Abstract:
Methods and apparatus for weighting data collected in a computed tomography scan using a digital flat panel are described. In one embodiment, the method includes the steps of selecting a weighting function in which (a) a sum of weights of complementary samples equals unity, the weighting function is continuous and differentiable along γ where γ is the fan angle, the weighting function approaches zero near an edge of the panel and approaches unity near a panel boundary, and the weighting function remains constant for a range ξ 1 &lt;ξ&lt;ξ 2 , where ξ 1  and ξ 2  are determined based on an end intersecting point of a complimentary ray within a reconstruction field of view.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates generally to image reconstruction using data collected in a computed tomography scan and, more particularly, to generating an volumetric computed tomography imaging using half-projection data. 
     In at least one known computed tomography (CT) imaging 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 of the array produces a separate electrical signal that is a measurement of the beam attenuation at the detector location. The attenuation measurements from all the detectors are acquired separately to produce a transmission profile. 
     In known third generation 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 so that the angle at which the x-ray beam intersects the object constantly changes. A group of x-ray attenuation measurements, i.e., projection data, from the detector array at one gantry angle is referred to as a “view”. A “scan” of the object comprises a set of views made at different gantry angles, or view angles, during one revolution of the x-ray source and detector. In an axial scan, the projection data is 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. 
     In volumetric CT, data is collected using a large flat panel digital x-ray device, or detector, having a plurality of pixels arranged in rows and columns. More specifically, the imaging system includes an x-ray source and at least one solid-state x-ray detector. To generate volumetric images, at least one of the x-ray source and the x-ray detector are rotated around the object of interest. For each identified view, x-rays are emitted from the x-ray source toward the x-ray detector and projection data is collected for the view. 
     Because of magnification in cone beam geometry, a system having even the largest available flat panel detector has a useful scan field of view too small to cover a typical patient. To overcome limited panel size, the panel can be offset from iso-center to increase scan field of view by utilizing 2π rotation of projections. In such a configuration, each projection is truncated and image artifacts typically result. 
     BRIEF SUMMARY OF THE INVENTION 
     Methods and apparatus for weighting data collected in a computed tomograph scan using a digital flat panel are described. In one embodiment, the method includes the steps of selecting a weighting function which satisfies the following criteria. 
     (a) A sum of weights of conjugate samples equals unity. 
     (b) The weighting function is continuous and differentiable along γ where γ is the fan angle. 
     (c) The weighting function approaches zero near an edge of the panel and approaches unity near a panel boundary. 
     (d) The weighting function remains constant for a range ξ 1 &lt;ξ&lt;ξ 2 , where ξ 1  and ξ 2  are determined based on an end intersecting point of a complimentary ray within a reconstruction field of view. 
     An exemplary weighting function is:          w        (   γ   )       =     {         0         γ   ≤     -     γ   b                     3          θ        (   γ   )       2       -     2          θ        (   γ   )       3                 -     γ   b       &lt;   γ   ≤     γ   b               1       otherwise                                  
     where:          θ        (   γ   )       =         γ   +     γ   b         2                   γ   b         .                            
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a pictorial view of a CT imaging system. 
     FIG. 2 is a block schematic diagram of the system illustrated in FIG.  1 . 
     FIG. 3 is a schematic illustration of the geometry associated with collecting data using a half panel configuration. 
     FIG. 4 illustrates an exemplary weighting function in relation to data sample. 
     FIG. 5 illustrates tilt angle dependency. 
     FIG. 6 illustrates an extrapolation of projection data. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIGS. 1 and 2, a computed tomography (CT) imaging system  10  is shown as including a gantry  12  representative of a “third generation” CT scanner. Gantry  12  has an x-ray source  14  that projects a beam of x-rays  16  toward a detector array  18  on the opposite side of gantry  12 . Detector array  18  is formed by detector elements  20  which together sense the projected x-rays that pass through an object  22 , for example a medical patient. Detector array  18  may be fabricated in a single slice or multi-slice configuration. Each detector element  20  produces an electrical signal that represents the intensity of an impinging x-ray beam and hence the attenuation of the beam as it passes through patient  22 . During a scan to acquire x-ray projection data, gantry  12  and the components mounted thereon rotate about a center of rotation  24 . 
     Rotation of gantry  12  and the operation of x-ray source  14  are governed by a control mechanism  26  of CT system  10 . Control mechanism  26  includes an x-ray controller  28  that provides power and timing signals to x-ray source  14  and a gantry motor controller  30  that controls the rotational speed and position of gantry  12 . A data acquisition system (DAS)  32  in control mechanism  26  samples analog data from detector elements  20  and converts the data to digital signals for subsequent processing. An image reconstructor  34  receives sampled and digitized x-ray data from DAS  32  and performs high speed image reconstruction. The reconstructed image is applied as an input to a computer  36  which stores the image in a mass storage device  38 . 
