the best matches is computationally unacceptable for practical applications. In 1993 Mallat and Zhang〔S. G. Mallat and Z. Zhang, , IEEE Transactions on Signal Processing, December 1993, pp. 3397–3415.〕 proposed a greedy solution that is known from that time as Matching Pursuit. The algorithm iteratively generates for any signal $f$ and any dictionary $D$ a sorted list of indexes and scalars which are the sub-optimal solution to the problem of sparse signal representation. The residual after calculating $\backslash gamma\_n$ and $a\_n$ is denoted by $R\_$. Input: Signal: $f(t)$, dictionary $D$. Output: List of coefficients: $\backslash left(\; a\_n,\; g\_\backslash right)$. Initialization: $R\_1\backslash ,\backslash leftarrow\backslash ,f(t)$; $n\backslash ,\backslash leftarrow\backslash ,1$; Repeat: find $g\_\; \backslash in\; D$ with maximum inner product $|\; \backslash langle\; R\_n,\; g\_\; \backslash rangle\; |$; $a\_n\backslash ,\backslash leftarrow\backslash ,\backslash langle\; R\_n,\; g\_\backslash rangle$; $R\_\backslash ,\backslash leftarrow\backslash ,R\_n\; -\; a\_n\; g\_$; $n\backslash ,\backslash leftarrow\backslash ,n\; +\; 1$; Until stop condition (for example: ) The concept of matching pursuit in signal processing is related to statistical projection pursuit, in which "interesting" projections were found; ones that deviate more from a normal distribution are considered to be more interesting. 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「Matching pursuit」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.