Patent Publication Number: US-7583777-B2

Title: Method and apparatus for 3D reconstruction of images

Description:
BACKGROUND OF THE INVENTION 
   This invention relates generally to the reconstruction of images and more particularly to methods and apparatus for 3D (three dimensional) reconstruction of images using virtual parallel sampling and/or view weighted backprojection. 
   With the development of three-dimensional (3D) or cone beam (CB) filtered backprojection (FBP) reconstruction algorithms, multi-detector-row CT scanners are evolving into volumetric CT (VCT) scanners. One of the most practical CB FBP reconstruction algorithm is the “FDK” algorithm proposed by Feldkamp, David and Kress in “Practical cone beam algorithm,” J. Opt. Soc. Am. A, vol. 1, pp. 612-619, 1984. A helical FDK algorithm to handle helical CB data acquisition geometry is described in G. Wang, T. H. Lin, P. C. Cheng and D. M. Shinozaki, “A general cone-beam reconstruction algorithm,” IEEE Trans. Med. Imag., vol. 12, pp. 486-496, 1993. 
   One common feature of both the original FDK and helical FDK algorithms is a 1/L 2  factor in the 3D backprojection, in which L is the distance between the x-ray focal spot and the image pixel to be reconstructed. It is well recognized that the location-dependent 1/L 2  factor results in computational complexity in the backprojection and non-uniform noise characteristics in tomographic images. To overcome these shortcomings, a modified FDK algorithm is described in U.S. Pat. No. 6,263,040 B1 (assigned to General Electric Company) by removing the 1/L 2  from the 3D backprojection, in which a sequential triggering technique is employed to obtain cone-tilted parallel sampling (namely real 3D parallel sampling) from 3D cone sampling. However, this sequential triggering technique involves increased design and manufacturing complexities. 
   BRIEF DESCRIPTION OF THE INVENTION 
   Some configurations of the present invention therefore provide a method for producing an image of an object. The method includes scanning an object with an imaging apparatus to collect projection data of the object utilizing cone sampling. The projection data is rebinned in a row-wise, fan-to-parallel fashion to produce rebinned data and the rebinned data is view-weighted to produce view-weighted data. The method further includes filtering the view-weighted data utilizing a row-wise ramp filter to produce filtered data and generating an image of the object utilizing the filtered data and a three-dimensional (3D) backprojection. 
   In another aspect, some configurations of the present invention provide a method producing an image of an object that includes scanning an object with an imaging apparatus to collect projection data of the object utilizing cone sampling and rebinning the projection data in a row-wise, fan-to-parallel fashion to produce rebinned data. The method further includes filtering the rebinned data utilizing a row-wise ramp filter to produce filtered data, view-weighting the filtered data utilizing a 3D weighting function to produce view-weighted data, and generating an image of the object utilizing the view-weighted data and a 3D backprojection. 
   In yet another aspect, some configurations of the present invention provide an imaging apparatus that includes a radiation source and a multi-row detector array. The radiation source is configured to project a radiation beam through an object towards the detector array. The apparatus is configured to scan the object to collect projection data of the object utilizing cone sampling, and rebin the projection data in a row-wise, fan-to-parallel fashion to produce rebinned data. The apparatus is also configured to view-weight the rebinned data to produce view-weighted data, filter the view-weighted data utilizing a row-wise ramp filter to produce filtered data, and generate an image of the object utilizing the filtered data and a three-dimensional (3D) backprojection. 
   In still another aspect, some configurations of the present invention provide an imaging apparatus having a radiation source and a multi-row detector array. The radiation source is configured to project a radiation beam through an object towards the detector array. The apparatus is configured to scan an object to collect projection data of the object utilizing cone sampling and rebin the projection data in a row-wise, fan-to-parallel fashion to produce rebinned data. The apparatus is further configured to filter the rebinned data utilizing a row-wise ramp filter to produce filtered data, view-weight the filtered data utilizing a three-dimensional (3D) weighting function to produce view-weighted data, and generate an image of the object utilizing the view-weighted data and a (3D) backprojection. 
   Configurations of the present invention that provide virtual 3D parallel sampling realize this sampling using row-wise fan-to-parallel rebinning. By incorporating a view weighting function, various configurations of the present invention are applicable in both partial and over-scanning cases in both axial and helical x-ray source trajectories, thereby facilitating development of VCT applications, although configurations of the present invention are not limited x-ray source or VCT applications. Moreover, reduced design and manufacturing complexities result in cost savings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a perspective view of a configuration of a computed tomographic imaging apparatus. 
