# Weighted backprojection approach to cone beam 3D projection reconstruction for truncated spherical detection geometry

## Abstract

A new analytical three-dimensional cone beam reconstruction algorithm is presented for truncated spherical detection geometry. The basic idea of the proposed algorithm is the formation of spatially invariant 3D blurred back-projected volumetric image by the use of the weighted backprojection of cone beam projection data and subsequent 3D filtering using an acceptance angle dependent [rho] filter. The backprojection weighting function is calculated on the basis of each given geometrical condition, i.e., detection geometry or degree of truncation, position of cone beam apex, and backprojection point. The proposed algorithm is derived analytically and is computationally efficient. Performance of the algorithm is evaluated by the reconstruction of 3D volumetric images using simulated data from arbitrarily truncated spherical detector geometries.

- Authors:

- (Univ. of California, Irvine, CA (United States). Dept. of Radiological Sciences)
- (Columbia Univ., New York, NY (United States). Dept. of Radiology)

- Publication Date:

- OSTI Identifier:
- 7000895

- 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; POSITRON COMPUTED TOMOGRAPHY; ALGORITHMS; ACCURACY; IMAGE PROCESSING; QUALITY CONTROL; COMPUTERIZED TOMOGRAPHY; CONTROL; DIAGNOSTIC TECHNIQUES; EMISSION COMPUTED TOMOGRAPHY; MATHEMATICAL LOGIC; PROCESSING; TOMOGRAPHY; 550601* - Medicine- Unsealed Radionuclides in Diagnostics

### Citation Formats

```
Cho, Z.H., Wu, E.X., and Hilal, S.K..
```*Weighted backprojection approach to cone beam 3D projection reconstruction for truncated spherical detection geometry*. United States: N. p., 1994.
Web. doi:10.1109/42.276149.

```
Cho, Z.H., Wu, E.X., & Hilal, S.K..
```*Weighted backprojection approach to cone beam 3D projection reconstruction for truncated spherical detection geometry*. United States. doi:10.1109/42.276149.

```
Cho, Z.H., Wu, E.X., and Hilal, S.K.. Tue .
"Weighted backprojection approach to cone beam 3D projection reconstruction for truncated spherical detection geometry". United States. doi:10.1109/42.276149.
```

```
@article{osti_7000895,
```

title = {Weighted backprojection approach to cone beam 3D projection reconstruction for truncated spherical detection geometry},

author = {Cho, Z.H. and Wu, E.X. and Hilal, S.K.},

abstractNote = {A new analytical three-dimensional cone beam reconstruction algorithm is presented for truncated spherical detection geometry. The basic idea of the proposed algorithm is the formation of spatially invariant 3D blurred back-projected volumetric image by the use of the weighted backprojection of cone beam projection data and subsequent 3D filtering using an acceptance angle dependent [rho] filter. The backprojection weighting function is calculated on the basis of each given geometrical condition, i.e., detection geometry or degree of truncation, position of cone beam apex, and backprojection point. The proposed algorithm is derived analytically and is computationally efficient. Performance of the algorithm is evaluated by the reconstruction of 3D volumetric images using simulated data from arbitrarily truncated spherical detector geometries.},

doi = {10.1109/42.276149},

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}

}