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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 ..."
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Cited by 22 (3 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.
DirectFourier Reconstruction In Tomography And Synthetic Aperture Radar
 Intl. J. Imaging Sys. and Tech
, 1998
"... We investigate the use of directFourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR ..."
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Cited by 9 (0 self)
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We investigate the use of directFourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR. We show that the CBP algorithm is equivalent to DF reconstruction using a Jacobianweighted 2D periodic sinckernel interpolator. This interpolation is not optimal in any sense, which suggests that DF algorithms utilizing optimal interpolators may surpass CBP in image quality. We consider use of two types of DF interpolation: a windowed sinc kernel, and the leastsquares optimal Yen interpolator. Simulations show that reconstructions using the Yen interpolator do not possess the expected visual quality, because of regularization needed to preserve numerical stability. Next, we show that with a concentricsquares sampling scheme, DF interpolation can be performed accurately and efficiently...
Signal Processing Issues In Synthetic Aperture Radar And Computer Tomography
, 1998
"... This paper also proposed another reconstruction method based on a direct approximation of the Fourier inversion formula using a twodimensional (2D) trapezoidal rule. In addition, the possibility of reconstruction from a concentricsquares raster was discussed. Numerous simple interpolators have bee ..."
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Cited by 1 (0 self)
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This paper also proposed another reconstruction method based on a direct approximation of the Fourier inversion formula using a twodimensional (2D) trapezoidal rule. In addition, the possibility of reconstruction from a concentricsquares raster was discussed. Numerous simple interpolators have been tried in DF reconstruction with the results compared with CBP [33]. In [34] and [35], the concept of angular bandlimiting was used to interpolate the polar data onto a Cartesian grid. In [36], a DF reconstruction using bilinear interpolation for diffraction tomography provided image quality that was comparable to that produced by the CBP algorithm. Very good reconstruction quality was obtained in [37] and [38] using a spline interpolator, or a hybrid type of spline interpolator. The notion of "gridding" was introduced in [39] as a method of obtaining optimal inversion of Fourier data. An optimal gridding function was proposed, and successful results were obtained when applied to the tomographic reconstruction problem. In [40], several different gridding functions were tried for DF reconstruction, and the performances were compared. In [41, 42], the linogram reconstruction method was proposed as a form of DF reconstruction. The data collection grid in the linogram method is the same as in the concentricsquares sampling scheme. The inversion of the Fourier data in [41, 42] was accomplished by first applying the chirpz transform in one direction and then computing FFTs in the other direction. In CT, many of these attempts at DF reconstruction have given a poorer result than the CBP algorithm, due to the error incurred in the process of the polartoCartesian interpolation. The attraction of DF reconstruction, however, is that it is thought to require less computation than ...
Brain Mapping by Positron Emission Tomography
, 1996
"... In this paper the basis of PET (Positron Emission Tomography) is reviewed, and it is shown that the measured signals can be modelled as the Radon transform of the desired spatial distribution of, e.g., the brain activity. Next, two of the direct reconstruction methods are presented. Both are derived ..."
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In this paper the basis of PET (Positron Emission Tomography) is reviewed, and it is shown that the measured signals can be modelled as the Radon transform of the desired spatial distribution of, e.g., the brain activity. Next, two of the direct reconstruction methods are presented. Both are derived from inversion of the Radon transform. It is shown that the reconstruction can be based on filtering and integration techniques. Another major class of reconstruction techniques is presented, namely the linear algebra based methods, which often are formed as iterative methods. A very fast way of implementing a set of iterative reconstruction techniques is shown along with a set of examples. 1.1 Introduction to PET The PET scanner is based on radioactive tracers. A small dosage of a fi + emitter, such as O15 or C11, is injected into the patient (or the object to be scanned). The fi + emitter will be distributed in the tissue due to the blood circulation. If for instance the brain is t...
Iterative Methods for Reconstructing PET Images
, 1995
"... In this report the fundamental theory of brain scanners is presented. It turns out that the wanted image of, e.g., the brain can be obtained by use of inverse Radon transformation. The Radon transform and several classical direct inversion schemes are presented. The inversion schemes are modified to ..."
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In this report the fundamental theory of brain scanners is presented. It turns out that the wanted image of, e.g., the brain can be obtained by use of inverse Radon transformation. The Radon transform and several classical direct inversion schemes are presented. The inversion schemes are modified to enable a numerical implementation, and some of the numerical problems are discussed. The theory is extended into 3D and some theoretical aspects are presented. Finally some basic properties of the Radon transform are shown and a model of a brain named the Shepp Logan phantom is presented, which can be used to test numerical implementations of the inversion algorithms. Contents 1 Introduction 1 2 Fundamental Theory of the CTScanner 2 3 The PET Scanner 5 3.1 The Two Transmission Scans : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 4 Inversion of the Radon Transform 10 4.1 The Fourier Slice Theorem : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 4.2...