Convolution reconstruction of fan beam projections

Dreike, P. L.; Boyd, Douglas P.

doi:10.1016/s0146-664x(76)80032-9

Cited by 61 publications

(24 citation statements)

References 13 publications

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“…An interpolation from the polar coordinates to the Cartesian coordinates is needed. This needed interpolation has a similar effect as the interpolation of nonparallel beam projection data to parallel-beam geometry projection data, followed by a parallelbeam geometry reconstruction algorithm [24]. While most previous work seems to prefer a coordinate transformation for an extended inversion formula, the approach of interpolating the projection data into parallel-beam geometry and then use of parallel-beam inversion formula to reconstruct the interpolated data is straightforward.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

An inversion formula for the exponential Radon transform in spatial domain with variable focal‐length fan‐beam collimation geometry

Wen¹,

Zhang²

2006

Medical Physics

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Inverting the exponential Radon transform has a potential use for SPECT (single photon emission computed tomography) imaging in cases where a uniform attenuation can be approximated, such as in brain and abdominal imaging. Tretiak and Metz derived in the frequency domain an explicit inversion formula for the exponential Radon transform in two dimensions for parallel-beam collimator geometry. Progress has been made to extend the inversion formula for fan-beam and varying focal-length fan-beam (VFF) collimator geometries. These previous fan-beam and VFF inversion formulas require a spatially-variant filtering operation, which complicates the implementation and imposes a heavy computing burden. In this paper, we present an explicit inversion formula, in which a spatially-invariant filter is involved. The formula is derived and implemented in the spatial domain for VFF geometry (where parallel-beam and fan-beam geometries are two special cases). Phantom simulations mimicking SPECT studies demonstrate its accuracy in reconstructing the phantom images and efficiency in computation for the considered collimator geometries.

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Section: Conclusion and Discussionmentioning

confidence: 99%

An inversion formula for the exponential Radon transform in spatial domain with variable focal‐length fan‐beam collimation geometry

Wen¹,

Zhang²

2006

Medical Physics

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“…Except where otherwise noted, the nonlinear partial volume effect was simulated in the studies below. In all cases, reconstruction of image slices after the helical interpolation proceeded by use of the hybrid fanbeam reconstruction approach we have developed [16], rather than by the standard fanbeam FFBP [17], [18], although we have found that the choice of transverse reconstruction algorithm has very little influence on the longitudinal properties considered here. The imaging parameters for all experiments are given in Table I.…”

Section: Evaluation Methodsmentioning

confidence: 99%

“…Substituting (7) into this expression yields (17) Reversing the order of the integrals and the summation and making the substitution yields (18) where and remain unchanged in their functional form, despite their dependence on , because they are periodic in with period . It can be shown that for any function (19) even if does not satisfy the consistency condition or the periodicity condition , for all .…”

Section: Appendix Amentioning

confidence: 99%

Anti-aliasing weighting functions for single-slice helical CT

Rivière¹,

Pan

2002

IEEE Trans. Med. Imaging

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Spatially variant longitudinal aliasing plagues most volumes reconstructed from single-slice helical computed tomography data, and its presence can degrade resolution and distort image structures. We have recently developed a Fourier-based approach to longitudinal interpolation in helical computed tomography that can, for scans performed at pitch 1 or lower, essentially eliminate this longitudinal aliasing by exploiting a generalization of the Whittaker-Shannon sampling theorem whose conditions are satisfied by the interlaced pairs of direct and complementary longitudinal samples. However, the algorithm is computationally intensive and cannot be pipelined. In this paper, we address this shortcoming by deriving two spatial-domain, projection-data weighting functions that approximate the application of the Fourier-based approach, and preserve its aliasing suppression properties to some degree, while allowing for a pipelined implementation. The first approach, which we call simply 180AA, for anti-aliasing, is a direct spatial-domain approximation of the 180FT approach. The second approach, which we call 180BSP, is based on an approximate generalized interpolation approach making use of B-splines. Studies of aliasing and resolution properties in reconstructions from simulated data indicate that while the 180AA and 180BSP approaches do not perfectly replicate the favorable aliasing suppression and resolution properties of the 180FT approach, they do represent an improvement over the clinically standard 180LI approach on these fronts.

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“…Details of the algorithm as well as the implementation on a computer can be found in Herman et al (1976). Another approach that is used for reconstructing fan beam projections is to first convert the fan-beam data to equivalent parallel beam projection measurements by a method known as rebining (Dreike & Boyd, 1976). The rebined data are then reconstructed using the parallel beam algorithm.…”

Section: Image Reconstruction From Projectionsmentioning

confidence: 99%

Computer Assisted Gamma and X-Ray Tomography: Applications to Multiphase Flow Systems.

Kumar

Duduković

1997

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Convolution reconstruction of fan beam projections

Cited by 61 publications

References 13 publications

An inversion formula for the exponential Radon transform in spatial domain with variable focal‐length fan‐beam collimation geometry

An inversion formula for the exponential Radon transform in spatial domain with variable focal‐length fan‐beam collimation geometry

Anti-aliasing weighting functions for single-slice helical CT

Computer Assisted Gamma and X-Ray Tomography: Applications to Multiphase Flow Systems.

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