锥束X射线CT图像重建的新型滤波函数
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摘要
针对X射线计算机断层成像(computed tomography,CT)图像重建FDK算法中,采用通常的滤波函数会导致明显的Gibbs现象,影响重建图像的质量.基于混合滤波和加权平均理论,设计了一种新型的NEW-MS-L滤波函数.先将S-L滤波函数加权平均为M3S-L滤波函数,再与NEW滤波函数叠加,得到NEW-MS-L滤波函数.通过数值仿真,分别对比NEW、R-L-S-L、R-L-NEW、R-L-MS-L和NEW-MS-L滤波函数的重建图像效果,结果表明,NEW-MS-L滤波函数能够在保持较高图像分辨率的情况下,更有效地抑制Gibbs现象,使重建图像效果更佳.
The conventional filter function of the FDK algorithm in X-ray computed tomography( CT) can result in the obvious Gibbs phenomenon,which has great effect on the CT image. A NEW-MS-L filter function is deduced based on the rationale of mixed filter theory and weighted average theory. First,the S-L filter function is weighted and averaged to form M3S-L filter function. Then,as a superposition of the M3S-L filter function and the NEW filter function,the NEW-MS-L filter function is obtained. Compared with the other filter functions such as NEW,R-L-S-L,R-L-NEW,and R-L-MS-L,the NEW-MS-L can suppress the Gibbs phenomenon while maintaining high resolution. The results show that the NEW-MS-L filter function can provide X-ray CT with better reconstruction images.
The conventional filter function of the FDK algorithm in X-ray computed tomography( CT) can result in the obvious Gibbs phenomenon,which has great effect on the CT image. A NEW-MS-L filter function is deduced based on the rationale of mixed filter theory and weighted average theory. First,the S-L filter function is weighted and averaged to form M3S-L filter function. Then,as a superposition of the M3S-L filter function and the NEW filter function,the NEW-MS-L filter function is obtained. Compared with the other filter functions such as NEW,R-L-S-L,R-L-NEW,and R-L-MS-L,the NEW-MS-L can suppress the Gibbs phenomenon while maintaining high resolution. The results show that the NEW-MS-L filter function can provide X-ray CT with better reconstruction images.
引文
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[2]Bieberle M,Barthel F.Combined phase distribution and particle velocity measurement in spout fluidized beds by ultrafast X-ray computed tomography[J].Chemical Engineering Journal,2016,285:218-227.
[3]Edlund R,Skorpil M,Lapidus G,et al.Cone-beam CT in diagnosis of scaphoid fractures[J].Skeletal Radiology,2016,45(2):197-204.
[4]Senyshyn A,Mühlbauer M J,Dolotko O,et al.Homogeneity of lithium distribution in cylinder-type Li-ion batteries[J].Scientific Reports,2015,5:18380.
[5]Plessis A D,Olawuyi B J,Boshoff W P,et al.Simple and fast porosity analysis of concrete using X-ray computed tomography[J].Materials and Structures,2016,49(1):553-562.
[6]Feldkamp L A,Davis L C,Kress J W.Practical conebeam algorithm[J].Journal of the Optical Society of America A,1984,1(6):612-619.
[7]Wei Yuchuan,Wang Ge,Hsieh J.An intuitive discussion on the ideal ramp filter in computed tomography(I)[J].Computers&Mathematics with Applications,2005,49(5/6):731-740.
