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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 Algebraic Reconstruction Technique ： ウィキペディア英語版 Algebraic Reconstruction Technique The Algebraic Reconstruction Technique (ART) is a class of iterative algorithms used in computed tomography. These reconstruct an image from a series of angular projections (a sinogram). Gordon, Bender and Herman first showed its use in image reconstruction; whereas the method is known as Kaczmarz method in numerical linear algebra. ART can be considered as an iterative solver of a system of linear equations. The values of the pixels are considered as variables collected in a vector $x$, and the image process is described by a matrix $A$. The measured angular projections are collected in a vector $b$. Given a real or complex $m\; \backslash times\; n$ matrix $A$ and a real or complex vector $b$, respectively, the method computes an approximation of the solution of the linear systems of equations as in the following formula, : $$ x^ = x^ + \lambda_k \frac, x^ \rangle} a_ where $i\; =\; k\; \backslash ,\; \backslash bmod\; \backslash ,\; m\; +\; 1$, $a\_i$ is the ''i''-th row of the matrix $A$, $b\_i$ is the ''i''-th component of the vector $b$, and $\backslash lambda\_k$ is a relaxation parameter. The above formulae gives a simple iteration routine. An advantage of ART over other reconstruction methods (such as filtered backprojection) is that it is relatively easy to incorporate prior knowledge into the reconstruction process. For further details see Kaczmarz method. ==References== 〔 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「Algebraic Reconstruction Technique」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.