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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 Local inverse ： ウィキペディア英語版 Local inverse The local inverse is a kind of inverse function or matrix inverse used in image and signal processing, as well as other general areas of mathematics. The concept of local inverse came from interior reconstruction of the CT image. One of the interior reconstruction methods was done through that first approximately reconstructs the image outside the ROI (region of interest) and then subtracts the re-projection data of the image at outside the ROI from the original projection data; then the above created data are used to make a new reconstruction. This idea can be widened to inverse. Instead of directly making an inverse, the unknowns at the outside of the local region can be first inverted. Recalculate the data from these unknowns (at outside the local region). Subtract this recalculated data from the original data, then the inverse for the unknowns inside the local region is done through the above newly produced data. This concept is a direct extension of local tomography, generalized inverse and iterative refinement method. It is used to solve the inverse problem with incomplete input data, similar to local tomography. However this concept of local inverse also can be applied to complete input data. ==Local inverse for full field of view system or over-determined system== :$$ \begin f \\ g \end = \begin A & B \\ C & D \end \begin x \\ y \end Assume there is $E$, $F$, $G$ and $H$ that satisfies, :$$ \begin E & F \\ G & H \end \begin A & B \\ C & D \end = J Here $J$ is not equal to $I$. $J$ is close to $I$. $I$ is identical matrix. Examples of this kind of matrix $$ \begin E & F \\ G & H \end are for example, filtered back-projection method for image reconstruction, the inverse with regularization. In this case an approximate solution can be found as following, and :$$ \begin x_0 \\ y_0 \end = \begin E & F \\ G & H \end \begin f \\ g \end A better solution for $x\_1$ can be found as following, :$$ \begin x_1 \\ y_1 \end = \begin E & F \\ G & H \end \begin f - B y_0\\ g - D y_0 \end In the above formula $y\_1$ is useless, hence :$$ x_1=E(f-B y_0)+F(g - D y_0) In the same way, there is :$$ y_1=G(f-A x_0)+H(g - C x_0) In the above the solution is only divided to as two parts. $x$ is inside the ROI(region of Interest) $y$ is at outside of ROI. f is inside of FOV(field of view) y is outside of FOV. The two parts can be extended to many parts, in this case, the extended method is referred as the sub-region iterative refinement method method 〔Shuangren Zhao, Xintie Yang, ''Iterative reconstruction in all sub-regions '', ''SCIENCEPAPER ONLINE''. 2006; 1(4): page 301–308, http://www.paper.edu.cn/uploads/journal/2007/42/1673-7180(2006)04-0301-08.pdf 〕 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「Local inverse」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.