SPECT中非均匀衰减扇束投影的局部重建问题研究
PDF下载 (323)沈正洁,王金平 *.SPECT中非均匀衰减扇束投影的局部重建问题研究[J].宁波大学学报(理工版),2016,29(4):61-66.DOI:
SHEN Zheng-jie,WANG Jing-ping *.Local Reconstruction of Nonuniform Attenuated Fan-beam Projection in SPECT[J].Journal of Ningbo University(Natural Science & Engineering Edition),2016,29(4):61-66.DOI:
| Title: | Local Reconstruction of Nonuniform Attenuated Fan-beam Projection in SPECT |
| 作者: | 沈正洁, 王金平 * |
| Author(s): | SHEN Zheng-jie, WANG Jing-ping * |
| 关键词: | 非均匀衰减; 衰减Radon变换; 感兴趣区域; 局部重建 |
| Keywords: | nonuniform absorption; attenuated Radon transform; region of interest; local image reconstruction |
| 分类号: | R311 |
| 文献标识码: | A |
| 摘要: | 通过将Natterer的结果推广到具有复系数的AtRT(衰减Radon变换)和应用针对ROI(感兴趣区域)的扇束扫描模式中, 得到平行束扫描几何中具有复系数的AtRT(衰减Radon变换)的明确反演公式, 以及SPECT(单光子发射计算机断层)中非均匀衰减扇束投影的精确局部重建公式. 重建结果基于平行束与扇束之间的坐标变换. |
| Abstract: | In this work, the inversion formula of the nonuniform attenuated Radon transform (AtRT) with complex coefficients in parallel-beam geometry, and the local reconstruction formula in SPECT with nonuniform absorption fan-beam data are derived by extending Natterer’s results to the AtRT with imaginary coefficients and applying the fan-beam acquisition geometry for the Region of Interest (ROI). The reconstruction result is achieved based on a usual transform between parallel-beam and fan-beam coordinates. |
| 参考文献 /References: | [1] NOVIKOV R G. An explicit inversion formula for the attenuated X-ray transform[J]. Ark Mat, 2002, 40:145- 167. [2] NATTERER F. Inversion of the attenuated Radon transform[J]. Inverse Problems, 2001, 17:113-119. [3] ARZUBOV E V, BUKHGEIM A L, KAZANTSEV S G. Two dimensional tomography problem and the theory of A-analytic functions[J]. Siberian Adv Math, 1998, 8:1-20. [4] WANG J P. Inversion and property characterization on generalized transform of Radon type[J]. Acta Mathema- tica Scientia, 2011, 31(3):636-643. [5] BOMAN J, STROMBERG J O. Novikov’s inversion formula for the attenuated Radon transform: A new approach[J]. J Geo Anal, 2004, 14:185-198. [6] YOU J S. The attenuated Radon transform with complex coefficients[J]. Inverse Problems, 2007, 23:1963-1971. [7] KUNYANSKY L. A new SPECT reconstruction algorithm based on the Novikov’s explicit inversion formula[J]. Inverse Problems, 2001, 17:293-306. [8] GUILLEMENT J P, JAUBERTEAU F, KUNYANSKY L et al. On single-photon emission computed tomography imaging based on an exact formula for the nonuniform attenuated correction[J]. Inverse Problems, 2002, 18:11- 19. [9] 马建华, 颜刚, 陈凌剑, 等. 扇形束CT超短扫描优质重建算法研究[J]. 中国生物医学工程学报, 2008, 27(3): 347-352. [10] YOU J S, ZENG G L, LIANG Z G. FBP algorithms for attenuated fan-beam projections[J]. Inverse Problems, 2005, 21:1179-1192. [11] LJUNGGREN S. A simple graphical representation of Fourier-based imaging methods[J]. J Magn Reson, 1983, 54:338-43. [12] JIANG L Y, OUYANG C H. Compact differences of composition operators on holomorphic function spaces in the unit ball[J]. Acta Mathematica Scientia, 2011, 31B(5): 1679-1693. [13] XIAN J. Weighted sampling and reconstruction in weighted reproducing kernel spaces[J]. J Math Anal Appl, 2010, 367(1):34-42. [14] 张惠韬, 陈明, 张朋. 一种针对感兴趣区域的CT扫描模式及其重建公式[J]. 自然科学发展, 2007, 17(11): 45-47. [15] NOO F, CLACKDOYLE R, PACK J. A two-step Hilbert transform method for 2D image reconstruction[J]. Phys Med Biol, 2004, 49:3903-3923. [16] ZENG G L, YOU J S, HUANG Q et al, Two finite inverse Hilbert transform forrmulae for region-of-interest tomography[J]. Int J Imag Technol, 2007, 17(4):219-223. |
| 备注/Memo: | 收稿日期: 2015-04-11. 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: 沈正洁(1987-), 女, 湖北咸宁人, 在读硕士研究生, 主要研究方向: 积分变换与图像处理络. E-mail: 742961863@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/ |