       FIG. 2  is a functional block diagram of the computed tomographic imaging apparatus illustrated in  FIG. 1 . 
       FIG. 3  is a perspective representation of the geometry of an x-ray source trajectory and cone sampling pattern in an associated x-ray detector, wherein the detector is either a curved array, such as the cylindrical detector array depicted in  FIG. 3 , or a flat panel array. 
       FIG. 4  is a representation of virtual 3D parallel sampling rebinned via row-wise fan-to-parallel interpolations from a series of cone sampling, such as from the cone sampling pattern represented by  FIG. 3 . 
       FIG. 5  is a representation of the geometry of a virtual 3D parallel resampling of a virtual flat x-ray detector resulting from rebinning projection data in the virtual convex x-ray detector shown in  FIG. 4 . 
       FIG. 6  is a flow chart representing some configurations of the reconstruction in which row-wise one-dimensional (1D) ramp filtering is performed after view weighting. 
       FIG. 7  is a flow chart representing some configurations of the present invention in which row-wise 1D ramp filtering is performed before view weighting. 
       FIG. 8  is a reconstructed image of an HBP phantom utilizing a prior art FDK reconstruction algorithm with horizontal 1D ramp filtering. 
       FIG. 9  is a reconstructed image of the same HBP phantom as  FIG. 8  utilizing a configuration of a 3D reconstruction method utilizing virtual parallel sampling in which tangential 1D ramp filtering is inherently implemented. In both  FIG. 7  and  FIG. 8 , W/L=100/0, the detector is 64×0.625 mm, the radius of the detector is 541.0 mm, and the pitch is 63/64. 
       FIG. 10  is a reconstructed image of a Defrise phantom in an axial view reconstructed using a prior art helical FDK algorithm with horizontal 1D ramp filtering. 
       FIG. 11  is a reconstructed image of the same Defrise phantom as  FIG. 10  in an axial view reconstructed using a configuration of a 3D reconstruction method utilizing virtual parallel sampling in which tangential 1D ramp filtering is inherently implemented. In both  FIG. 10  and  FIG. 11 , W/L=300/0, the detector is 64×0625 mm, the radius of the detector is 541.0 mm, and the pitch is 63/64. 
       FIG. 12  is a reconstructed image of a Defrise phantom in a coronal reformatted view reconstructed using a prior art helical FDK algorithm with horizontal 1D ramp filtering. 
       FIG. 13  is a reconstructed image of the same Defrise phantom as  FIG. 12  in a coronal reformatted view reconstructed using a configuration of a 3D reconstruction method utilizing virtual parallel sampling in which tangential 1D ramp filtering is inherently implemented. In both  FIG. 12  and  FIG. 13 , W/L=300/0, the detector is 64×0.625 mm, the radius of the detector is 541.0 mm, and the pitch is 63/64. 
       FIG. 14  is a reconstructed image of a Defrise phantom in a sagittal reformatted view reconstructed using a prior art helical FDK algorithm with horizontal 1D ramp filtering. 
       FIG. 15  is a reconstructed image of the same Defrise phantom as  FIG. 14  in a sagittal reformatted view reconstructed using a configuration of a 3D reconstruction method utilizing virtual parallel sampling in which tangential 1D ramp filtering is inherently implemented. In both  FIG. 14  and  FIG. 15 , W/L=300/0, the detector is 64×0.625 mm, the radius of the detector is 541.0 mm, and the pitch is 63/64. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   In some known CT imaging system configurations, 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 an “imaging plane”. The x-ray beam passes through an 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 radiation beam received at the detector array is dependent upon the attenuation of an x-ray beam by the object. Each detector element of the array produces a separate electrical signal that is a measurement of the beam intensity at the detector location. The intensity measurements from all the detectors are acquired separately to produce a transmission profile. 
   In 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 such 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 backprojection technique. This process converts the attenuation measurements from a scan into integers called “CT numbers” or “Hounsfield units” (HU), which are used to control the brightness of a corresponding pixel on a cathode ray tube display. 
   To reduce the total scan time, a “helical” scan may be performed. To perform a “helical” scan, the patient is moved while the data for the prescribed number of slices is acquired. Such a system generates a single helix from a fan beam helical scan. The helix mapped out by the fan beam yields projection data from which images in each prescribed slice may be reconstructed. 
   Reconstruction algorithms for helical scanning typically use helical weighing algorithms that weight the collected data as a function of view angle and detector channel index. Specifically, prior to a filtered backprojection process, the data is weighted according to a helical weighing factor, which is a function of both the gantry angle and detector angle. The weighted data is then processed to generate CT numbers and to construct an image that corresponds to a two-dimensional slice taken through the object. 