     Computer  36  also receives commands and scanning parameters from an operator via console  40  that has a keyboard. An associated cathode ray tube display  42  allows the operator to observe the reconstructed image and other data from computer  36 . The operator supplied commands and parameters are used by computer  36  to provide control signals and information to DAS  32 , x-ray controller  28  and gantry motor controller  30 . In addition, computer  36  operates a table motor controller  44  which controls a motorized table  46  to position patient  22  in gantry  12 . Particularly, table  46  moves portions of patient  22  through gantry opening  48 . 
     FIG. 3 illustrates the geometry of a half panel CT system. A single panel covers slightly over half the field of view, and the x-ray source and the panel rotate 360 degrees. By reducing the data collection requirement to about one-half the data collected by a panel, the useful scan field of view is increased. 
     To eliminate artifacts resulting from truncated projections, the following weighting algorithm can be utilized. The weighting algorithm may be performed, for example, by a processor in image reconstructor  34  or by computer  36 . 
     Specifically, and for a simple fan beam scanning geometry (the center slice in VCT), a weighing function using the redundant samples of the projection data in 2π range can be utilized to weight the collected data. In a fan beam geometry, the samples (γ,β) and (−γ,β+π−2 γ) form a conjugate sampling pair where γ is a fan angle and β a projection view angle. 
     For a flat panel, and when the panel is positioned slightly beyond the isochannel, the overlapped (or redundant sampling) regions can be depicted as illustrated in FIG.  4 . FIG. 4 illustrates a Radon space sampling pattern. The weighting function satisfies the following three conditions: 
     (a) the sum of the weights of the complementary samples equal unity, 
     (b) the weighting function is continuous and differentiable along γ, and 
     (c) the weight approaches zero near the edge of the panel and approaches unity near the other boundary. 
     The term “complementary” is used instead of conjugate because the two rays are not redundant samples. The rays merely share the property that their β angles are 180 degrees apart. 
     An example of the weighting function is:                w        (   γ   )       =     {         0         γ   ≤     -     γ   b                     3          θ        (   γ   )       2       -     2          θ        (   γ   )       3                 -     γ   b       &lt;   γ   ≤     γ   b               1       otherwise                   (   1   )                                
     where          θ        (   γ   )       =       γ   +     γ   b         2                   γ   b                                
     For the projection samples that do not form a fan beam sampling (i.e., the off-centered slices), the conjugate samples do not exist and for different image reconstruction locations, the cone beam tilting angle changes. Referring to FIG. 5, each projection sample is denoted as (γ,β,ξ) where γ, β, and ξ are the fan angle, projection view angle, and tilt angle, respectively. For the center plane, if two points (labeled by A and B) coincide with a projection ray, the points will also be coincide with the conjugate sampling ray. If the same two points moved vertically off the center plane (labeled by A′ and B′), the ray pairs that form the complementary samples for A″ will be different from those for B′. 
     To ensure the property that the total contribution to each reconstructed point remains constant, the additional constraint that the weighting function remain constant for the range ξ 1 &lt;ξ&lt;ξ 2 , where ξ 1  and ξ 2  are determined based on the end intersecting point of the complimentary ray with the reconstruction field of view, is utilized. A simple example of the weighting function that satisfies this condition is described in Equation 1. The weights remain constant for the entire range of ξ. 
     With the weighting function described above, the size of the panel is slightly larger than the radius of the field of view (to cover the range −γ o &lt;γ&lt;0). Although fewer than all the channels are needed for weighting in accordance with the foregoing weighting algorithm (typically around 20 channels are required), the weighting algorithm can further be configured so that no additional overlapped channels are required. 
     Specifically, the projection data at the edge of the panel is further extrapolated for the range −γ o &lt;γ&lt;0. Such extrapolation can be performed using many known extrapolation techniques. For example, the extrapolated data could be formed based on the slope of the projection data near the edge or a polynomial fit of the projection data at the edge of the projection can be performed. The results of the extrapolation is illustrated in FIG.  6 . 
     With the extrapolated projection data, the above weighting scheme is then applied to suppress the discontinuity of the projection at the edge. Since the extrapolated data is, in general, less reliable than the real measurement, the weighting function can be configured to provide higher weights to the measured data than to the extrapolated data. 
     From the preceding description of various embodiments of the present invention, it is evident that the objects of the invention are attained. Although the invention has been described and illustrated in detail, it is to be clearly understood that the same is intended by way of illustration and example only and is not to be taken by way of limitation. In addition, the CT system described herein is a “third generation” system in which both the x-ray source and detector rotate with the gantry. Many other CT systems including “fourth generation” systems wherein the detector is a full-ring stationary detector and only the x-ray source rotates with the gantry, may be used if individual detector elements are corrected to provide substantially uniform responses to a given x-ray beam. Moreover, the system described herein performs an axial scan, however, the invention may be used with a helical scan although more than 360° of data are required. Accordingly, the spirit and scope of the invention are to be limited only by the terms of the appended claims.