Method for image reconstruction in a computed tomography apparatus
First Claim
Patent Images
1. A method for obtaining an image of a subject in a computed tomography apparatus comprising the steps of:
- irradiating a subject with x-rays from a plurality of projections pk at respective projection angles θ
l ;
detecting said x-rays, attenuated by said subject, in a radiation detector having N detector channels to obtain data f(pk, θ
l);
supplying said data f(pk, θ
l) from the detector to a computer in a parallel beam geometry so that Δ
tan θ
=const in an angle region [-45°
, 45°
] or Δ
cot θ
=const in an angle region [45°
, 135°
], and pk =(k-0.5+am)a (a is a sampling grid and am is an alignment factor);
reconstructing a sectional image of said subject by the following steps;
one-dimensionally Fast Fourier transforming f(pk, θ
l) relative to pk, with NFFT ≧
2N values to obtain fl (mΔ
ρ
);
multiplying fl (mΔ
ρ
) by the Fourier transform of a convolution Kernel Lc (mΔ
ρ
) and by a phase factor exp (-2π
imΔ
ρ
(xz cos θ
l +yz sin θ
l)), which defines the position of the center of the sectional image to obtain frequency values on a polar grid;
conducting a Fast Fourier transformation of length NFFT of said frequency values on a polar grid back into the spatial domain to obtain a plurality of convoluted, centered projections f'"'"'c (pq,θ
l);
limiting each convoluted, centered projection f'"'"'c (pq,θ
l)to ##EQU43## values for -45°
≦
θ
i ≦
45°
or to ##EQU44## values for 45°
<
θ
i ≦
135°
to obtain a plurality of bounded projections f'"'"'c (pq,θ
l);
one-dimensionally chirp-z transforming each bounded projection f'"'"'c (pq, θ
l) to a grid ##EQU45## for -45°
≦
θ
l ≦
45°
or ##EQU46## for 45°
<
θ
l ≦
135°
, whereby the number of points is dependent on the size of the represented image segment and on the maximum frequency of reconstruction to obtain projections Fl (sΔ
ρ
Fl) by the Fourier transform of a smoothing Kernel Ls (sΔ
ρ
Fl);
calculating first and second sub-images respectively for the angle regions [-45°
, 45°
] and [45°
, 135°
];
calculating said first sub-image by, for each frequency values sΔ
ρ
x in the px direction, interpolating said values with T(ρ
y) in the ρ
y direction, using the gridding method on the basis of NP frequency support points in an s-dependent grid Δ
ρ
yLG (s), to 2NPix values in a grid ##EQU47## (NPix) is a number of pixels in one column of the sectional image) rearranging aliasing components, and Fourier transforming the 2NPix ·
2NPix frequency values in the spatial domain and correcting inner NPix ·
NPix pixels in the y direction by multiplication with 1/T(y);
calculating said second sub-image by, for each frequency value sΔ
ρ
y in the ρ
y direction, interpolating said values with T(ρ
x) in the ρ
x direction, using the gridding method on the basis of NP frequency support points in an s-dependent grid Δ
ρ
xLG (s), to 2NPix values in a grid ##EQU48## (NPix is a number of pixels in one column of the sectional image) rearranging aliasing components, and Fourier transforming the 2NPix ·
2NPix frequency values in the spatial domain and correcting inner NPix ·
NPix pixels in the x direction by multiplication with 1/T(x); and
adding said first and second sub-images.
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Abstract
An image reconstruction method for a computer tomograph produces arbitrary eccentric segments of images. The method is a modified linogram reconstruction, more precisely a combination of linogram and gridding methods, by means of which it is possible to reconstruct arbitrary eccentric segments directly, by producing points directly on a Cartesian grip, without the necessity of transformations or interpolations.
9 Citations
1 Claim
-
1. A method for obtaining an image of a subject in a computed tomography apparatus comprising the steps of:
-
irradiating a subject with x-rays from a plurality of projections pk at respective projection angles θ
l ;detecting said x-rays, attenuated by said subject, in a radiation detector having N detector channels to obtain data f(pk, θ
l);supplying said data f(pk, θ
l) from the detector to a computer in a parallel beam geometry so that Δ
tan θ
=const in an angle region [-45°
, 45°
] or Δ
cot θ
=const in an angle region [45°
, 135°
], and pk =(k-0.5+am)a (a is a sampling grid and am is an alignment factor);reconstructing a sectional image of said subject by the following steps; one-dimensionally Fast Fourier transforming f(pk, θ
l) relative to pk, with NFFT ≧
2N values to obtain fl (mΔ
ρ
);multiplying fl (mΔ
ρ
) by the Fourier transform of a convolution Kernel Lc (mΔ
ρ
) and by a phase factor exp (-2π
imΔ
ρ
(xz cos θ
l +yz sin θ
l)), which defines the position of the center of the sectional image to obtain frequency values on a polar grid;conducting a Fast Fourier transformation of length NFFT of said frequency values on a polar grid back into the spatial domain to obtain a plurality of convoluted, centered projections f'"'"'c (pq,θ
l);limiting each convoluted, centered projection f'"'"'c (pq,θ
l)to ##EQU43## values for -45°
≦
θ
i ≦
45°
or to ##EQU44## values for 45°
<
θ
i ≦
135°
to obtain a plurality of bounded projections f'"'"'c (pq,θ
l);one-dimensionally chirp-z transforming each bounded projection f'"'"'c (pq, θ
l) to a grid ##EQU45## for -45°
≦
θ
l ≦
45°
or ##EQU46## for 45°
<
θ
l ≦
135°
, whereby the number of points is dependent on the size of the represented image segment and on the maximum frequency of reconstruction to obtain projections Fl (sΔ
ρ
Fl) by the Fourier transform of a smoothing Kernel Ls (sΔ
ρ
Fl);calculating first and second sub-images respectively for the angle regions [-45°
, 45°
] and [45°
, 135°
];calculating said first sub-image by, for each frequency values sΔ
ρ
x in the px direction, interpolating said values with T(ρ
y) in the ρ
y direction, using the gridding method on the basis of NP frequency support points in an s-dependent grid Δ
ρ
yLG (s), to 2NPix values in a grid ##EQU47## (NPix) is a number of pixels in one column of the sectional image) rearranging aliasing components, and Fourier transforming the 2NPix ·
2NPix frequency values in the spatial domain and correcting inner NPix ·
NPix pixels in the y direction by multiplication with 1/T(y);calculating said second sub-image by, for each frequency value sΔ
ρ
y in the ρ
y direction, interpolating said values with T(ρ
x) in the ρ
x direction, using the gridding method on the basis of NP frequency support points in an s-dependent grid Δ
ρ
xLG (s), to 2NPix values in a grid ##EQU48## (NPix is a number of pixels in one column of the sectional image) rearranging aliasing components, and Fourier transforming the 2NPix ·
2NPix frequency values in the spatial domain and correcting inner NPix ·
NPix pixels in the x direction by multiplication with 1/T(x); andadding said first and second sub-images.
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Current AssigneeSiemens AG
-
Original AssigneeSiemens AG
-
InventorsFlohr, Thomas, Schaller, Stefan
-
Primary Examiner(s)Wong, Don
-
Application NumberUS08/682,023Time in Patent Office238 DaysField of Search378/15, 378/4, 378/901US Class Current378/15CPC Class CodesG06T 11/006 Inverse problem, transforma...G06T 2211/421 Filtered back projection [FBP]Y10S 378/901 Computer tomography program...