   To further reduce the total acquisition time, multi-slice CT has been introduced. In multi-slice CT, multiple rows of projection data are acquired simultaneously at any time instant. When combined with helical scan mode, the system generates a single helix of cone beam projection data. Similar to the single slice helical, weighting scheme, a method can be derived to multiply the weight with the projection data prior to the filtered backprojection algorithm. 
   As used herein, an element or step recited in the singular and proceeded with the word “a” or “an” should be understood as not excluding plural said elements or steps, unless such exclusion is explicitly recited. Furthermore, references to “one embodiment” of the present invention are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. 
   Also as used herein, the phrase “reconstructing an image” is not intended to exclude embodiments of the present invention in which data representing an image is generated but a viewable image is not. However, many embodiments generate (or are configured to generate) at least one viewable image. Thus, methods and apparatus are described herein that have a technical effect of producing a three-dimensional (3D) image of a scanned object. 
   Referring to  FIGS. 1 and 2 , a multi-slice scanning imaging system, for example, a Computed Tomography (CT) imaging system  10 , is shown as including a gantry  12  representative of a “third generation” CT imaging system. Gantry  12  has a radiation source such as an x-ray tube  14  (also called x-ray source  14  herein) that projects a beam of radiation such as x-rays  16  toward a detector array  18  on the opposite side of gantry  12 . Detector array  18  is formed by a plurality of detector rows (not shown) including a plurality of detector elements  20  which together sense the projected x-rays that pass through an object, such as a medical patient  22  between array  18  and source  14 . Each detector element  20  produces an electrical signal that represents the intensity of an impinging radiation (e.g., x-ray) beam and hence can be used to estimate the attenuation of the beam as it passes through object or patient  22 . During a scan to acquire x-ray projection data, gantry  12  and the components mounted therein rotate about a center of rotation  24 .  FIG. 2  shows only a single row of detector elements  20  (i.e., a detector row). However, multi-slice detector array  18  includes a plurality of parallel detector rows of detector elements  20  such that projection data corresponding to a plurality of quasi-parallel or parallel slices can be acquired simultaneously during a scan. 
   Rotation of components on 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 components on 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 storage device  38 . Image reconstructor  34  can be specialized hardware or computer programs executing on computer  36 . 
   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  or other suitable display device 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 . 
   In one embodiment, computer  36  includes a device  50 , for example, a floppy disk drive, CD-ROM drive, DVD drive, magnetic optical disk (MOD) device, or any other digital device including a network connecting device such as an Ethernet device for reading instructions and/or data from a computer-readable medium  52 , such as a floppy disk, a CD-ROM, a DVD or another digital source such as a network or the Internet, as well as yet to be developed digital means. In another embodiment, computer  36  executes instructions stored in firmware (not shown). In some configurations, computer  36  and/or image reconstructor  34  is/are programmed to perform functions described herein. Also, as used herein, the term computer is not limited to just those integrated circuits referred to in the art as computers, but broadly refers to computers, processors, microcontrollers, microcomputers, programmable logic controllers, application specific integrated circuits, and other programmable circuits, and these terms are used interchangeably herein. Although the specific embodiment mentioned above refers to a third generation CT system, the methods described herein equally apply to fourth generation CT systems (stationary detector-rotating x-ray source) and fifth generation CT systems (stationary detector and x-ray source). Additionally, it is contemplated that the benefits of the invention accrue to imaging modalities other than CT. Additionally, although the herein described methods and apparatus are described in a medical setting, it is contemplated that the benefits of the invention accrue to non-medical imaging systems such as those systems typically employed in an industrial setting or a transportation setting, such as, for example, but not limited to, a baggage scanning system for an airport or other transportation center. 
