Novel Properties Of The Fourier Decomposition Of The Sinogram

Edholm, Paul; Lewitt, R.M.; Lindholm, Bernt

doi:10.1117/12.966672

Cited by 110 publications

(55 citation statements)

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“…Ivan G. Kazantsev (1) , Gabor T. Herman (2) , Laslo Cernetic (3) (1) Materials Science Department, RISØ, DTU, Roskilde, Denmark (2) Dept. of Computer Science, The Graduate Center, CUNY, New York, USA (3) Dept.…”

Section: Backprojection-based Reconstruction and Correction For Distamentioning

confidence: 99%

“…and Comp. Graphics, University of Szeged, Szeged, Hungary (1) kazantsev1@netzero.com, (2) gabortherman@yahoo.com, (3) cslaszlo@inf.u-szeged.hu…”

Section: Backprojection-based Reconstruction and Correction For Distamentioning

confidence: 99%

“…It is estimated by a correction ofĜ(n, k), the 2D Fourier transform of the corrupted projection data g(ϕ, x). The correction is based on the FDR principle [2] (see also (26)), which implieŝ…”

Section: Ctf Correction Of Micrographsmentioning

confidence: 99%

“…Correction for the CTF in the micrographs aims at estimating enhanced data that can be treated as if they were line integrals, so that algorithms from computerized tomography (CT) become applicable. Specialized filters that correct for distance-dependent distortions in 1D projections of 2D objects via the frequency-distance relation (FDR) and using a stationary phase approximation have been known for years [2]. This approach was adapted by Dubowy and Herman [3] to the 3D case in which the 2D micrographs are gathered from directions lying on a big circle around the object.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Backprojection-based reconstruction and correction for distance-dependent defocus in cryoelectron microscopy

Kazantsev

Herman²,

Cernetic

2008

2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro

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Section: Backprojection-based Reconstruction and Correction For Distamentioning

confidence: 99%

“…and Comp. Graphics, University of Szeged, Szeged, Hungary (1) kazantsev1@netzero.com, (2) gabortherman@yahoo.com, (3) cslaszlo@inf.u-szeged.hu…”

Section: Backprojection-based Reconstruction and Correction For Distamentioning

confidence: 99%

Section: Ctf Correction Of Micrographsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Backprojection-based reconstruction and correction for distance-dependent defocus in cryoelectron microscopy

Kazantsev

Herman²,

Cernetic

2008

2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro

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“…1, left panel͒. A thorough discussion of these properties can be found in Edholm et al 7 The Fourier rebinning algorithm, a rebinning method widely used in PET studies to compact a 3D acquisition dataset into a stack of ordinary 2D data, 8,9 makes use of this property through the so-called consistency condition for the 2D Radon transform. 10 In this case, it is common not to take into account the actual radius of support ͑object dependent͒ but to consider the whole field of view ͑FOV͒.…”

Section: Introductionmentioning

confidence: 99%

Sinogram bow‐tie filtering in FBP PET reconstruction

Abella¹,

Vaquero²,

Soto-Montenegro³

et al. 2009

Medical Physics

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Low-pass filtering of sinograms in the radial direction is the most common practice to limit noise amplification in filtered back projection ͑FBP͒ reconstruction of positron emission tomography studies. Other filtering strategies have been proposed to prevent the loss in resolution due to low-pass radial filters, although results have been diverse. Using the well-known properties of the Fourier transform of a sinogram, the authors defined a binary mask that matches the expected shape of the support region in the Fourier domain of the sinogram ͑"bow tie"͒. This mask was smoothed by a convolution with a ten-point Gaussian kernel which not only avoids ringing but also introduces a pre-emphasis at low frequencies. A new filtering scheme for FBP is proposed, comprising this smoothed bow-tie filter combined with a standard radial filter and an axial filter. The authors compared the performance of the bow-tie filtering scheme with that of other previously reported methods: Standard radial filtering, angular filtering, and stackgram-domain filtering. All the quantitative data in the comparisons refer to a baseline reconstruction using a ramp filter only. When using the smallest size of the Gaussian kernel in the stackgram domain, the authors achieved a noise reduction of 33% at the cost of degrading radial and tangential resolutions ͑14.5% and 16%, respectively, for cubic interpolation͒. To reduce the noise by 30%, the angular filter produced a larger degradation of contrast ͑3%͒ and tangential resolution ͑46% at 10 mm from the center of the field of view͒ and showed noticeable artifacts in the form of circular blurring dependent on the distance to the center of the field of view. For a similar noise reduction ͑33%͒, the proposed bow-tie filtering scheme yielded optimum results in resolution ͑gain in radial resolution of 10%͒ and contrast ͑1% increase͒ when compared with any of the other filters alone. Experiments with rodent images showed noticeable image quality enhancement when using the proposed bow-tie filtering scheme.

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Two-step navigatorless correction algorithm for radialk-space MRI acquisitions

et al. 2001

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A new way to correct magnetic resonance image artifacts resulting from view‐dependent phase variations and view‐dependent variations in rigid body object translation is presented by exploiting basic properties of the trajectory of radial k‐space acquisitions. Simulations, phantom studies, and in vivo experiments are used to demonstrate the feasibility and the utility of this method. While somewhat analogous to navigator echo correction, in which special gradients are interleaved into the imaging sequence so echoes at the center of k‐space can be acquired prior to or after collection of the image data, the current method does not require additional new gradient structures within the pulse sequence or increases in scan time. The new method uses the phase information from all collected radial k‐space data points rather than only the navigator echo, which permits correction of multiple sources of view‐dependent phase variation in the image data. The resultant effect is improved image quality in radial MRI acquisitions. Magn Reson Med 45:277–288, 2001. © 2001 Wiley‐Liss, Inc.

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Novel Properties Of The Fourier Decomposition Of The Sinogram

Abstract: The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel -ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections.

Cited by 110 publications

References 0 publications

Backprojection-based reconstruction and correction for distance-dependent defocus in cryoelectron microscopy

Backprojection-based reconstruction and correction for distance-dependent defocus in cryoelectron microscopy

Sinogram bow‐tie filtering in FBP PET reconstruction

Two-step navigatorless correction algorithm for radialk-space MRI acquisitions

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