The Image Reconstruction Iterative Algorithm Based on Calculating Points with Fractal Corrector
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摘要: 本文在计算点图像重建离散化模型的代数迭代算法中,引入分形校正单元构造迭代校正逼近。本文选取Hilbert曲线的最小开口方向作为校正单元连成折线来覆盖投影射线,由校正单元构成的近似曲线具有自相似结构。Hilbert曲线对计算点的投影衰减贡献的几何、物理意义清楚明确。通过加密计算点,由基本校正单元表达的线积分更为逼近地近似投影射线的线积分。分形结构的自相似性可以充分用于迭代校正的计算,形成统一的计算模板,利用几何结构的对称性,加快计算速度、提高成像精度。这一方法可以推广到三维成像模型,内容丰富。Abstract: We introduce fractal corrector in the iterative algorithm for image reconstruction based on calculating points discrete model.The projection line is surrounded by a self-similar string formed by the Hilbert curve units.The Hilbert curve unit’s attenuation weight to projection has clear geometrical meaning as well as physical meaning.The line integral of projection is approximated accurately by compacting the calculating points.The Hilbert curve unit is an effective corrector in improving the algorithm since the uniform templates are formed by the self-similarity of fractal structure.In addition,the symmetry of the model could be used to accelerate the computing speed as well as to improve the imaging precision.
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