Methods and apparatus for cone beam multislice CT correction

Claim 3

A method in accordance with claim 1 and further wherein determining contributions of segments along the trajectory to voxels in a reconstruction volume of the object comprises the step of filtering and backprojecting using a double integral over a fan angle and source angle for each point in the reconstruction volume.

Claim 4

A method in accordance with claim 2 wherein backprojecting using a double integral comprises backprojecting onto a polar reconstruction lattice.

Claim 5

A method in accordance with claim 1 , wherein the curved detector is a cylindrical detector, and compensating the determined contributions for curvature of the detector and x-ray cone beam geometry comprises the step of compensating the determined contributions for curvature of the cylindrical detector.

Claim 6

A method in accordance with claim 1 , wherein moving an x-ray source through a trajectory comprising moving the x-ray source through a helical trajectory relative to the object.

Claim 9

A method in accordance with claim 6 , wherein said weighting is performed prior to said filtering, and said filtering is performed prior to said backprojecting.

Claim 10

A method in accordance with claim 6 , wherein said weighting is performed prior to said filtering, and said filtering is performed prior to said backprojection.

Claim 11

A method in accordance with claim 8 , wherein weighting, filtering, and backprojecting a signal representative of detected x-rays passing through the object to produce a tomographic image comprises determining a reconstruction image function ƒ(v) written as: f  ( v ) = ∫ 0 π + 2   Γ  S L 2  ( v , β )  [ g ⊗ (  p * × HSW  ( β , γ ) ) ]   ( γ ; ξ ′ , β )   cos  3 / 2  ( γ   cos   α )   β ( cos 2  γ + sin 2  γ   cos 2   α ) 3 / 2 where: {circle around (×)} represents convolution; S is a source to isocenter distance; v is a voxel with cylindrical coordinates (r, ψ,κ); ξ′=ξ′ (v,β) is a z-elevation for a projection of v onto a detector; L is a voxel to source distance (in three-dimensional space); g( ) denotes a fan-beam reconstruction convolution kernel; p* is data that has been interpolated onto a tilted plane; HSW( ) denotes the half-scan weights; γ is a fan angle; β is a source angle; α is an angle between a horizontal plane and the tilted planes; and Γ is a maximum fan angle of the fan beam.

Claim 12

A method in accordance with claim 9 wherein g  ( γ - γ ~ ) = ( γ - γ ~ sin   ( η   ( γ ) - η   ( γ ~ ) ) ) 2  h  ( γ - γ ~ ) ≈ A  ( γ )   K  ( γ - γ ~ )  h  ( γ - γ ~ )  B  ( γ ~ ) ; where h( ) is a parallel kernel and A, B, and K are written as: A  ( γ ) = 1 + cos 2  α   tan 2  γ 1 + tan 2  γ ; B  ( γ ~ ) = 1 + cos 2  α   tan 2  γ ~ 1 + tan 2  γ ~ ; K  ( γ - γ ~ ) = 1 + tan 2  ( γ - γ ~ ) 1 + cos 2  α   tan 2  ( γ - γ ~ ) × ( γ - γ ~ sin  { a   tan  [ cos   α   tan   ( γ - γ ~ ) ] } ) 2 ; and η(γ)=arctan[(cos α)×tan(γ)]; and where {tilde over (γ)} is a fan angle for a ray passing through a voxel being reconstructed.

Claim 13

A method in accordance with claim 7 wherein moving the x-ray source through a trajectory comprises the step of moving the x-ray source in a helical trajectory relative to the object.

Claim 14

A method in accordance with claim 7 wherein projecting an x-ray cone beam from the moving x-ray source through an object towards a curved detector comprises the step of projecting the x-ray cone beam from the moving x-ray source through an object towards a cylindrical detector.

Claim 15

A method in accordance with claim 6 , wherein weighting, filtering, and backprojecting a signal representative of detected x-rays passing through the object to produce a tomographic image comprises determining a reconstruction image function ƒ(v)=ƒ(r, φ, κ) written as: f  ( r , φ , κ ) = ∫ 0 2  π + BΓ   ∫ - Γ Γ  S L 2 + κ 2  l × SW  ( β , γ ) cos  ( α )  g  ( γ - γ ~ )  p *  ( β , γ , ξ ′ )  cos  ( γcos  ( α ) )    γ   β where: B denotes an overscan angle; SW(β,γ) denotes a member of a group consisting of overscan and underscan weight functions; S is a source to isocenter distance; v is a voxel with cylindrical coordinates (r, ψ,κ); ξ′=ξ′ (v,β) is a z-elevation for a projection of v onto a detector; L is a voxel to source distance (in three-dimensional space); g( ) denotes a fan-beam reconstruction convolution kernel; p* is data that has been interpolated onto a tilted plane; γ is a fan angle; {tilde over (γ)} is a fan angle for a ray passing through a voxel being reconstructed; β is a source angle; α is an angle between a horizontal plane and the tilted planes; and Γ is a maximum fan angle of the fan beam.

