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

Guang-Hong Chen; Ting-Liang Zhuang; Shuai Leng; Brian E. Nett

doi:10.1117/1.2771643

1 August 2007 Cone-beam filtered backprojection image reconstruction using a factorized weighting function

Guang-Hong Chen, Ting-Liang Zhuang, Shuai Leng, Brian E. Nett

Author Affiliations +

Optical Engineering, Vol. 46, Issue 8, 087006 (August 2007). https://doi.org/10.1117/1.2771643

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,k;t) for redundant data was decomposed into three components w1(x,k), w₂(x,t), and sgn[k·y′(t)], viz. w(x,k;t)=[w₁(x,k)w₂(x,t)sgn(k·y(t))]. Based upon the normalization condition of the weighting function, the first component w₁(x,k) 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.

©(2007) Society of Photo-Optical Instrumentation Engineers (SPIE)

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Guang-Hong Chen, Ting-Liang Zhuang, Shuai Leng, and Brian E. Nett "Cone-beam filtered backprojection image reconstruction using a factorized weighting function," Optical Engineering 46(8), 087006 (1 August 2007). https://doi.org/10.1117/1.2771643

Published: 1 August 2007

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