# A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection

## Abstract

An exact inversion formula written in the form of shift-variant filtered-backprojection (FBP) is given for reconstruction from cone-beam data taken from any orbit satisfying Tuy's sufficiency conditions. The method is based on a result of Grangeat, involving the derivative of the three-dimensional (3-D) Radon transform, but unlike Grangeat's algorithm, no 3D rebinning step is required. Data redundancy, which occurs when several cone-beam projections supply the same values in the Radon domain, is handled using an elegant weighting function and without discarding data. The algorithm is expressed in a convenient cone-beam detector reference frame, and a specific example for the case of a dual orthogonal circular orbit is presented. When the method is applied to a single circular orbit, it is shown to be equivalent to the well-known algorithm of Feldkamp et al.

- Authors:

- (University Hospital, Brussels (Belgium). Div. of Nuclear Medicine)
- (Univ. of Utah, Salt Lake City, UT (United States). Dept. of Radiology)

- Publication Date:

- OSTI Identifier:
- 7242922

- Resource Type:
- Journal Article

- Journal Name:
- IEEE Transactions on Medical Imaging (Institute of Electrical and Electronics Engineers); (United States)

- Additional Journal Information:
- Journal Volume: 13:1; Journal ID: ISSN 0278-0062

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 62 RADIOLOGY AND NUCLEAR MEDICINE; SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY; ALGORITHMS; ACCURACY; DATA COVARIANCES; IMAGE PROCESSING; COMPUTERIZED TOMOGRAPHY; DIAGNOSTIC TECHNIQUES; EMISSION COMPUTED TOMOGRAPHY; MATHEMATICAL LOGIC; PROCESSING; TOMOGRAPHY; 550601* - Medicine- Unsealed Radionuclides in Diagnostics

### Citation Formats

```
Defrise, M., and Clack, R.
```*A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection*. United States: N. p., 1994.
Web. doi:10.1109/42.276157.

```
Defrise, M., & Clack, R.
```*A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection*. United States. doi:10.1109/42.276157.

```
Defrise, M., and Clack, R. Tue .
"A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection". United States. doi:10.1109/42.276157.
```

```
@article{osti_7242922,
```

title = {A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection},

author = {Defrise, M. and Clack, R.},

abstractNote = {An exact inversion formula written in the form of shift-variant filtered-backprojection (FBP) is given for reconstruction from cone-beam data taken from any orbit satisfying Tuy's sufficiency conditions. The method is based on a result of Grangeat, involving the derivative of the three-dimensional (3-D) Radon transform, but unlike Grangeat's algorithm, no 3D rebinning step is required. Data redundancy, which occurs when several cone-beam projections supply the same values in the Radon domain, is handled using an elegant weighting function and without discarding data. The algorithm is expressed in a convenient cone-beam detector reference frame, and a specific example for the case of a dual orthogonal circular orbit is presented. When the method is applied to a single circular orbit, it is shown to be equivalent to the well-known algorithm of Feldkamp et al.},

doi = {10.1109/42.276157},

journal = {IEEE Transactions on Medical Imaging (Institute of Electrical and Electronics Engineers); (United States)},

issn = {0278-0062},

number = ,

volume = 13:1,

place = {United States},

year = {1994},

month = {3}

}