Claim 16

A method in accordance with claim 13 wherein g  ( γ - γ ~ ) = ( γ - γ ~ sin  ( η  ( γ ) - η  ( γ ~ ) ) ) 2  h  ( γ - γ ~ ) ≈ A  ( γ )  K  ( γ - γ ~ )  h  ( γ - γ ~ )  B  ( γ ~ ) ; where h( ) is a parallel kernel and A, B, and K are written as: A  ( γ ) = 1 + cos 2  α   tan 2  γ 1 + tan 2  γ ; B  ( γ ~ ) = 1 + cos 2  α   tan 2  γ ~ 1 + tan 2  γ ~ ; K  ( γ - γ ~ ) = 1 + tan 2  ( γ - γ ~ ) 1 + cos 2   α   tan 2  ( γ - γ ~ ) × ( γ - γ ~ sin  { a   tan  [ cos   α   tan  ( γ - γ ~ ) ] } ) 2 ; and η(γ)=arctan[(cos α)×tan(γ)].

Claim 17

A method in accordance with claim 13 wherein said SW(β,γ) is an underscan weight function, and said weighting is performed prior to said filtering, and said filtering is performed prior to said backprojection.

Claim 18

A method in accordance with claim 13 wherein said SW(β,γ) is an overscan weight function, and said filtering is performed prior to said weighting, and said weighting is performed prior to said backprojection.

Claim 19

A multi-slice, computed tomography CT imaging system, said imaging system comprising a moveable x-ray source and a curved detector, said system configured to: move said x-ray source through a trajectory; project an x-ray cone beam from said moving x-ray source through an object towards said curved detector; and determine contributions of segments along the trajectory to voxels in a reconstruction volume of the object, including compensating the determined contributions for curvature of said detector and x-ray cone beam geometry.

Claim 20

A multi-slice, computed tomography CT imaging system, said imaging system comprising a moveable x-ray source and a curved detector, said system configured to: move said x-ray source through a trajectory; project an x-ray cone beam from said moving x-ray source through an object towards said curved detector; and determine contributions of segments along the trajectory to voxels in a reconstruction volume of the object, including compensating the determined contributions for curvature of said detector and x-ray cone beam geometry.

Claim 21

A multi-slice, computed tomography CT imaging system in accordance with claim 17 , wherein said system being configured to move said x-ray source through a trajectory comprises said system being configured to move said x-ray source through a helical trajectory relative to the object.

Claim 22

A multi-slice, computed tomography CT imaging system in accordance with claim 17 and further wherein said system being configured to determine contributions of segments along the trajectory to voxels in a reconstruction volume of the object comprises said system being configured to filter and backproject using a double integral over a fan angle and source angle for each point in the reconstruction volume.

Claim 23

A multi-slice, computed tomography CT imaging system in accordance with claim 19 wherein said system being configured to backproject using a double integral comprises said system being configured to backproject onto a polar reconstruction lattice.

Claim 24

A multi-slice, computed tomography CT imaging system in accordance with claim 17 , wherein said detector is a cylindrical detector, and said system being configured to compensate the determined contributions for curvature of said detector and x-ray cone beam geometry comprises said system being configured to compensate the determined contributions for curvature of said cylindrical detector.

Claim 25

A multi-slice, computed tomography CT imaging system, said imaging system comprising a moveable x-ray source and a curved detector, said system configured to: move an x-ray source through a trajectory; project an x-ray cone beam from said moving x-ray source through an object towards a curved detector; and weight, filter, and backproject a signal representative of detected x-rays passing through the object to produce a tomographic image; said system further configured to backproject in a three-dimensional space, with compensation for x-ray cone-beam geometry; and wherein said system being configured to backproject using a signal representative of detected x-rays comprises said system being configured to backproject onto a polar reconstruction lattice.

Claim 26

A multi-slice, computed tomography CT imaging system, said imaging system comprising a moveable x-ray source and a curved detector, said system configured to: move an x-ray source through a trajectory; project an x-ray cone beam from said moving x-ray source through an object towards a curved detector; and weight, filter, and backproject a signal representative of detected x-rays passing through the object to produce a tomographic image; said system further configured to backproject in a three-dimensional space, with compensation for x-ray cone-beam geometry; and wherein said system being configured to backproject using a signal representative of detected x-rays comprises said system being configured to backproject onto a polar reconstruction lattice.

Claim 27

A multi-slice, computed tomography CT imaging system in accordance with claim 22 , wherein said system is configured to perform said weighting prior to said filtering, and said filtering prior to said backprojecting.

Claim 28

A multi-slice, computed tomography CT imaging system in accordance with claim 22 wherein said curved detector is a cylindrical detector.

Claim 29

A multi-slice, computed tomography CT imaging system in accordance with claim 22 , wherein said system is configured to weight said signal prior to filtering said signal, and to filter said signal prior to said backprojecting.

