Fast reconstruction with uniform noise properties in half-scan tomography
AssigneeArch Development Corporation
InventorXiaochuan Pan
Life of this patent
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Abstract
A method and apparatus are provided for reconstructing a tomographic image from a halfscan fan-beam sinogram using the parallel beam reconstruction algorithms. The method includes the steps of weighting at least some elements of the halfscan fan-beam sinogram to forming a weighted fan-beam sinogram and expanding the weighted fan-beam sinogram into a Fourier series. The method further includes the steps of linearly interpolating at least some elements of the Fourier series to form a parallel beam sinogram of linearly interpolated data and reconstructing the image from the parallel beam sinogram using the parallel beam reconstruction algorithms.
Claims25
A method of reconstructing a tomographic image from a halfscan fan-beam sinogram using the parallel beam reconstruction algorithms, such method comprising the steps of:
- weighting at least some elements of the halfscan fan-beam sinogram to a weighted fan-beam sinogram;
- expanding the weighted fan-beam sinogram into a Fourier series;
- linearly interpolating at least some elements of the Fourier series to form a parallel beam sinogram of linearly interpolated data;
- and
- reconstructing the image from the parallel beam sinogram using the parallel beam reconstruction algorithms.
An apparatus for reconstructing a tomographic image from a halfscan fan-beam sinogram using the parallel beam reconstruction algorithms, such apparatus comprising:
- means for weighting at least some elements of the halfscan fan-beam sinogram to form a weighted fan-beam sinogram;
- means for expanding the weighted fan-beam sinogram into a Fourier series;
- means for linearly interpolating at least some elements of the Fourier series to form a parallel beam sinogram of linearly interpolated data;
- and
- means for reconstructing the image from the parallel beam sinogram using the parallel beam reconstruction algorithms.
An apparatus for reconstructing a tomographic image from a halfscan fan-beam sinogram using the parallel beam reconstruction algorithms, such apparatus comprising:
- a weighting processor adapted to weight at least some elements of the halfscan fan-beam sinogram to form a weighted fan-beam sinogram;
- an expansion processor adapted to expand the weighted fan-beam sinogram into a Fourier series;
- an interpolation processor adapted to linearly interpolating at least some elements of the Fourier series to form a parallel beam sinogram of linearly interpolated data;
- and
- a reconstruction processor adapted to reconstruct the image from the parallel beam sinogram using the parallel beam reconstruction algorithms.
A method of reconstructing an tomographic image from a halfscan fan-beam sinogram using the parallel beam reconstruction algorithms, such method comprising the steps of:
- forming a weighted fan-beam sinogram from the halfscan fan-beam sinogram;
- forming a Fourier series expansion of the weighted fan-beam sinogram;
- linearly interpolating the Fourier series expansion to form a parallel beam sinogram;
- and
- reconstructing the image using the parallel beam reconstruction algorithms.
A method of reconstructing a tomographic image using the parallel beam reconstruction algorithms and a halfscan fan-beam sinogram, such method comprising the steps of:
- obtaining a weighted fan-beam sinogram, q(α,β), from the halfscan fan-beam sinogram, q(α,β), and a selected weighting function, ω(α,β);
- performing a Fourier series expansion of the weighted fan-beam sinogram, q(α,β), with respect to a set of projection angles, β;
- linearly interpolating the Fourier expanded sinogram to obtain a regularly spaced set of data, Pk(ξ), in Fourier space;
- reconstructing an image, a(r,υ) using the linearly interpolated data.
Dependencies are inferred from the claim text.