   In some configurations, x-ray detector array  18  is either a flat panel or curved array and x-ray source  14  follows a trajectory  54 , a portion of which is illustrated in  FIG. 3 . Trajectory  54  is either a circle or helix. In following trajectory  54 , x-ray source  14  passes successively through positions A, B, C, D, and E. X-ray source  14  emits an x-ray beam  16  that impinges upon x-ray detector array  18 . Two exemplary positions A and E of x-ray detector array  18  are shown. In a rotating gantry CT imaging system such as system  10 , x-ray detector array  18  also follows a trajectory that corresponds to x-ray source  14 , although the trajectory is not explicitly indicated in  FIG. 3 ; hence, positions A and E of x-ray detector array  18  correspond, respectively, to positions A and E of x-ray source  14 . Between positions A and E of x-ray source  14  on trajectory  54 , several intermediate positions B, C, and D of x-ray source  14  are also indicated, although corresponding x-ray beam  16  orientations and x-ray detector array  18  positions are omitted for clarity of illustration. (Positions A, B, C, D, and E represent discrete positions in a trajectory. The discrete positions are indicative of certain positions of a single x-ray source and a single x-ray detector array, and are not intended to suggest that the single x-ray source and/or single x-ray detector array are operative only at discrete locations along their trajectories.) 
   In some configurations,  FIG. 4  is representative of the geometry of a virtual 3D parallel sampling rebinned from a series of cone sampling illustrated in  FIG. 3 , obtained via row-wise fan to parallel interpolation. Such configurations utilize any of several row-wise fan-to-parallel interpolation methods to carry out the fan-to-parallel rebinning process. Also, any of several known techniques can be utilized for fan-to-parallel rebinning to trade off between image quality (for example, spatial resolution and spatial resolution uniformity) and image generation speed. Suitable techniques include but are not limited to: 
   (a) Up-sampling or under-sampling in virtual parallel sampling, i.e., the view number per rotation of virtual parallel sampling can be larger or smaller than that of cone sampling. This technique is referred to herein as interview up-sampling or under-sampling. 
   (b) Interview up-sampling or under-sampling that need not be uniform over the virtual source trajectory, and which can be adaptively adjusted according to the spatial frequency variation of the object to be reconstructed as a function over view angle. This technique is referred to herein as adaptive interview up-sampling or under-sampling. 
   (c) Up-sampling or under-sampling within each virtual parallel view rebinned from cone views. This technique is referred to herein as intraview up-sampling or under-sampling. 
   (d) Intraview up-sampling or under-sampling that need not be uniform over the whole virtual parallel view, and which can be adaptively adjusted according to the spatial frequency variation of the object to be reconstructed as a function over virtual detector cells. This technique is referred to herein as adaptive intraview up-sampling and under-sampling. 
   (e) Intraview up-sampling or under-sampling that depends upon view angle relative to the reconstruction plane (i.e., the intraview up-sampling or under-sampling varies over view angle) is referred to herein as view-angle or location dependent intraview up-sampling or under-sampling. 
   In some configurations and referring to  FIGS. 4 and 5 , virtual convex x-ray detector  18  is transformed into a virtual flat x-ray detector  62  by appropriately rebinning projection data. A representation of the transformed geometry is shown in  FIG. 5 . Due to the geometrical transformation or data rebinning, detector rows (not shown in  FIG. 5 ) in virtual flat x-ray detector  62  may no longer be parallel even though their counterpart detector rows  64  in virtual convex x-ray detector  18  are parallel to one another. 
   (f) Any of techniques (a) through (e), given a non-uniform grid on which a tomographic image is to be reconstructed and adjusted accordingly. 
   Let f(x,y,z) represent the object to be reconstructed. In some configurations of the present invention, a reconstruction using virtual 3D parallel sampling is written: 
                     f   ⁡     (     x   ,   y   ,   z     )       =       π     (       β   max     -     β   min       )       ⁢       ∫     β   min       β   max       ⁢         [       ⅆ   2     ⁢     /       (       d   2     +       Z   2     ⁡     (   z   )         )       1   /   2           ]     ⁢     
     [       ∫     -   ∞       +   ∞       ⁢       w   ⁡     (     α   ,   β   ,     t   ⁡     (     x   ,   y     )         )       ⁢       S   β     ⁡     (     ω   ,     Z   ⁡     (   z   )         )       ⁢     ⅇ     j2πω   ⁢           ⁢   x       ⁢        ω        ⁢     ⅆ           ⁢   ω         ]     ⁢     ⅆ   β             ⁢     
     ⁢   and           (   1   )                   S   β     ⁡     (     ω   ,     Z   ⁡     (   z   )         )       =       ∫     -   ∞     ∞     ⁢         P   β     ⁡     (       t   ⁡     (     x   ,   y     )       ⁢     Z   ⁡     (   z   )         )       ⁢     ⅇ       -   j2πω     ⁢           ⁢   t       ⁢     ⅆ   t                 (   2   )               
wherein P β (t(x,y),Z(z)) is the projection of the pixel to be reconstructed on the virtual detector under virtual 3D parallel sampling;
 
