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Iterative tomographic image reconstruction using Fourierbased forward and back projectors
 IEEE Trans. Med. Imag
, 2004
"... Fourierbased reprojection methods have the potential to reduce the computation time in iterative tomographic image reconstruction. Interpolation errors are a limitation of Fourierbased reprojection methods. We apply a minmax interpolation method for the nonuniform fast Fourier transform (NUFFT) t ..."
Abstract

Cited by 23 (4 self)
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Fourierbased reprojection methods have the potential to reduce the computation time in iterative tomographic image reconstruction. Interpolation errors are a limitation of Fourierbased reprojection methods. We apply a minmax interpolation method for the nonuniform fast Fourier transform (NUFFT) to minimize the interpolation errors. Numerical results show that the minmax NUFFT approach provides substantially lower approximation errors in tomographic reprojection and backprojection than conventional interpolation methods.
A fast and accurate multilevel inversion of the radon transform
 SIAM J. Appl. Math
, 1999
"... Abstract. A number of imaging technologies reconstruct an image function from its Radon projection using the convolution backprojection method. The convolution is an O(N 2 log N) algorithm, where the image consists of N ×N pixels, while the backprojection is an O(N 3) algorithm, thus constituting th ..."
Abstract

Cited by 12 (2 self)
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Abstract. A number of imaging technologies reconstruct an image function from its Radon projection using the convolution backprojection method. The convolution is an O(N 2 log N) algorithm, where the image consists of N ×N pixels, while the backprojection is an O(N 3) algorithm, thus constituting the major computational burden of the convolution backprojection method. An O(N 2 log N) multilevel backprojection method is presented here. When implemented with a Fourierdomain postprocessing technique, also presented here, the resulting image quality is similar or superior to the image quality of the classical backprojection technique. Key words. Radon transform, inversion of the Radon transform, computed tomography, convolution backprojection, multilevel, Fourierdomain postprocessing AMS subject classifications. 92C55, 44A12, 65R10, 68U10 PII. S003613999732425X 1. Background. Reconstruction of a function of two or three variables from its Radon transform has proven vital in computed tomography (CT), nuclear magnetic resonance imaging, astronomy, geophysics, and a number of other fields [13]. One of the best known reconstruction algorithms is the convolution backprojection method (CB), which is widely used in commercial CT devices [13] (with rebinning for divergentbeam projections [18]). Recently, it has been applied to spotlightmode synthetic aperture radar image reconstruction [14, 23] in which the conventional method is the direct Fourier method (DF), i.e., Fourierdomain interpolation followed by twodimensional (2D) FFT [21]. Originally, CB was preferred to DF since the former provided better images [18, 20]. However, since the backprojection part of CB raises the computational complexity of the method to O(N 3), while DF’s complexity is O(N 2 log N), there has been
An O(N² log N) Multilevel Backprojection Method
"... A number of imaging technologies reconstruct an image function from its Radon projection using the convolution backprojection method. The convolution is an O(N² log N ) algorithm, where the image consists of N x N pixels, while the backprojection is an O(N³) algorithm, thus constituting the major c ..."
Abstract
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A number of imaging technologies reconstruct an image function from its Radon projection using the convolution backprojection method. The convolution is an O(N² log N ) algorithm, where the image consists of N x N pixels, while the backprojection is an O(N³) algorithm, thus constituting the major computational burden of the convolution backprojection method. An O(N² log N ) multilevel backprojection method is presented here. When implemented with a Fourierdomain postprocessing technique, also presented here, the resulting image quality is similar to or superior than the image quality of the classical backprojection technique.