X-ray or gamma ray systems or devices – Specific application – Computerized tomography
Reexamination Certificate
2002-03-25
2004-08-17
Bruce, David V. (Department: 2882)
X-ray or gamma ray systems or devices
Specific application
Computerized tomography
C378S004000, C378S901000
Reexamination Certificate
active
06778630
ABSTRACT:
CROSS-REFERENCE TO RELATED APPLICATIONS
The present application claims priority from Japanese Application JP2001-084988, the contents of which are herein incorporated by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method and system for image reconstruction in fan- or cone-beam X-ray computed tomography and, in particular, to a method and system for reconstructing images using weighting coefficients to weight exposure data.
2. Discussion of the Background
Fan- and cone-beam computed tomography (CT) reconstructs the interior of an object of interest or patient from one-dimensional and two-dimensional projections, respectively, of transmitted x-rays through the object of interest or patient. An x-ray source and an x-ray detector are arranged in a number of different positions so that x-rays transmitted through the object of interest are received at the detector. The detector, either alone or in conjunction with other devices, generates image data for each position of the source and/or detector. The image data is then stored, manipulated, and/or analyzed to reconstruct the interior of the object. In a fan-beam system, the detector forms a linear array of x-ray sensing elements while in a cone-beam system, the detector forms an array of x-ray sensing elements.
The classical path of the x-ray source and detector is along a complete circular orbit, i.e. 360°, about the object of interest. The source and detector are mechanically joined so as to maintain a constant separation distance and position relative to each other and then revolved around the object.
As shown in
FIG. 1
, an X-ray source S emits either a cone- or a fan-beam of X-rays toward a detector D. The X-rays emitted by source S are incident upon a three-dimensional object of interest (not shown) such as a calibration phantom, a patient, a test object, or other article of interest. At least a portion of the X-rays generated at point source S pass through or around the object and are received at the detector D. The source S and the detector D are fixed relative to one another and revolve in a substantially circular orbit about an axis A in, for example, a C-arm gantry or ring gantry device. The angular position of the X-ray source S is illustrated here as the angle &bgr; relative to an arbitrary half-line L that terminates at the rotation axis A.
Several disadvantages of complete circular orbits of the source and detector about the object arise due to the nature of the complete orbit itself. Electrical leads must be capable of circumscribing one or more complete revolutions about the object of interest. In medical CT, since the patient must be contained within the orbiting detector and source, access to the patient by medical personnel is hindered. Furthermore, many patients dislike being enclosed within the CT mechanism for the extended times necessary to gather sufficient image data for meaningful reconstruction.
In fan-beam CT, the detector D is a substantially linear array of detector elements typically in arc form on the array source. In cone-beam CT, detector D is an area array of detector elements. Curved line and curved surface arrays of detector elements are also suitable for use as detector element D. In all of these cases, detector element D will have a cross sectional area with a width W in a plane orthogonal to the axis of rotation A. In this particular embodiment, the midpoint of the width of a linear array detector D is substantially positioned at a line N passing through the center of the source S and the axis A.
The angle &ggr; illustrated in
FIG. 1
describes the angle of a ray O joining the source S and one element selected from the matrix of elements that constitutes the detector D. In fan-beam CT, the angle &ggr;
m
describes the rays M with the largest (maximum) angle relative to the line N, where the ray M is emitted by the source S and received by the detector D. The physical limit on ray M and hence angle &ggr;
m
can arise due to, for example, the finite length of the detector D (as illustrated), collimation of the source emission (not shown), or the non-omnidirectional emission of X-rays by the source S (also not shown). In
FIG. 1
with the midpoint of the cross-sectional area of detector D located at line N, the angle &ggr;
m
on one side of the axis is equal and opposite to angle &ggr;
m
on the other side of the axis. Shifting the detector D relative to line N will change this relationship between the two &ggr;
m
's and can be accounted for using traditional geometric rules.
FIGS. 2
a-c
illustrate three example rays O
a
, O
b
, and O
c
over which the same x-ray transmittance is measured at two different angular positions of the source &bgr; relative to an arbitrary half-line L and fan beam angles &ggr;. For illustrative purposes, the first angular positions of the source &bgr; is equal to zero in all three examples. In
FIG. 2
a
, ray O
a
is the first ray sampled twice, while
FIGS. 2
b
and
2
c
show respective rays O
b
and O
c
that are sampled twice at other positions.
In recent years, there has been an attempt to implement fan- and cone-beam CT on gantries that only revolve around a portion of the object or patient during imaging. Such partial orbits are capable of providing complete image data for reconstruction of the interior of an object since many views in a complete circular orbit are redundant, i.e., the image data provide little or no new information. For example, if the object of interest is immobile and the system is ideal (i.e., no noise), switching the location of the source and detector will provide no new information along the ray through the axis even though image data from a second view has been collected.
The advantages of such partial orbits include easier and less expensive mechanical realization, providing access to a patient during medical imaging and enabling supporting mechanisms for the source and detector that do not require complete enclosure of the patient. Also, it allows the use of x-ray imaging and primarily designed for non-CT imaging application to also be used to obtain a CT-image for special needs.
A method for reconstruction of one particular partial orbit, namely an orbit that covers the “minimal complete data set” has been described by Dennis Parker (“Optimal Short Scan Convolution Reconstruction for Fanbeam CT,” Med. Phys. 9, 254-257, 1982) which is incorporated herein by reference. The “minimal complete data set” is the collection of equally-spaced projection image data that can be used in conventional, convolution type, reconstruction methods. The “minimal complete data set” spans more than one half of a complete orbit. Namely, it spans 180° plus the maximum fan angle 2&ggr;
m
, where the maximum channel angle &ggr;
m
is the largest angle of a ray emitted by the X-ray source that is received at the (substantially two- or three-dimensional) X-ray detector relative to the ray emitted from the source that passes through the axis of rotation of the X-ray source and detector.
FIG. 1
schematically illustrates this and other terminology used to describe the current invention.
One disadvantage with the use of such a “minimal complete data set” orbit lies in the fact that certain rays are sampled twice as often as other rays. In other words, certain image data is collected twice as often as other image data and are redundant. Illustrative examples are illustrated diagrammatically in
FIGS. 2
a-c
. This can be better illustrated in
FIG. 3
, where the image data is represented in Radon space. The horizontal axis in
FIG. 3
corresponds to the channel angle &ggr;, the vertical axis corresponds to the angular position &bgr; of the x-ray source, and, in an actual Radon space representation of a collection of x-ray image data, the grey level of each point in Radon space would correspond to the line integral of the x-ray transmittance along the particular ray defined by the fan angle &ggr; and the angular position of the source &bgr;.
FIG. 3
indicates the angular positions of the source and th
Silver Michael D.
Taguchi Katsuyuki
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