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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 Restricted isometry property ： ウィキペディア英語版 Restricted isometry property In linear algebra, the restricted isometry property characterizes matrices which are nearly orthonormal, at least when operating on sparse vectors. The concept was introduced by Emmanuel Candès and Terence Tao〔E. J. Candes and T. Tao, "Decoding by Linear Programming," IEEE Trans. Inf. Th., 51(12): 4203–4215 (2005).〕 and is used to prove many theorems in the field of compressed sensing.〔E. J. Candes, J. K. Romberg, and T. Tao, "Stable Signal Recovery from Incomplete and Inaccurate Measurements," Communications on Pure and Applied Mathematics, Vol. LIX, 1207–1223 (2006).〕 There are no known large matrices with bounded restricted isometry constants (and computing these constants is strongly NP-hard〔A. M. Tillmann and M. E. Pfetsch, "(The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing )," IEEE Trans. Inf. Th., 60(2): 1248–1259 (2014)〕), but many random matrices have been shown to remain bounded. In particular, it has been shown that with exponentially high probability, random Gaussian, Bernoulli, and partial Fourier matrices satisfy the RIP with number of measurements nearly linear in the sparsity level.〔F. Yang, S. Wang, and C. Deng, "''Compressive sensing of image reconstruction using multi-wavelet transform''", IEEE 2010〕 The current smallest upper bounds for any large rectangular matrices are for those of Gaussian matrices.〔B. Bah and J. Tanner "Improved Bounds on Restricted Isometry Constants for Gaussian Matrices"〕 Web forms to evaluate bounds for the Gaussian ensemble are available at the Edinburgh Compressed Sensing RIC page.〔http://ecos.maths.ed.ac.uk/ric_bounds.shtml〕 == Definition == Let ''A'' be an ''m'' × ''p'' matrix and let ''1'' ≤ ''s'' ≤ ''p'' be an integer. Suppose that there exists a constant $\backslash delta\_s\; \backslash in\; (0,1)$ such that, for every ''m'' × ''s'' submatrix ''A''''s'' of ''A'' and for every vector ''y'', :$(1-\backslash delta\_s)\backslash |y\backslash |\_^2\; \backslash le\; \backslash |A\_s\; y\backslash |\_^2\; \backslash le\; (1+\backslash delta\_s)\backslash |y\backslash |\_^2.\; \backslash ,$ Then, the matrix ''A'' is said to satisfy the ''s''-restricted isometry property with restricted isometry constant $\backslash delta\_s$. 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「Restricted isometry property」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.