[8]谢强.计算机断层成像技术:原理、设计、伪像和进展[M].张朝宗,郭志平,王宗贤,译.北京:科学出版社,2006.Hsieh J.Computed tomography:principle,design,artifacts and recent advances[M].Zhang Chaozong,Guo Zhiping,Wang Zongxian,trans.Beijing:Science Press,2006.(in Chinese)
[9]胡永梅,全红,徐利明,等.新型混合滤波器在FDK算法中的应用[J].中国医学影像技术,2011,27(2):397-400.Hu Yongmei,Quan Hong,Xu Liming,et al.Application of a new mixed filter in FDK algorithm[J].Chinese Journal of Medical Imaging Technology,2011,27(2):397-400.(in Chinese)
[10]王晓鹏,王明泉,侯慧玲.基于R-L-MS-L滤波函数的CT图像重建[J].电视技术,2014,38(7):26-28.Wang Xiaopeng,Wang Mingquan,Hou Huilin.CT image reconstruction based on R-L-MS-L filter function[J].Video Engineering,2014,38(7):26-28.(in Chinese)
[11]闫镔,李磊.CT图像重建算法[M].北京:科学出版社,2014.Yan Bin,Li Lei.CT image reconstructinalgorithm[M].Beijing:Science Press,2014.(in Chinese)
[12]郑君里.信号与系统[M].北京:高等教育出版社,2002.Zhen Junli.Signals and systems[M].Beijing:Higher Education Press,2002.(in Chinese)
[13]杨位钦,顾岚.时间序列分析与动态数据建模[M].北京:北京工业学院出版社,1986.Yang Weiqin,Gu Lan.Time series analysis and dynamic data modeling[M].Beijing:Beijing Institute of Tchnology Press,1986.(in Chinese)
[14]范惠荣,徐茂林,邱钧,等.关于CBP算法的一种新型滤波函数和它的性质[J].电子学报,2004,32(2):232-235.Fan Huirong,Xu Maolin,Qiu Jun,et al.A new filter function in CBP and its properties[J].Acta Electronica Sinica,2004,32(2):232-235.(in Chinese)
[15]刘晓,杨朝文.RL滤波函数的改进对卷积反投影图像重建的影响[J].四川大学学报自然科学版,2004,41(1):112-117.Liu Xiao,Yang Chaowen.The influence of modified-RL filter function on the quality of image reconstruction using convolution backprojection algorithm[J].Journal of Sichuan University Natural Science Edition,2004,41(1):112-117.(in Chinese)
[16]刘泽,孙丰荣,李艳玲,等.基于3D Shepp-Logan头部模型的三维医学图像重建仿真[J].生物医学工程学杂志,2006,23(5):938-943.Liu Ze,Sun Fengrong,Li Yanling,et al.The threedimension medical image reconstruction simulation on 3D Shepp-Logan head phantom[J].Journal of Biomedical Engineering,2006,23(5):938-943.(in Chinese)
[17]Lei Yaohu,Huang Jianheng,Liu Xin,et al.Improvement of visibility of moir fringe in X-ray differential phasecontrast imaging[J].Journal of Shenzhen University Science and Engineering,2016,33(5):506-510.
[18]刘鑫,郭金川.部分相干光源微分相衬双图像相位恢复[J].深圳大学学报理工版,2014,31(2):169-173.Liu Xin,Guo Jinchuan.Dual-images phase retrieval in differential phase-contrast imaging with partial coherence source[J].Journal of Shenzhen University Science and Engineering,2014,31(2):169-173.(in Chinese)
[19]Jerjen I,Revol V,Kottler C,et al.Phase contrast cone beam tomography with an X-ray grating interferometer[C]//International Conference on Advanced Phase Measurement Methods in Optics&Imaging.Ascona,Switzerland:American Institute of Physics,2010,1236(1):227-231.
[20]Huang Zhifeng,Kang Kejun,Li Zheng,et al.Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging[J].Applied Physics Letters,2006,89(4):041124.
[21]Mc Cann M T,Nilchian M,Stampanoni M,et al.Fast 3D reconstruction method for differential phase contrast X-ray CT[J].Optics Express,2016,24(13):14564-14581.
[22]Fu Jian,Hu Xinhua,Velroyen A,et al.3D algebraic iterative reconstruction for cone-beam X-ray differential phasecontrast computed tomography[J].Plo S One,2015,10(3):e0117502.