Method for rebinning and for correcting cone beam error in a fan beam computed tomographic scanner system

Claim 1

A computer-implemented method for correcting cone beam error in an image reconstructed from data in a sinogram acquired from a fan beam computer tomography X-ray system, the method comprising the following steps: (a) rebinning fan beam data acquired from said system into parallel beam format, said step of rebinning including the steps of: (1) performing a first one-dimensional interpolation of columns in said fan beam data sinogram to generate an intermediate sinogram having a rectangular portion that includes non-redundant X-ray data and having first and second corner portions that include redundant X-ray data; (2) weighting said redundant data in said intermediate sinogram such that a sum of a redundant X-ray weight plus a central X-ray weight is unity, wherein said redundant data are folded over into said rectangular portion such that said weighted central X-ray plus said weighted redundant X-ray replaces said central X-ray value in said intermediate sinogram; (3) performing a second one-dimensional interpolation of rows in said intermediate sinogram, wherein said fan beam data are now represented in a parallel beam sinogram that includes said redundant data folded into said rectangular portion; and (b) reconstructing data acquired by said fan beam CT system, said step of reconstructing including the steps of: (1) filtering with a parallel beam kernel said parallel beam sinogram data for each view therein; (2) circularly shifting data resulting from said step 1 (b) (1); (3) transforming data resulting from said step 1(b) (2); (4) replicating data resulting from said step 1(b) (3); (5) multiplying by an interpolation filter data resulting from said step 1(b)(4); (6) using a gridding function, gridding data resulting from said step 1(b)(5) into a Fourier image at an angle corresponding to the view angle; (7) convolving each view in said step 1(b)(6) with the transform of a cone beam weight function by multiplying by each non-zero coefficient of the weight function and gridding at an offset from the view angle into a Fourier image; (8) repeating steps (b) (1) through (b)(7) for each said view; (9) forming a preliminary image by taking a two-dimensional inverse Fourier transform of said views; (10) extracting a center portion of said preliminary image; (11) forming a reconstructed image by multiplying said preliminary image with its center portion extracted by an inverse of the transform of said gridding function; wherein said reconstructed image is substantially free of cone beam error.

Claim 9

An apparatus for correcting cone beam error in an image reconstructed from data in a sinogram acquired from a fan beam computer tomography X-ray system, the apparatus comprising: (a) means for rebinning fan beam data acquired from said system into parallel beam format, said means for rebinning including: (1) means for performing a first one-dimensional interpolation of columns of the fan beam data sinogram to generate an intermediate sinogram having a rectangular portion that includes non-redundant data, and having first and second corner portions that include redundant data; (2) means for weighting said redundant data such that a sum of a redundant ray weight plus a central ray weight is unity, wherein said redundant data are folded over into said rectangular portion of said intermediate sinogram such that a sum of said weighted central ray plus said weighted redundant ray replaces said central ray value in said intermediate sinogram; (3) means for performing a second one-dimensional interpolation of rows in said intermediate sinogram, wherein said fan beam data are now represented in a parallel beam sinogram that includes said redundant data folded into said rectangular portion; and (b) means for reconstructing views acquired by said fan beam CT system, said means for reconstructing including: (1) means for filtering with a parallel beam kernel said parallel beam sinogram for each view therein; (2) means for circularly shifting output data from said means for filtering; (3) means for transforming output data from said means for circularly shifting; (4) means for replicating output data from said means for transforming; (5) means for multiplying by an interpolation filter output data from said means for replicating; (6) gridding function means for gridding out put data from said means for multiplying into a Fourier image at an angle corresponding to the view angle; (8) means for convolving each view in output data provided by said gridding function means with the transform of a cone beam weight function by multiplying by each non-zero coefficient of the weight function and gridding at an offset from the view angle into a Fourier image; (9) means for subjecting each such view to said means described in (b)(1) through (b) (4); (10) means for forming a preliminary image by taking a two-dimensional inverse Fourier transform of said views; (11) means for extracting a center portion of said preliminary image; (12) means for forming a reconstructed image by multiplying said preliminary image with its center portion extracted by an inverse of the transform of said gridding function; wherein said reconstructed image is substantially free of cone beam error.

Claim 10

An apparatus for correcting cone beam error in an image reconstructed from data in a sinogram acquired from a fan beam computer tomography X-ray system, the apparatus comprising: (a) means for rebinning fan beam data acquired from said system into parallel beam format, said means for rebinning including: (1) means for performing a first one-dimensional interpolation of columns of the fan beam data sinogram to generate an intermediate sinogram having a rectangular portion that includes non-redundant data, and having first and second corner portions that include redundant data; (2) means for weighting said redundant data such that a sum of a redundant ray weight plus a central ray weight is unity, wherein said redundant data are folded over into said rectangular portion of said intermediate sinogram such that a sum of said weighted central ray plus said weighted redundant ray replaces said central ray value in said intermediate sinogram; (3) means for performing a second one-dimensional interpolation of rows in said intermediate sinogram, wherein said fan beam data are now represented in a parallel beam sinogram that includes said redundant data folded into said rectangular portion; and (b) means for reconstructing views acquired by said fan beam CT system, said means for reconstructing including: (1) means for filtering with a parallel beam kernel said parallel beam sinogram for each view therein; (2) means for circularly shifting output data from said means for filtering; (3) means for transforming output data from said means for circularly shifting; (4) means for replicating output data from said means for transforming; (5) means for multiplying by an interpolation filter output data from said means for replicating; (6) gridding function means for gridding out put data from said means for multiplying into a Fourier image at an angle corresponding to the view angle; (8) means for convolving each view in output data provided by said gridding function means with the transform of a cone beam weight function by multiplying by each non-zero coefficient of the weight function and gridding at an offset from the view angle into a Fourier image; (9) means for subjecting each such view to said means described in (b)(1) through (b) (4); (10) means for forming a preliminary image by taking a two-dimensional inverse Fourier transform of said views; (11) means for extracting a center portion of said preliminary image; (12) means for forming a reconstructed image by multiplying said preliminary image with its center portion extracted by an inverse of the transform of said gridding function; wherein said reconstructed image is substantially free of cone beam error.