锥束FDK反投影重建算法的三角函数优化  

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

作　　者：刘辉[1] 张权[1] 刘祎[1] 白云蛟 桂志国[1,2] LIU Hui;ZHANG Quan;LIU Yi;BAI Yunjiao;GUI Zhiguo(State Key Laboratory of Electronic Measurement Technology,North University of China, Taiyuan 030051, China;Key Laboratory of Instrument Science and Dynamic Measurement, North University of China, Ministry of Education,Taiyuan 030051, China)

机构地区：[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

出　　处：《计算机工程与应用》2017年第19期179-183,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.61271357);国家重大科学仪器设备开发专项(No.2014YQ240445);山西省自然科学基金(No.2015011046);爆炸科学与技术国家重点实验室(北京理工大学)开放课题(No.KFJJ15-08M);2013年中北大学科学基金

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。To accelerate the reconstruction speed of traditional FDK(Feldkamp-Davis-Kress)algorithm,an improvedFDK method based on polar coordinates and the periodic characteristics of trigonometric function is proposed.The modifiedalgorithm is able to implement back projection reconstruction from projection data obtained at different angles at the sametime,which greatly reduces the operation volume of trigonometric function.In addition,during the transformation ofreconstructed image from Polar coordinates to Cartesian coordinates,several pixels can be switched simultaneously dueto the symmetry of cotangent function.Experimental results show that,compared with the traditional FDK reconstructionalgorithm,this optimal method can improve the speed by about10times.

关 键 词：反投影 极坐标 三角函数 周期性 对称性 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]