Comments on the filtered backprojection algorithm, range conditions, and the pseudoinverse solution

被引：12

作者：

Anastasio, MA

Pan, XC

Clarkson, E

机构：

[1] Univ Chicago, Grad Program Med Phys, Dept Radiol, Chicago, IL 60637 USA

[2] Univ Arizona, Dept Radiol, Tucson, AZ 85724 USA

来源：

IEEE TRANSACTIONS ON MEDICAL IMAGING | 2001年 / 20卷 / 06期

关键词：

computed tomography; filtered backprojection algorithm; radon transform;

D O I：

10.1109/42.929620

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The filtered backprojection (FBP) algorithm is widely used in computed tomography for inverting the two-dimensional Radon transform. In this paper, we analyze the processing of an inconsistent data function by the FBP algorithm (in its continuous form). Specifically, me demonstrate that an image reconstructed using the FBP algorithm can be represented as the sum of a pseudoinverse solution and a residual image generated from an inconsistent component of the measured data. This reveals that, when the original data function is in the range of the Radon transform, the image reconstructed using the FBP algorithm corresponds to the pseudoinverse solution. When the data function is inconsistent, we demonstrate that the FBP algorithm makes use of a nonorthogonal projection of the data function to the range of the Radon transform.

引用

页码：539 / 542

页数：4

共 10 条

[1]

Abramowitz M., 1974, HDB MATH FUNCTIONS

[2]

Bertero M., 1998, Introduction to Inverse Problems in Imaging (Advanced Lectures in Mathematics)

[3] Projections onto the range of the exponential Radon transform and reconstruction algorithms [J].