X-ray or gamma ray systems or devices – Specific application – Computerized tomography
Reexamination Certificate
1999-09-20
2001-10-23
Bruce, David V. (Department: 2882)
X-ray or gamma ray systems or devices
Specific application
Computerized tomography
C378S015000, C378S901000
Reexamination Certificate
active
06307908
ABSTRACT:
BACKGROUND OF THE INVENTION
This invention relates generally to x-ray computed tomography (CT) imaging, and more particularly, to a multi-slice x-ray CT imaging system.
In at least one known CT system configuration, an x-ray source projects a fan-shaped beam which is collimated to lie within an X-Y plane of a Cartesian coordinate system and generally referred to as the “imaging plane.” The x-ray beam passes through the object being imaged, such as a patient. The beam, after being attenuated by the object, impinges upon an array of radiation detectors. The intensity of the attenuated beam radiation received at the detector array is dependent upon the attenuation of the x-ray beam by the object. Each detector element or cell of the array produces a separate electrical signal that is a measurement of the beam attenuation at that detector location. The attenuation measurements from all the detector cells are acquired separately to produce a transmission profile.
In known CT systems, the x-ray source and the detector array are rotated with a gantry within the imaging plane and around the object to be imaged. As such, the rotational angle at which the x-ray beam intersects the object constantly changes, resulting in numerous x-ray attenuation measurements of the imaged object. A group of x-ray attenuation measurements, i.e., projection data, from the detector array at one gantry rotational angle is referred to as a “view.” A “scan” of the object comprises a set of views made at different gantry rotational angles, or view angles, during one revolution of the x-ray source and detector. For example, in an axial scan, the projection data are processed to construct an image that corresponds to a two dimensional slice taken through the object. One method for reconstructing an image from a set of projection data is referred to in the art as the filtered back projection technique. This process converts the attenuation measurements from a scan into integers called “CT numbers” or “Hounsfield units,” which are used to control the brightness of a corresponding pixel on a cathode ray tube display and hence produce the image. Other similar reconstruction methods include direct Fourier reconstruction and iterative reconstruction algorithms.
One problem in reconstructing an image is that the position of the measured projection data do not necessarily correspond to the position of the desired image. In this case, projection data at the position of the desired image are linearly interpolated from the measured projection data or from a combination of measured and linearly interpolated projection data. In order to increase the number of data points used in the image reconstruction interpolation, and thereby decrease the error of the interpolation, some prior art systems create estimated projection data at the mid-points of the measured projection data by interpolation. This interpolation, however, may lead to artifacts in the reconstructed image as the interpolated projection data may not correspond to the actual patient anatomy in the position of the desired image.
Using this type of interpolation in the x-direction (compared to the z-direction, for example) is less susceptible to error, however, because the x-direction projection data are in the plane of rotation of the x-ray source and detector. Typically, for a given detector cell size, the distribution of measured projection data is a function of the size of the detector cell. For example, if a detector contains a row of 10 detector cells that measure 1 mm square each, the set of actual projection data will be collected at 1 mm intervals. Because the x-direction projection data are in the plane of rotation, however, the inherent sampling frequency of a given size detector cell may become interlaced with additional measured projection data upon the rotation of the x-ray source and detector. For example, using the 10 cell detector described above, the rotation may cause a second set of actual projection data to be measured 0.5 mm from the first set of projection data. Using both sets of measured projection data then reduces the potential error when interpolating between measured data points.
Image reconstruction problems are more pronounced in volumetric CT systems and in third generation CT systems using detectors generally known as 2-D detectors that acquire multiple rows (in the z-direction) of data per slice. 2-D detectors comprise a plurality of columns and rows of detector cells, where detector cells lined up at the same z-location but different x-locations form a row and detector cells lined up at the same x-location but different z-locations form columns. In a CT system having such a 2-D detector, sometimes referred to as a multislice system, an image may be formed by combining the detector measurements of multiple rows and/or columns of detector cells. Since the measurements in the z-direction are not in the plane of rotation, there is less likelihood of interlacing measurements that help to reduce interpolation error. In some applications, such as helical scanning, the object being scanned is moved in the z-direction. The possible interlacing of these measurements in the z-direction is typically negated, however, by the rotation of the x-ray source and detector. Thus, interpolation in the z-direction necessarily involves larger steps, and hence a greater chance of error, than interpolation in the x-direction.
Therefore, it would be desirable to more accurately and efficiently create an image from projection data interpolated in the z-direction. Further, it would be desirable to provide such imaging without significantly increasing the cost of the system.
SUMMARY OF THE INVENTION
A system for producing from x-rays a tomographic image of an object at an exact spatial position in an x, y, z coordinate system, comprises a plurality of adjacently located detector cells forming at least one column for generating a corresponding plurality of measured projection data from the x-rays, wherein desired projection data corresponding to the exact spatial position are located between adjacent ones of the plurality of measured projection data. The system further comprises a high order interpolator for receiving the plurality of measured projection data and estimating the desired projection data for reconstructing the image at the exact spatial position. The high order interpolator comprises a linear interpolator and a non-linear interpolator, where the linear interpolator provides a linear interpolation estimate between the adjacent ones of the plurality of measured projection data and the non-linear interpolator provides a non-linear interpolation estimate from the plurality of measured projection data. Further, the high order interpolator adds the linear interpolation estimate to the non-linear interpolation estimate to produce the desired projection data at the exact spatial position. The high order interpolator comprises a cubic spline interpolator.
The high order interpolator generates the desired projection data, y, according to the following equation:
y=Ay
j
+By
j+1
+Cy″
j
+Dy″
j+1
j=
1 . . .
N
where:
y=desired projection data to be estimated at a projected exact spatial position, denoted as z, for reconstruction of the image;
A
=
z
j
+
1
-
z
z
j
+
1
-
z
j
;
B
=
1
-
A
=
z
-
z
j
z
j
+
1
-
z
j
;
C
=
1
6
(
A
3
-
A
)
(
z
j
+
1
-
z
j
)
2
;
D
=
1
6
(
B
3
-
B
)
(
z
j
+
1
-
z
j
)
2
;
y
j
=the projection data measured at a spatial position z
j
;
y
j+1
=the projection data measured at a spatial position z
j+1
;
y″
j
=the second derivative of Z
j
at a spatial position z
j
;
y″
j+1
=the second derivative of z
j+1
at a spatial position z
j+1
; and
where the spatial position z located between the spatial positions z
j
and z
j+1
.
Additionally, the y″
j
are N unknown, and may be evaluated using the following N−2 equations (for j=2, . . . N−1):
z
j
-
z
j
-
1
6
y
j
-
1
″
+
z
Bindseil James J.
Bruce David V.
Calkins Charles W.
General Electric Company
Kilpatrick & Stockton LLP
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