SPECT均匀衰减投影数据的反演公式
PDF下载 (330)常生明,王金平 *.SPECT均匀衰减投影数据的反演公式[J].宁波大学学报(理工版),2015,28(02):56-59.DOI:
CHANG Sheng-ming,WANG Jin-ping *.Inversion Formula from Uniformly Attenuated SPECT Projection Data[J].Journal of Ningbo University(Natural Science & Engineering Edition),2015,28(02):56-59.DOI:
| Title: | Inversion Formula from Uniformly Attenuated SPECT Projection Data |
| 作者: | 常生明, 王金平 * |
| Author(s): | CHANG Sheng-ming, WANG Jin-ping * |
| 关键词: | 单光子发射断层成像; 指数型拉动变换; 反演公式; 函数 |
| Keywords: | SPECT; exponential radon transform; inversion formula; function |
| 分类号: | Q819 |
| 文献标识码: | A |
| 摘要: | 依据近年来公开发表的有关单光子发射断层成像(SPECT)成像技术的文献, 探索SPECT均匀衰减投影数据的反投影问题. 主要采用指数型拉动变换的性质和构造特殊函数—– 函数的方法, 进而应用 函数的特殊性得到了一个精确的反演公式. 结果表明, 由这种方法得到的反演公式能够更加有效和精确地实现图像的重建. |
| Abstract: | Based on the recently published literature on SPECT imaging technology, the projection problem of the SPECT homogeneous attenuation projection data is explored in a bid to obtain a more accurate inversion formula. Based on the nature of the exponential transform and the method of constructing special function function, an accurate inversion formula is attained by further applying the particularity of the function. The results show that the obtained inversion formula can implement image reconstruction in a more effective and accurate way. |
| 参考文献 /References: | [1] Natterer F. The mathematic of computerized tomography [M]. New York: John Wiley & Sons, 1986:86-95. [2] Zeng G L, Gullberg G. T. Exact intertive reconstruction for the interior problem[J]. Phys Med Biol, 2009, 54: 5805-5814. [3] Huang Q, You J S, Zeng G L, et al. Reconstruction from uniformly attenuated SPECT projection data using the DBH method[J]. IEEE Trans Med Imaging, 2009, 28(1): 17-29. [4] Kunyansky L. A new SPECT reconstruction algorithm based on the Novikovs explicit inversion formula[J]. Inverse problems, 2001, 17:293-306. [5] Wang J P. Inversion and property characterization on generalized transform of Radon type[J]. Acta Mathema- tica Scientia, 2011, 31(3):636-643. [6] Shi T T, Wang J P. A Fourier reconstruction algorithm in π-scheme short-scan SPECT[J]. Wuhan University Journal of Natural Sciences, 2013, 18(2):97-101. [7] Natterer F. Inversion of the attenuated Radon transform[J]. Inverse problems, 2001, 17:113-119. [8] Inouye T, Kose K, Hasegawa A. Image reconstruction algorithm for single-photon-emission computed tomo- graphy with uniform attenuation[J]. Phys Med Biol, 1989, 34:299-304. [9] 刘式适, 刘式达. 特殊函数[M]. 北京: 气象出版社, 1988:66-81. |
| 备注/Memo: | 收稿日期: 2013－05－06. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/基金项目: 国家自然科学基金（61271398）.第一作者: 常生明（1982－）, 男, 甘肃武威人, 在读硕士研究生, 主要研究方向: 积分变换与图像处理. E-mail: 343715432@qq.com*通信作者: 王金平（1962－）, 男, 湖北武汉人, 博士/教授, 主要研究方向: 积分变换与图像处理. E-mail: wangjinping@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
