### 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,k̂;t) for redundant data was decomposed into three components w_{1}(x,k̂), w_{2}(x,t), and sgn[k̂·y′(t)], viz. w(x,k̂;t) =[w_{1}(x,k̂)w_{2}(x,t)sgn(k̂-y(t))]. Based upon the normalization condition of the weighting function, the first component w_{1} (x, k̂) may be calculated using the second component w_{2}(x, t) Thus, the design of the weighting function was reduced to the selection of the second component w_{2}(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.

Original language | English (US) |
---|---|

Article number | 087006 |

Journal | Optical Engineering |

Volume | 46 |

Issue number | 8 |

DOIs | |

State | Published - Aug 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- Computed tomography
- Cone-beam
- Image reconstruction

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Optical Engineering*,

*46*(8), [087006]. https://doi.org/10.1117/1.2771643

**Cone-beam filtered backprojection image reconstruction using a factorized weighting function.** / Chen, Guang Hong; Zhuang, Ting Liang; Leng, Shuai; Nett, Brian E.

Research output: Contribution to journal › Article

*Optical Engineering*, vol. 46, no. 8, 087006. https://doi.org/10.1117/1.2771643

}

TY - JOUR

T1 - Cone-beam filtered backprojection image reconstruction using a factorized weighting function

AU - Chen, Guang Hong

AU - Zhuang, Ting Liang

AU - Leng, Shuai

AU - Nett, Brian E.

PY - 2007/8

Y1 - 2007/8

N2 - 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,k̂;t) for redundant data was decomposed into three components w1(x,k̂), w2(x,t), and sgn[k̂·y′(t)], viz. w(x,k̂;t) =[w1(x,k̂)w2(x,t)sgn(k̂-y(t))]. Based upon the normalization condition of the weighting function, the first component w1 (x, k̂) 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.

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

KW - Computed tomography

KW - Cone-beam

KW - Image reconstruction

UR - http://www.scopus.com/inward/record.url?scp=36048980062&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36048980062&partnerID=8YFLogxK

U2 - 10.1117/1.2771643

DO - 10.1117/1.2771643

M3 - Article

VL - 46

JO - Optical Engineering

JF - Optical Engineering

SN - 0091-3286

IS - 8

M1 - 087006

ER -