Claim 30

A multi-slice, computed tomography CT imaging system in accordance with claim 25 , wherein said system being configured to weight, filter, and backproject a signal representative of detected x-rays passing through the object to produce a tomographic image comprises said system being configured to determine a reconstruction image function ƒ(v) written as: f  ( v ) = ∫ 0 π + 2  Γ  S L 2  ( v , β )  [ g ⊗ ( p * × HSW  ( β , γ ) ) ]  ( γ ; ξ ′ , β )  cos 3 / 2  ( γ   cos   α )   β ( cos 2  γ + sin 2  γ   cos 2   α ) 3 / 2 where: {circle around (×)} represents convolution; S is a source to isocenter distance; v is a voxel with cylindrical coordinates (r, ψ,κ); ξ′=ξ′ (v,β) is a z-elevation for a projection of v onto a detector; L is a voxel to source distance (in three-dimensional space); g( ) denotes a fan-beam reconstruction convolution kernel; p* is data that has been interpolated onto a tilted plane; HSW( ) denotes the half-scan weights; γ is a fan angle; β is a source angle; α is an angle between a horizontal plane and the tilted planes; and Γ is a maximum fan angle of the fan beam.

Claim 31

A method in accordance with claim 26 wherein g  ( γ - γ ~ ) = ( γ - γ ~ sin  ( η  ( γ ) - η  ( γ ~ ) ) ) 2  h  ( γ - γ ~ ) ≈ A  ( γ )  K  ( γ - γ ~ )  h  ( γ - γ ~ )  B  ( γ ~ ) ; where h( ) is a parallel kernel and A, B, and K are written as: A  ( γ ) = 1 + cos 2  α   tan 2  γ 1 + tan 2  γ ; B  ( γ ~ ) = 1 + cos 2  α   tan 2  γ ~ 1 + tan 2  γ ~ ; K  ( γ - γ ~ ) = 1 + tan 2  ( γ - γ ~ ) 1 + cos 2   α   tan 2  ( γ - γ ~ ) × ( γ - γ ~ sin  { a   tan  [ cos   α   tan  ( γ - γ ~ ) ] } ) 2 ; and η(γ)=arctan[(cos α)×tan(γ)]; and where {tilde over (γ)} is a fan angle for a ray passing through a voxel being reconstructed.

Claim 32

A multi-slice, computed tomography CT imaging system in accordance with claim 22 wherein said system being configured to move said x-ray source through a trajectory comprises said system being configured to move said x-ray source in a helical trajectory relative to the object.

Claim 33

A multi-slice, computed tomography CT imaging system in accordance with claim 22 , wherein said system being configured to weight, filter, and backproject a signal representative of detected x-rays passing through the object to produce a tomographic image comprises said system being configured to determine a reconstruction image function ƒ(v)=ƒ(r, φ, κ) written as: f  ( r , φ , κ ) = ∫ 0 2  π + BΓ   ∫ - Γ Γ  S L 2 + κ 2  l × SW  ( β , γ ) cos  ( α )  g  ( γ - γ ~ )  p *  ( β , γ , ξ ′ )  cos  ( γcos  ( α ) )    γ   β where: B denotes an overscan angle; SW(β,γ) denotes a member of a group consisting of overscan and underscan weight functions; S is a source to isocenter distance; v is a voxel with cylindrical coordinates (r, φ,κ); ξ′=ξ′ (v,β) is a z-elevation for a projection of v onto a detector; L is a voxel to source distance (in three-dimensional space); g( ) denotes a fan-beam reconstruction convolution kernel; p* is data that has been interpolated onto a tilted plane; γ is a fan angle; {tilde over (γ)} is a fan angle for a ray passing through a voxel being reconstructed; β is a source angle; α is an angle between a horizontal plane and the tilted planes; and Γ is a maximum fan angle of the fan beam.

Claim 34

A multi-slice, computed tomography CT imaging system in accordance with claim 29 wherein said SW(β,γ) is an overscan weight function, and said system is configured to perform said filtering prior to said weighting, and said weighting prior to said backprojection.

Claim 35

A method in accordance with claim 29 wherein g  ( γ - γ ~ ) = ( γ - γ ~ sin  ( η  ( γ ) - η  ( γ ~ ) ) ) 2  h  ( γ - γ ~ ) ≈ A  ( γ )  K  ( γ - γ ~ )  h  ( γ - γ ~ )  B  ( γ ~ ) ; where h( ) is a parallel kernel and A, B, and K are written as: A  ( γ ) = 1 + cos 2  α   tan 2  γ 1 + tan 2  γ ; B  ( γ ~ ) = 1 + cos 2  α   tan 2  γ ~ 1 + tan 2  γ ~ ; K  ( γ - γ ~ ) = 1 + tan 2  ( γ - γ ~ ) 1 + cos 2   α   tan 2  ( γ - γ ~ ) × ( γ - γ ~ sin  { a   tan  [ cos   α   tan  ( γ - γ ~ ) ] } ) 2 ; and η(γ)=arctan[(cos α)×tan(γ)].

Claim 36

A multi-slice, computed tomography CT imaging system in accordance with claim 29 wherein said SW (β,γ) is an underscan weight function, and said system is configured to perform said weighting prior to said filtering, and said filtering prior to said backprojection.