衍射层析成像的Voronoi图密度补偿算法的研究

方杰; 刘仁金

doi:10.3969/j.issn.0372-2112.2014.07.004

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衍射层析成像的Voronoi图密度补偿算法的研究

学术论文 | 更新时间：2025-07-16

- 衍射层析成像的Voronoi图密度补偿算法的研究
- Study on Image Reconstruction of Diffraction Tomography with Density Compensation Algorithm by Voronoi Diagrams
- 电子学报 2014年42卷第7期页码：1268-1272
- 作者机构：
  
  皖西学院机械与电子工程学院,安徽,六安,237012
- 作者简介：
- 基金信息：
  
  国家自然科学基金 (No.61302179，No.61303209）;安徽省青年优秀人才重点基金 (No.2010SQRL184）;安徽省高校自然科学基金 (No.KJ2011ZD10）;安徽省自然基金 (No.11040606M150）
- DOI：10.3969/j.issn.0372-2112.2014.07.004
  中图分类号： TN911.72
- 纸质出版：2014
- 稿件说明：
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方杰, 刘仁金. 衍射层析成像的Voronoi图密度补偿算法的研究[J]. 电子学报, 2014,42(7):1268-1272.

FANG Jie, LIU Ren-jin. Study on Image Reconstruction of Diffraction Tomography with Density Compensation Algorithm by Voronoi Diagrams[J]. Acta Electronica Sinica, 2014, 42(7): 1268-1272.
方杰, 刘仁金. 衍射层析成像的Voronoi图密度补偿算法的研究[J]. 电子学报, 2014,42(7):1268-1272. DOI： 10.3969/j.issn.0372-2112.2014.07.004.

FANG Jie, LIU Ren-jin. Study on Image Reconstruction of Diffraction Tomography with Density Compensation Algorithm by Voronoi Diagrams[J]. Acta Electronica Sinica, 2014, 42(7): 1268-1272. DOI： 10.3969/j.issn.0372-2112.2014.07.004.

摘要

网格算法是最常见的衍射层析成像的频域重建算法，然而这种算法却容易引入误差，且对采样点的分布形状较敏感，因此，本文提出了一种基于Voronoi图密度补偿的超声衍射层析成像重建算法.首先，用三角剖分快速生成算法生成投影数据的Voronoi图，并对在外凸壳上对应的Voronoi图面积是无穷大的点通过拟合、插值处理使之变为有限的补偿面积，从而得到整个点集的补偿面积.其次，提出了基于Voronoi图面积密度补偿的衍射层析成像的非均匀傅里叶变换网格重建算法，重建图像的质量较没有补偿的有很大提高.最后，提出了选取1/4圆弧的数据集重建方案，实验结果表明：在重建质量相当的情况下，1/4圆弧的重建时间比1/2圆弧少27.32%.

Abstract

A common way for image reconstruction in frequency domain is the gridding algorithm.However

this approach is liable to introduce inaccuracies and is sensitive to the configuration of the sample points.So a new reconstruction method based on Voronoi diagrams is proposed in this paper.Firstly

the projection data of Voronoi diagram is generated quickly based on triangulation algorithm

data points on the convex shell with the infinite area of Voronoi diagram is turned into the finite compensation area by polynomial fitting and interpolation processing

then all the data points obtained the compensation area of Voronoi diagram.Secondly

the reconstruction algorithm of diffraction tomography using NUFFT(non-uniform FFT) and the density compensation by the area of Voronoi diagram is proposed

and the quality of reconstructed image has been greatly improved.Finally

the results of simulation showed that there is 27.32% less reconstructive time of 1/4 arc than the time of 1/2 arc in the case of considerable quality of reconstruction.

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