Image reconstruction from linograms: implementation and evaluation

Edholm, Paul; Herman, Gabor T.; Roberts, David A.

doi:10.1109/42.7788

Cited by 71 publications

(34 citation statements)

References 9 publications

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“…This has a substantial impact on the interpolation speed, since only 2-D interpolations within the transverse planes (rather than full 3-D ones) are needed [30]. This reduction of the interpolation dimensionality enabled by proper (oblique-angle dependent) axial sampling is based on a similar principle to the linogram reconstruction in which the 2-D interpolations within the planes of the image spectrum are reduced to 1-D ones by properly designed (polar-angle dependent) radial sampling of projection data [12], [31], [32]. For the continuous detector systems, the list mode data are often rebinned into bins of the same axial size for each tilt, although they can be rebinned into any reasonable geometry including the ring scanner geometry.…”

Section: Axial Samplingmentioning

confidence: 99%

3D-FRP: direct Fourier reconstruction with Fourier reprojection for fully 3-D PET

Matej

Lewitt

2001

IEEE Trans. Nucl. Sci.

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The direct Fourier method (DFM) for three-dimensional (3-D) reconstruction of a 3-D volume is based on the relationship between the 3-D Fourier transform (FT) of the volume and the two-dimensional (2-D) FT of a parallel-ray projection of the volume. The direct Fourier method has the potential for very fast reconstruction, but a straightforward implementation of the method leads to unsatisfactory results. This paper presents an implementation of the direct Fourier method for fully 3-D positron emission tomography (PET) data with incomplete oblique projections (3D-FRP) that gives results as good as, or better than, those of a much slower 3-D filtered backprojection method (3DRP), and in the same time as a fast but less accurate method using Fourier rebinning (FORE) followed by slice-by-slice reconstruction. In common with 3DRP, 3D-FRP is based on a discretization of an inversion formula, so it is geometrically accurate for large oblique angles, and both methods involve reprojection of an initial image. The critical two steps in the 3D-FRP method are the estimations of the samples of the 3-D transform of the image from the samples of the 2-D transforms of the projections on the planes through the origin of Fourier space, and vice versa for reprojection. These steps use a gridding strategy, combined with new approaches for weighting in the transform and image domains. Our experimental results confirm that good image accuracy can be achieved together with a short reconstruction time.

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Section: Axial Samplingmentioning

confidence: 99%

3D-FRP: direct Fourier reconstruction with Fourier reprojection for fully 3-D PET

Matej

Lewitt

2001

IEEE Trans. Nucl. Sci.

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“…For LR MRI, the signal corresponding to water protons appears both at the right and at the top, while the fat signal appears to the left and the bottom of the image, as expected from Eq. [5]. This is similar to the 2DFT spin-echo case where the water and fat signals are displaced along one direction (the readout direction).…”

Section: Methods Simulationsmentioning

confidence: 74%

Characterization of and correction for artifacts in linogram MRI

Gai

Axel

1997

Magnetic Resonance in Med

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Chemical shift differences, field inhomogeneity, and gradient nonlinearity result in artifacts in magnetic resonance imaging. Three artifacts are characterized for linogram imaging and it is shown that, based on computer simulations and theory, linogram MRI behaves similarly to 2DFT. A correction technique similar to a scheme for 2DFT imaging based on the Dixon technique and coordinate transform methods is proposed. The algorithm is applied to correct for field inhomogeneity and gradient nonlinearity-induced artifacts in both simulations and images of a clinical phantom. The results show good correlation with the theory. It is concluded that linogram imaging offers certain attractive features of both 2DFT and PR imaging techniques, and is a potentially viable alternative to PR imaging in the presence of field inhomogeneity.

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“…This approach differs from the previously described linogram method (LM) (2) (which was presented as a general reconstruction algorithm outside the context of reconstruction from MRI data) in that the data in k-space directly correspond to an intermediate step of the DFM approach to linogram image reconstruction.…”

Section: Introductionmentioning

confidence: 98%

“…The two sets are denoted by ST(k,, k,) and Sc(k,, k,), respectively (after remapping from ( n , t) to (ky, kv), using Eq. [2]). Sampling is carried…”

mentioning

confidence: 93%

A dual approach to linogram imaging for MRI

Gai

Axel

1997

Magnetic Resonance in Med

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An alternate scheme for linogram image reconstruction, which is more logical from the viewpoint of its applicability to MRI data, is presented here. As a result, an intermediate step for this method, the direct Fourier method (DFM) gives the same results as the earlier developed general reconstruction algorithm labeled as the linogram method (LM). However, the two differ in the pathways taken to the solution. As a result, an intermediate step for DFM corresponds directly with the geometry of linogram data collected for MRI, in contrast to the LM reconstruction. The two reconstruction methods are delineated within the context of MRI data reconstruction, and applied to reconstruct images from linogram spin-echo data of a physical phantom, obtained on a clinical 1.5 T scanner.

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Image reconstruction from linograms: implementation and evaluation

Cited by 71 publications

References 9 publications

3D-FRP: direct Fourier reconstruction with Fourier reprojection for fully 3-D PET

3D-FRP: direct Fourier reconstruction with Fourier reprojection for fully 3-D PET

Characterization of and correction for artifacts in linogram MRI

A dual approach to linogram imaging for MRI

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