O(N/sup 3/ log N) backprojection algorithm for the 3-D Radon transform

Author

Basu, Samit ; Bresler, Yoram

Author_Institution

Coordinated Sci. Lab., Illinois Univ., Urbana, IL, USA

Volume

21

Issue

2

fYear

2002

Firstpage

76

Lastpage

88

Abstract

We present a novel backprojection algorithm for three-dimensional (3-D) Radon transform data that requires O(N³ log₂ N) operations for reconstruction of an N×N×N volume from O(N²) plane-integral projections. Our algorithm uses a hierarchical decomposition of the 3-D Radon transform to recursively decompose the backprojection operation. Simulations are presented demonstrating reconstruction quality comparable to the standard filtered backprojection, which requires O(N⁵) computations under the same circumstances.

Keywords

Radon transforms; computational complexity; computerised tomography; image reconstruction; inverse problems; medical image processing; 3-D head phantom; Dirac delta distribution; backprojection algorithm; complexity requirements; cone beam tomography; convolutional angular smoothing; fast algorithm; hierarchical decomposition; inversion techniques; plane-integral projections; recursive application; three-dimensional Radon transform; volume reconstruction; Computational modeling; Data acquisition; Image reconstruction; Magnetic resonance imaging; Optical imaging; Radar imaging; Robustness; Synthetic aperture radar; Tomography; X-ray imaging; Algorithms; Head; Humans; Imaging, Three-Dimensional; Models, Theoretical; Phantoms, Imaging; Radiographic Image Enhancement; Reproducibility of Results; Sensitivity and Specificity; Tomography, X-Ray Computed;

fLanguage

English

Journal_Title

Medical Imaging, IEEE Transactions on

Publisher

ieee

ISSN

0278-0062

Type

jour

DOI

10.1109/42.993127

Filename

993127