Method and apparatus for producing a three-dimensional computerized tomography image of an object with improved conversion of cone beam data to radon data
First Claim
Patent Images
1. A method of imaging comprising the steps of:
- (a) using a computed tomography cone beam source to apply cone beam energy, dependent upon an object of interest, to an area detector;
(b) detecting the cone beam energy to define a cone beam data image X(i,j) based upon the cone beam energy detected at points (i,j) on the area detector, each point (i,j) having a corresponding detector element;
(c) determining the value of line integral J on the detector where ##EQU7## and where X(t) is cone beam data image at point t along a line of integration, SC'"'"' is the distance from a source S of cone beam energy to a rotation center C'"'"' on the detector, SC is the distance from the source S to a point C, wherein point C is the closest point to the origin on the line of integration and Δ
C is the displacement of C'"'"' from C, the value of J being determined by the substeps of;
(c1) calculating a modified image F(i,j)=X(i,j)/R(i,j) where R(i,j) is the distance from source S to point (i,j) on the area detector;
(c2) calculating a two-dimensional Fourier transform g(m,n) in (m,n) space using a fast Fourier transform and dependent on F(i,j);
(c3) interpolating from g(m,n) a line of Fourier components g.sub.α
(k) where α
is a desired projection angle, k are inputs to g.sub.α
along the line of Fourier components passing through an origin in (m,n) space and oriented perpendicular to the desired projection angle;
(c4) performing a one-dimensional fast Fourier transform on g.sub.α
(k) to obtain a one-dimensional projection p.sub.α
(1);
(c5) obtaining p.sub.α
(s) by one-dimensional interpolation from p.sub.α
(1) where p.sub.α
(s) is a line integral on a particular line at a location s in the desired projection angle α
;
(d) using a Radon inversion process on p.sub.α
(s) to produce a reconstructed three-dimensional image of the object; and
(e) displaying the reconstructed three-dimensional image of the object.
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Abstract
Cone beam geometry imaging uses an area or two-dimensional array detector and a cone beam x-ray source. Image reconstruction by inverse Radon transformation is used following the calculation of planar integrals. Specifically, the integral is calculated by first changing it to a form wherein fast Fourier transforms can be used to minimize the number of operations in the calculations of the integral.
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Citations
18 Claims
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1. A method of imaging comprising the steps of:
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(a) using a computed tomography cone beam source to apply cone beam energy, dependent upon an object of interest, to an area detector; (b) detecting the cone beam energy to define a cone beam data image X(i,j) based upon the cone beam energy detected at points (i,j) on the area detector, each point (i,j) having a corresponding detector element; (c) determining the value of line integral J on the detector where ##EQU7## and where X(t) is cone beam data image at point t along a line of integration, SC'"'"' is the distance from a source S of cone beam energy to a rotation center C'"'"' on the detector, SC is the distance from the source S to a point C, wherein point C is the closest point to the origin on the line of integration and Δ
C is the displacement of C'"'"' from C, the value of J being determined by the substeps of;(c1) calculating a modified image F(i,j)=X(i,j)/R(i,j) where R(i,j) is the distance from source S to point (i,j) on the area detector; (c2) calculating a two-dimensional Fourier transform g(m,n) in (m,n) space using a fast Fourier transform and dependent on F(i,j); (c3) interpolating from g(m,n) a line of Fourier components g.sub.α
(k) where α
is a desired projection angle, k are inputs to g.sub.α
along the line of Fourier components passing through an origin in (m,n) space and oriented perpendicular to the desired projection angle;(c4) performing a one-dimensional fast Fourier transform on g.sub.α
(k) to obtain a one-dimensional projection p.sub.α
(1);(c5) obtaining p.sub.α
(s) by one-dimensional interpolation from p.sub.α
(1) where p.sub.α
(s) is a line integral on a particular line at a location s in the desired projection angle α
;(d) using a Radon inversion process on p.sub.α
(s) to produce a reconstructed three-dimensional image of the object; and(e) displaying the reconstructed three-dimensional image of the object. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
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10. A method of imaging comprising the steps of:
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(a) using a computed tomography cone beam source to apply cone beam energy, dependent upon an object of interest, to an area detector; (b) detecting the cone beam energy to define a cone beam data image X(i,j) based upon the cone beam energy detected at points (i,j) on the area detector, each point (i,j) having a corresponding detector element; (c) determining the value of line integral J on the detector where ##EQU8## and where X(t) is cone beam data image at point t along a line of integration, SC'"'"' is the distance from a source S of cone beam energy to a rotation center C'"'"' on the detector, SC is the distance from the source S to a point C, wherein point C is the closest point to the origin on the line of integration and Δ
C is the displacement of C'"'"' from C, the value of J being determined by the substeps of;(c1) calculating a modified image F(i,j)=X(i,j)/R(i,j) where R(i,j) is the distance from source S to point (i,j) on the area detector; (c2) calculating a two-dimensional Fourier transform g(m,n) in (m,n) space using a fast Fourier transform and dependent on F(i,j); (c3) interpolating from g(m,n) a line of Fourier components g.sub.α
(k) where α
is a desired projection angle, k are inputs to g.sub.α
along the line of Fourier components passing through an origin in (m,n) space and oriented perpendicular to the desired projection angle;(c4) performing a one-dimensional fast Fourier transform on g.sub.α
(k) to obtain a one-dimensional projection p.sub.α
(1);(c5) obtaining p.sub.α
(s) by one-dimensional interpolation from p.sub.α
(1) where p.sub.α
(s) is a line integral on a particular line at a location s in the desired projection angle α
; and(d) using a Radon inversion process on p.sub.α
(s) to produce a reconstructed three-dimensional image of the object. - View Dependent Claims (11, 12, 13)
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14. An imaging system comprising:
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a computed tomography source of cone beam energy; an area detector for detecting cone beam energy from the source to provide a cone beam data image X(i,j) of an object of interest; a processor operably connected to the area detector to receive the image S(i,j) from the area detector, said processor having means for determining the value of line integral J on the detector where ##EQU9## and where X(t) is cone beam data image at point t along a line of integration, SC'"'"' is the distance from a source S of cone beam energy to a rotation center C'"'"' on the detector, SC is the distance from the source S to a point C, wherein point C is the closest point to the origin on the line of integration and Δ
C is the displacement of C'"'"' from C, the value of J being determined by the substeps of;means for calculating a modified image F(i,j)=X(i,j)/R(i,j) where R(i,j) is the distance from source S to point (i,j) on the area detector; means for calculating a two-dimensional Fourier transform g(m,n) in (m,n) space using a fast Fourier transform and dependent on F(i,j); means for interpolating from g(m,n) a line of Fourier components g.sub.α
(k) where α
is a desired projection angle, k are inputs to g.sub.α
along the line of Fourier components passing through an origin in (m,n) space and oriented perpendicular to the desired projection angle;means for performing a one-dimensional fast Fourier transform on g.sub.α
(k) to obtain a one-dimensional projection p.sub.α
(1);means for obtaining p.sub.α
(s) by one-dimensional interpolation from p.sub.α
(1) where p.sub.α
(s) is a line integral on a particular line at a location s in the desired projection angle α
; andmeans for reconstructing a three-dimensional image of the object from p.sub.α
(S) using a Radon inversion process; anda display operably connected to said processor to display the reconstructed three-dimensional image of the object. - View Dependent Claims (15, 16, 17, 18)
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Specification