X-ray or gamma ray systems or devices – Specific application – Computerized tomography
Reexamination Certificate
1999-01-11
2001-05-29
Bruce, David V. (Department: 2882)
X-ray or gamma ray systems or devices
Specific application
Computerized tomography
C378S004000, C378S065000
Reexamination Certificate
active
06240157
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to complete helical cone-beam scanning and non-redundant data acquisition for three-dimensional imaging of arbitrarily long objects.
2. Description of Related Art
A two-dimensional detector
11
and a point-shaped ray source (e g X-ray) S are assumed to move synchronously around the object in a helical trajectory as shown in FIG.
1
. In a medical tomograph the helical source movement is achieved by translating the patient through the rotating source-detector gantry with constant speed. Two-dimensional projections are acquired (detected) at arbitrarily short intervals along the trajectory. The detector
16
consists of a large number of sensors (detector elements) which are evenly spaced and placed in a plane or, as in
FIG. 1
, on the surface of the helix cylinder
12
. Although the rotation axis
14
is normally horizontal in medical tomographs, rather than vertical as in
FIG. 1
, we will adopt the following convention. In the sequel, vertical means a direction parallel to the rotation axis
14
(the z-axis) in
FIG. 1
, while horizontal means a direction parallel to the xy-plane
15
.
A projection consists primarily of intensity measures for the incoming rays to a detector element. The logarithms of these primary data represent the sum of the attenuation along the rays, i.e. line integrals over the three-dimensional attenuation function f we want to retrieve. But to be able to reconstruct f from its projections in a correct way, all points in the object have to be fully exposed and the projection data utilized in a balanced way. Thus, if back-projection is used for the reconstruction, projections from all projection angles must be available and brought in with the correct weight to obtain what is called exact reconstruction. Also, the projection data have to be filtered correctly to compensate for the inherent low-pass filtering in the projection-back-projection procedure.
In the literature several mathematically exact methods have been proposed for reconstruction from cone-beam projections. In most cases these methods demand that the object is of finite extension, i.e. restricted in size, so that its total projection never falls outside the available detector. Unfortunately, this requirement is not realistic in most cases of computer tomography, e.g. when one is to reconstruct a full body, or long objects in general. Traditionally, 1D-detector arrays are made large (wide) enough to cover the object across its maximum width. However, for several reasons, it is out of question to extend these 1D-detectors to 2D-detectors, which cover the patient from head-to-toe. Instead, in the foreseeable future, available 2D-detectors will be used to cover and record projections of a section of a long object.
Today, three-dimensional volume data are reconstructed slice-by-slice. The patient is translated slowly (typically 2 mm/sec) while the X-ray source and a one-dimensional detector array are synchronously and continuously rotated at speeds of around 1 r/sec. Relative to a patient which is not moving, the source and detector are then performing a helical movement with very low pitch, say, 2 mm. The reconstruction employs a modified versions of traditional 2D-reconstruction methods for circular scanning of a single slice. However, with the given numbers, it takes approximately 100 sec to fetch data for a 200 mm long section of the body. During this time, due to breathing and other body functions, the body is not fully at rest which blurs the reconstructed object. A second drawback is that the anode of the X-ray tube is subjected to severe strain and extreme temperatures during longer exposure times.
In a 1D-detector system the major part of the generated photons are collimated away without being utilized, while a 2D-detector system is able to utilize a substantial part of these otherwise wasted photons. Hence, by using a 2D-detector with, say, n parallel 1D-detectors in the above example, the velocity can be increased to 2n mm/sec and the scanning time reduced to 100
sec. Alternatively, speed can be traded for strain on the X-ray source so that, for instance, if the photon flow is halved, the velocity is more moderately increased to n mm/sec and the scanning time reduced to 200
sec. However, in any case it is no longer possible to perform the reconstruction using conventional 2D-methods since the projection rays are no longer, not even approximately, in the same plane during one turn of the source trajectory.
Circular Source Trajectory
A well-known method for inexact reconstruction from cone-beam projections taken along a circular path was proposed in [Feld84]. The 2D-detector is placed on a planar surface and extended horizontally to cover the width of the object. The width of the object and its distance to the source defines the maximum fan-angle &ggr;
max
of the source-detector system. In the vertical direction the planar detector is limited by two horizontal lines. Along the vertical axis where these lines are closest to the source we find the maximum cone-angle. The image reconstruction consists of the following steps taken for each detector recording. All corrections of geometrical and radiometric nature, including the ever necessary logarithm computation have been left out here for the sake of brevity.
1 Pre-weighting of the recorded detector data with a factor that is proportional to the cosine of the angle between the central ray and the ray that originated the detected value.
2. Filtering with traditional ramp-filtering techniques along each horizontal detector row.
3. Back-projection along the original ray in which process the filtered detector value is multiplied with a so called magnification factor which depends on the distance between the ray source and the object point to receive a contribution from the ray.
This method gives perfect results for image slices in, or close to the mid-section of the object. For slices which have been subjected to more oblique rays at higher cone angles, the image quality deteriorates.
Helical Source Trajectory. Non-exact Methods
Extensions of [Feld84] to helical source paths were first proposed by [Wang93]. Here, the planar 2D-detector is given a vertical extension large enough to ascertain that every point is exposed to the source at least once for every projection angle during a full 360 degree source rotation. The effect of this requirement is that for any given projection angle an object point will be exposed by the source from various numbers of source positions; at least one but often many more, depending on the given fan-angle, cone-angle and detector size. This has to be taken into account during the back-projection. Hence, [Feld84] is employed in [Wang93] but augmented with the following rule.
3a. During the back-projection, for a certain projection angle, among all possible source positions which illuminate an object point, contributions are accepted only from the position which is closest to the actual point in the z-direction.
A way to achieve a more efficient and balanced exposure of the object points was proposed in [Scha96]. Here, the detector is located (wrapped) onto the surface of the source cylinder
41
, which in
FIG. 2
is seen to be centered in S. The radius of this cylinder equals the source-detector distance, which is different from the radius R of the helix cylinder
12
. The helix cylinder is coaxial with the object cylinder in
FIG. 1
which is defined by the maximum object width r. In [Scha96] the detector is limited in the vertical direction by two horizontal circles (cross-sections) of the source cylinder
41
. However, it is not quite clear what the minimum or optimal height is to be recommended for the detector. In the horizontal direction the detector is limited by two vertical lines, set to let the detector cover the object cylinder. In the following we may use
FIG. 1
to clarify some prior art such as this.
The main novelty in [Scha96] is the i
Bruce David V.
Hobden Pamela R.
U.S. Philips Corporation
Vodopia John F.
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