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Optical Engineering

Cone-beam filtered backprojection image reconstruction using a factorized weighting function
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Paper Abstract

We present several new families of mathematically exact cone-beam image reconstruction algorithms for a general source trajectory that fulfills Tuy's data sufficiency condition. The basic structure of the new algorithms is to reconstruct images via filtered backprojection (FBP) with a 1-D shift-invariant filter. Specifically, the general weighting function w(x,kˆ;t) for redundant data was decomposed into three components w1(x,kˆ), w2(x,t), and sgn[kˆ·y′(t)], viz. w(x,kˆ;t)=[w1(x,kˆ)w2(x,t)sgn(kˆ·y(t))]. Based upon the normalization condition of the weighting function, the first component w1(x,kˆ) may be calculated using the second component w2(x,t) Thus, the design of the weighting function was reduced to the selection of the second component w2(x,t). Using this scheme, it has been demonstrated that, for a given scanning configuration, one may develop infinitely many different, exact cone-beam FBP image reconstruction algorithms. To demonstrate how this general procedure may be used to develop FBP image reconstruction algorithms, a two-concentric-circle scanning configuration is discussed in detail. Numerical simulations have been conducted to validate several of the derived image reconstruction algorithms. Several possible scan strategies are presented, and the possibility of performing multiple reconstructions with different scan configurations to reduce image noise is described. Noise properties also have been numerically studied for the implemented image reconstruction algorithms, then compared with two other shift-invariant FBP reconstruction algorithms.

Paper Details

Date Published: 1 August 2007
PDF: 14 pages
Opt. Eng. 46(8) 087006 doi: 10.1117/1.2771643
Published in: Optical Engineering Volume 46, Issue 8
Show Author Affiliations
Guang-Hong Chen, Univ. of Wisconsin/Madison (United States)
Ting-Liang Zhuang, Univ. of Wisconsin/Madison (United States)
Shuai Leng, Univ. of Wisconsin/Madison (United States)
Brian E. Nett, Univ. of Wisconsin/Madison (United States)

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