Computer Engineering and Applications ›› 2017, Vol. 53 ›› Issue (19): 179-183.DOI: 10.3778/j.issn.1002-8331.1604-0368

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Optimization of FDK cone-beam back-projection reconstruction algorithm with trigonometric function

LIU Hui1, ZHANG Quan1, LIU Yi1, BAI Yunjiao1, GUI Zhiguo1,2   

  1. 1.State Key Laboratory of Electronic Measurement Technology,North University of China, Taiyuan 030051, China
    2.Key Laboratory of Instrument Science and Dynamic Measurement, North University of China, Ministry of Education, Taiyuan 030051, China
  • Online:2017-10-01 Published:2017-10-13


刘  辉1,张  权1,刘  祎1,白云蛟1,桂志国1,2   

  1. 1.电子测试技术国家重点实验室(中北大学),太原 030051
    2.仪器科学与动态测试教育部重点实验室(中北大学),太原 030051

Abstract: To accelerate the reconstruction speed of traditional FDK(Feldkamp-Davis-Kress)algorithm, an improved FDK method based on polar coordinates and the periodic characteristics of trigonometric function is proposed. The modified algorithm is able to implement back projection reconstruction from projection data obtained at different angles at the same time, which greatly reduces the operation volume of trigonometric function. In addition, during the transformation of reconstructed image from Polar coordinates to Cartesian coordinates, several pixels can be switched simultaneously due to the symmetry of cotangent function. Experimental results show that, compared with the traditional FDK reconstruction algorithm, this optimal method can improve the speed by about 10 times.

Key words: back-projection, Polar coordinate, trigonometric function, periodicity, symmetry

摘要: 为了提高传统FDK(Feldkamp-Davis-Kress)重建算法的重建速度,根据三角函数在一定程度上表现出来的周期性的特点对极坐标下的FDK重建算法进行了改进。改进的算法能够一次性对多幅投影数据进行反投影重建,并且大大减少了三角函数的运算量。同时利用正余切函数的对称性,在将重建后的图像从极坐标向笛卡尔坐标的转换过程中一次性将多个重建后的像素点进行转换。实验结果表明,对比传统FDK重建算法,经过该优化的算法在重建速度上提高了近10倍。

关键词: 反投影, 极坐标, 三角函数, 周期性, 对称性