Method and apparatus for CT reconstruction

Claim 3

A method in accordance with claim 1 , wherein filtering and backprojecting the projection data comprises the step of discretely reconstructing the image as an approximation to a continuous weighted-convolution backprojection written as: f  ( r , φ ) = 1 4  π 2  S 2  ∫ 0 2  π  1 G  ( ν ~ ) 2  { Lim ɛ → 0  ∫ ν inf ν sup  f ɛ  ( ν - ν ~ ) H 2  ( ν - ν ~ ) × J  ( ν ) E  ( ν ) × p  ( β , ν )   ν }   β where: r, φ, and θ are polar coordinates in a polar coordinate system; f(r,φ) is a polar representation of an x-ray attenuation coefficient distribution to be reconstructed; ν is a detector cell coordinate on a straight line defined by an intersection of an imaging plane and a plane defined by the flat panel detector; β is an angle from a y-axis to a radiation source; p(β,ν) is a representation of a radon transform of f , which itself is a Cartesian representation of an x-ray attenuation distribution to be reconstructed; S is a distance from a radiation source to an isocenter; ν sup is a maximum detector cell coordinate on the flat panel detector; ν inf is a minimum detector cell coordinate; H(ν−{tilde over (ν)}) and F ε (ν−{tilde over (ν)}) are convolution kernels; η({tilde over (ν)}) is a fan angle for a ray passing through a voxel being reconstructed, and {tilde over (ν)} is a cell index for the ray; E(ν) is a preconvolution weight that is a function of detector cell position ν; G({tilde over (ν)}) is a post convolution weighting; and J(ν) is a Jacobian function.

Claim 4

A method in accordance with claim 2 wherein the pre-convolution weights are independent of an image point described by (r,φ).

Claim 5

A method in accordance with claim 2 , wherein: sin  [ η  ( ν ) ] - sin  [ η  ( ν ~ ) ] = { η ′  ( ν )  cos  [ η  ( ν ) ]  η ′  ( ν ~ )  cos  [ η  ( ν ~ ) ] η ′  ( 0 )  η ′  ( ν - ν ′ )  cos  [ η  ( ν - ν ~ ) ] } 1 / 2  sin  [ η  ( ν - ν ~ ) ] ; where η(ν) is a fan angle as a function of detector cell coordinate ν.

Claim 6

A method in accordance with claim 2 , wherein acquiring projection data of an object utilizing a flat-panel detector comprises the step of acquiring projection data of the object utilizing a cone beam of radiation from a radiation source having a circular trajectory.

Claim 7

A method in accordance with claim 5 wherein the detector is a multi-row detector and further comprising the step of rebinning data on a row-by-row basis.

Claim 8

A method in accordance with claim 2 wherein acquiring projection data of an object utilizing a flat-panel detector comprises the step of acquiring projection data of the object utilizing a cone beam of radiation from a radiation source having a helical trajectory.

Claim 9

A method in accordance with claim 7 wherein the detector is a multi-row detector and further comprising the steps of weighting the projection data to account for individual ray cone-angles, and using an average cone angle of a fan-parallel projection equal to a cone angle for a ray at η=0 to determine dβ′ in a tilted plane, where dβ′ is a source rotation in the tilted plane.

Claim 10

A CT imaging system having a flat panel radiation detector and a radiation source, the flat panel radiation detector having a plurality of detector cells, and said imaging system being configured to: acquire projection data of an object utilizing the flat-panel detector; and filter and backproject the projection data, without radially interpolating, to reconstruct a three-dimensional image of the object.

Claim 11

A CT imaging system having a flat panel radiation detector and a radiation source, the flat panel radiation detector having a plurality of detector cells, and said imaging system being configured to: acquire projection data of an object utilizing the flat-panel detector; and filter and backproject the projection data, without radially interpolating, to reconstruct a three-dimensional image of the object.

Claim 12

A CT imaging system in accordance with claim 9 , wherein said system being configured to filter and backproject the projection data comprises said system being configured to reconstruct the image as a weighted-convolution backprojection written as: f  ( r , φ ) = 1 4  π 2  S 2  ∫ 0 2  π  1 G  ( ν ~ ) 2  { Lim ɛ → 0  ∫ ν inf ν sup  f ɛ  ( ν - ν ~ ) H 2  ( ν - ν ~ ) × J  ( ν ) E  ( ν ) × p  ( β , ν )   ν }   β where: r, φ, and θ are polar coordinates in a polar coordinate system; f(r,φ) is a polar representation of an x-ray attenuation coefficient distribution to be reconstructed; ν is a detector cell coordinate on a straight line defined by an intersection of an imaging plane and a plane defined by the flat panel detector; β is an angle from a y-axis to a radiation source; p(β,ν) is a representation of a radon transform of f , which itself is a Cartesian representation of an x-ray attenuation distribution to be reconstructed; S is a distance from a radiation source to an isocenter; ν sup is a maximum detector cell coordinate on the flat panel detector; ν inf is a minimum detector cell coordinate; H(ν−{tilde over (ν)}) and F ε (ν−{tilde over (ν)}) are convolution kernels; η({tilde over (ν)}) is a fan angle for a ray passing through a voxel being reconstructed, and {tilde over (ν)} is a cell index for the ray; E(ν) is a preconvolution weight that is a function of detector cell position ν; G({tilde over (ν)}) is a post convolution weighting; and J(ν) is a Jacobian function.

Claim 13

A CT imaging system in accordance with claim 10 wherein the pre-convolution weights are independent of an image point described by (r,φ).

Claim 14

A CT imaging system in accordance with claim 10 , wherein: sin  [ η  ( ν ) ] - sin  [ η  ( ν ~ ) ] = { η ′  ( ν )  cos  [ η  ( ν ) ]  η ′  ( ν ~ )  cos  [ η  ( ν ~ ) ] η ′  ( 0 )  η ′  ( ν - ν ′ )  cos  [ η  ( ν - ν ~ ) ] } 1 / 2  sin  [ η  ( ν - ν ~ ) ] ; where η is a fan angle associated with a detector cell indexed by ν.

Claim 15

A CT imaging system in accordance with claim 10 , wherein said system being configured to acquire projection data of an object utilizing a flat-panel detector comprises said system being configured to acquire projection data of the object utilizing a cone beam of radiation from the radiation source in a circular trajectory.

Claim 16

A CT imaging system in accordance with claim 13 wherein the radiation detector is a multi-row detector, the CT imaging system further being configured to rebin data on a row-by-row basis.

Claim 17

A CT imaging system in accordance with claim 10 wherein said imaging system being configured to acquire projection data of an object utilizing a flat-panel detector comprises said system being configured to acquire projection data of the object utilizing a cone beam of radiation from the radiation source in a helical trajectory.

Claim 18

A CT imaging system in accordance with claim 15 wherein the radiation detector is a multi-row detector and said imaging system is further configured to weight the projection data to account for individual ray cone-angles, and and use an average cone angle of a fan-parallel projection equal to a cone angle for a ray at η=0 to determine dβ′ in a tilted plane, where dβ′ is a source rotation in the tilted plane.