A fast and accurate Fourier algorithm for iterative parallel-beam tomography
- 1 May 1996
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Image Processing
- Vol. 5 (5), 740-753
- https://doi.org/10.1109/83.495957
Abstract
We use a series-expansion approach and an operator framework to derive a new, fast, and accurate Fourier algorithm for iterative tomographic reconstruction. This algorithm is applicable for parallel-ray projections collected at a finite number of arbitrary view angles and radially sampled at a rate high enough that aliasing errors are small. The conjugate gradient (CG) algorithm is used to minimize a regularized, spectrally weighted least-squares criterion, and we prove that the main step in each iteration is equivalent to a 2-D discrete convolution, which can be cheaply and exactly implemented via the fast Fourier transform (FFT). The proposed algorithm requires O(N/sup 2/logN) floating-point operations per iteration to reconstruct an N/spl times/N image from P view angles, as compared to O(N/sup 2/P) floating-point operations per iteration for iterative convolution-backprojection algorithms or general algebraic algorithms that are based on a matrix formulation of the tomography problem. Numerical examples using simulated data demonstrate the effectiveness of the algorithm for sparse- and limited-angle tomography under realistic sampling scenarios. Although the proposed algorithm cannot explicitly account for noise with nonstationary statistics, additional simulations demonstrate that for low to moderate levels of nonstationary noise, the quality of reconstruction is almost unaffected by assuming that the noise is stationary.Keywords
This publication has 23 references indexed in Scilit:
- A Bayesian approach to image expansion for improved definitionIEEE Transactions on Image Processing, 1994
- Matrix formulation of computed tomogram reconstructionPhysics in Medicine & Biology, 1993
- A generalized Gaussian image model for edge-preserving MAP estimationIEEE Transactions on Image Processing, 1993
- Preconditioning methods for improved convergence rates in iterative reconstructionsIEEE Transactions on Medical Imaging, 1993
- B-spline signal processing. I. TheoryIEEE Transactions on Signal Processing, 1993
- A local update strategy for iterative reconstruction from projectionsIEEE Transactions on Signal Processing, 1993
- Bayesian estimation of transmission tomograms using segmentation based optimizationIEEE Transactions on Nuclear Science, 1992
- Alternatives to voxels for image representation in iterative reconstruction algorithmsPhysics in Medicine & Biology, 1992
- Convergence of EM image reconstruction algorithms with Gibbs smoothingIEEE Transactions on Medical Imaging, 1990
- Iterative convolution backprojection algorithms for image reconstruction from limited dataJournal of the Optical Society of America, 1983