Claims
- 1. 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.
- 2. The method of reconstructing a tomographic image as in claim 1 wherein the step of reconstructing the image from the parallel beam sinogram further comprises performing an inverse Fourier transform on the linearly interpolated data.
- 3. The method of reconstructing a tomographic image as in claim 1 wherein the step of expanding the weighted fan-beam sinogram into a Fourier series further comprises performing a fast Fourier transform on data elements, q(α,β), of the halfscan fan-beam sinogram with respect to a set of projection angles, β.
- 4. The method of reconstructing a tomographic image as in claim 3 further comprising forming a linear combination of complementary data elements of the transformed data, lying at projection bin α and −α.
- 5. The method of reconstructing a tomographic image as in claim 4 wherein the step of linearly interpolating further comprises forming a regularly spaced set of data, Pk(ξ), in Fourier space.
- 6. The method of reconstructing a tomographic image as in claim 5 wherein the step of forming a regularly spaced set of data, Pk(ξ), in Fourier space further comprises selecting a projection angle, φ1, and an offset distance, ξ1, in a parallel beam sinogram coordinate space.
- 7. The method of reconstructing a tomographic image as in claim 6 further comprising determining a projection angle, β1, of the halfscan fan-beam sinogram which corresponds to the selected projection angle, φ1.
- 8. The method of reconstructing a tomographic image as in claim 7 wherein the step of linearly interpolating the linear combination further comprises determining a set of offset angles, α1, and associated pair of data elements of the halfscan fan-beam sinogram which correspond to the determined projection angle and the offset distance ξ1.
- 9. The method of reconstructing a tomographic image as in claim 8 further comprising calculating a pair of fan beam offset distances, ξfb1, ξfb2, for the set of offset angles, α1.
- 10. The method of reconstructing a tomographic image as in claim 9 further comprising linearly interpolating a data element of the regularly spaced set of data at projection angle φ1 and offset distance ξ1 based on the pair of data elements at offset distances ξfb1 and ξfb2.
- 11. 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.
- 12. The apparatus for reconstructing a tomographic image as in claim 11 wherein the means for reconstructing the image from the parallel beam sinogram further comprises means for performing an inverse Fourier transform on the linearly interpolated data.
- 13. The apparatus for reconstructing a tomographic image as in claim 11 wherein the means for expanding the weighted fan-beam sinogram into a Fourier series further comprises means for performing a fast Fourier transform on data elements, q(α,β), of the halfscan fan-beam sinogram with respect to a set of projection angles, α.
- 14. The apparatus for reconstructing a tomographic image as in claim 13 further comprising means for forming a linear combination of complementary data elements of the transformed data, lying at projection bin α and −α.
- 15. The apparatus for reconstructing a tomographic image as in claim 14 wherein the means for linearly interpolating further comprises means for forming a regularly spaced set of data, Pk(ξ), in Fourier space.
- 16. The apparatus for reconstructing a tomographic image as in claim 15 wherein the means for forming a regularly spaced set of data, Pk (ξ), in Fourier space further comprises means for selecting a projection angle, φ1, and an offset distance, ξ1, in a parallel beam sinogram coordinate space.
- 17. The apparatus for reconstructing a tomographic image as in claim 16 further comprising means for determining a projection angle, β1, of the halfscan fan-beam sinogram which corresponds to the selected projection angle, φ1.
- 18. The apparatus for reconstructing a tomographic image as in claim 17 wherein the means for linearly interpolating the linear combination further comprises means for determining a set of offset angles, α1, and associated pair of data elements of the halfscan fan-beam sinogram which correspond to the determined projection angle, β1, and the offset distance ξ1.
- 19. The apparatus for reconstructing a tomographic image as in claim 18 further comprising means for calculating a pair of fan beam offset distances, ξfb1, ξfb2, for the set of offset angles, α1.
- 20. The apparatus for reconstructing a tomographic image as in claim 19 further comprising means for linearly interpolating a data element of the regularly spaced set of data at projection angle φ1 and offset distance ξ1 based the pair of data elements at offset distances ξfb1 and ξfb2.
- 21. 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.
- 22. The apparatus for reconstructing a tomographic image as in claim 21 wherein the reconstruction processor further comprises a Fourier processor adapted to perform an inverse Fourier transform on the linearly interpolated data.
- 23. 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.
- 24. 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.
- 25. The method of reconstructing a tomographic image as in claim 24 wherein the step of linearly interpolating further comprises forming a linear combination of data elements of the transformed data, lying at projection bin locations α and −α.
Parent Case Info
This application is a continuation-in-part of U.S. patent application Ser. No. 09/289,297, filed on Apr. 9, 1999 and assigned to the assignee of the present invention.
Government Interests
The U.S. Government has a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of Grant #R29CA70449 as awarded by the National Institute of Health.
US Referenced Citations (4)
Continuation in Parts (1)
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Number |
Date |
Country |
Parent |
09/289297 |
Apr 1999 |
US |
Child |
09/503609 |
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US |