Algorithm for X-ray CT Reconstruction Using Two-dimensional Sampling Model and Singular Value Decomposition

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  • 2次元標本化モデルと特異値分解によるX線CT画像再構成アルゴリズム
  • 2ジゲン ヒョウホンカ モデル ト トクイチ ブンカイ ニ ヨル Xセン CT ガゾウ サイコウセイ アルゴリズム

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Abstract

This paper describes a new approach to the X-ray computed tomography in order to find defects of the products in manufacturing industry. Our approach which is Fast Model Reconstruction Computed Tomography (FMR-CT), involves two key ideas: 1) for forward problem, integration two dimensional sinc functions along the X-ray on the sampled two-dimentional planee model and 2) for inverse problem, solving the liner inverse problem using a truncated singular value decomposition (SVD) method.<br>Our algorithm is favorable fast computation capability because image vector can be obtained simple formula such as pseudo-inverse matrix (constant) multiplied by projection data vector, and is also compatible with multiprocessor implementations. The combination of sampling theorem and the SVD allows smooth reconstruction image with even smaller numbers of projections, because each techniques contribute interpolation and least-squares optimization, respectively.<br>We demonstrate the cross section image which is reconstructed real projection data sets acquired by using the micro-focused X-ray TV. Further, we discuss practical determination of truncation rank with the visualization of decomposed v-singular vector and the distribution of singular values.

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