Fourier Inversion of the Mojette Transform

被引:0
|
作者
Kingston, Andrew [1 ]
Li, Heyang [1 ]
Normand, Nicolas [2 ]
Svalbe, Imants [3 ]
机构
[1] Australian Natl Univ, RSPE, Dept Appl Maths, Canberra, ACT 2600, Australia
[2] Univ Nantes, Ecole Polytech, IRCCyN, F-44306 Nantes, France
[3] Monash Univ, Sch Phys, Clayton, Vic 3800, Australia
来源
DISCRETE GEOMETRY FOR COMPUTER IMAGERY, DGCI 2014 | 2014年 / 8668卷
关键词
Radon transform; Mojette transform; Fourier inversion; tomography; RECONSTRUCTION;
D O I
暂无
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
The Mojette transform is a form of discrete Radon transform that maps a 2D image (P x Q pixels) to a set of I 1D projections. Several fast inversion methods exist that require O(PQI) operations but those methods are ill-conditioned. Several robust (or well-conditioned) inversion methods exist, but they are slow, requiring O(P(2)Q(2)I) operations. Ideally we require an inversion scheme that is both fast and robust to deal with noisy projections. Noisy projection data can arise from data that is corrupted in storage or by errors in data transmission, quantisation errors in image compression, or through noisy acquisition of physical projections, such as in X-ray computed tomography. This paper presents a robust reconstruction method, performed in the Fourier domain, that requires O(P-2 Qlog P) operations.
引用
收藏
页码:275 / 284
页数:10
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