翻訳と辞書 Words near each other ・ Sheboygan Light, Power and Railway Company Car ・ Shearers and Rural Workers' Union ・ Sheares brothers ・ Shearing (manufacturing) ・ Shearing (physics) ・ Shearing Bossa Nova ・ Shearing interferometer ・ Shearing layers ・ Shearing Pinx ・ Shearing shed ・ Shearing the Rams ・ Shearings ・ Shearinine ・ Shearjashub Bourne ・ Shearjashub Spooner ・ Shearlet ・ Shearline Boatworks ・ Shearling ・ Shearling coat ・ Shearman ・ Shearman & Sterling ・ Shearn Moody, Jr. ・ Shearography ・ Shearon Harris Nuclear Power Plant ・ Shears ・ Shearsby ・ Shearson ・ Shearson (disambiguation) ・ Shearson, Hammill & Co. ・ Shearson-Lehman Brothers Senior Classic Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Shearlet ： ウィキペディア英語版 Shearlet In applied mathematical analysis, shearlets are a multiscale framework which allows to efficiently encode anisotropic features in multivariate problem classes. Originally, shearlets were introduced in 2006 〔 for the analysis as well as sparse approximation of functions $f\; \backslash in\; L^2(\backslash R^2)$. They are a natural extension of wavelets to accommodate the fact that multivariate functions are typically governed by anisotropic features such as edges in images, however, wavelets as isotropic objects are not capable of capturing such phenomena. Shearlets are constructed by parabolic scaling, shearing and translation applied to few generating functions. At fine scales, they are essentially supported within skinny and directional ridges following the parabolic scaling law, which reads ''length² ≈ width''. Similar to wavelets, shearlets arise from the affine group and allow a unified treatment of the continuum and digital situation leading to faithful implementations. Although they do not constitute an orthonormal basis for $L^2(\backslash R^2)$, they still form a frame allowing stable expansions of arbitrary functions $f\; \backslash in\; L^2(\backslash R^2)$. One of the most important properties of shearlets is the fact that they provide optimally sparse approximations (in the sense of optimality in 〔) for cartoon-like functions $f$. In imaging sciences, ''cartoon-like functions'' serve as a model for anisotropic features and are compactly supported in $()^2$ while being $C^2$ apart from a closed piecewise $C^2$ singularity curve with bounded curvature. The decay rate of the $L^2$-error of the $N$-term shearlet approximation obtained by taking the $N$ largest coefficients from the shearlet expansion is in fact optimal up to a log-factor:〔〔 :$\backslash |\; f\; -\; f\_N\; \backslash |\_^2\; \backslash leq\; C\; N^\; (\backslash log\; N)^3,\; \backslash quad\; N\; \backslash to\; \backslash infty,$ where the constant $C$ depends only on the maximum curvature of the singularity curve and the maximum magnitudes of $f$, $f^$ and $f^$. This approximation rate significantly improves the best $N$-term approximation rate of wavelets providing only $O(N^)$ for such class of functions. Shearlets are to date the only directional representation system which provides sparse approximation of anisotropic features while providing a unified treatment of the continuum and digital realm in the sense of allowing faithful implementation. Extensions of shearlet systems to $L^2(\backslash R^d),\; d\; \backslash ge\; 2$ are also available. A comprehensive presentation of the theory and applications of shearlets can be found in: 〔 == Definition == 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「Shearlet」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.