t(x,y) is the orthogonal distance between (x,y,z), the pixel to be reconstructed, and the z axis;
 
w(α,β,t(x,y)) is the 3D view weighting function;
 
d is the orthogonal distance between the x-ray focal spot and the virtual detector; and
 
Z(z) is the height of the projection of the pixel (x,y,z) in the virtual detector under virtual 3D parallel sampling.
 
α represents the cone angle of the x-ray passing through pixel (x,y,z); and β represents the view angle associated with (x,y,z);
 
β min  is the start view angle in radians; and
 
β max  is the end view angle in radians.
 
   In principle, the view weighting function w(α,β,t(x,y)) in eq. (1) can be dependent on cone angle α and view angle β only, i.e., w(α,β,t(x,y))=w(α,β,∘)≡w(α,β). Consequently, eq. (1) can be rearranged as 
   
     
       
         
           
             
               
                 
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   Thus, in various configurations of the present invention, view weighting is applied after filtering. However, eq. (1) still provides flexibility in dealing with imperfect x-ray detectors under practical situations, as well as the potentiality of obtaining the most achievable temporal resolution in functional CT imaging. 
   The inner integration over variable ω in eqs. (1) and (3) represents a row-wise 1D ramp filtering as used in known methods of CT reconstruction. The row-wise 1D ramp filtering is spatially parallel to the x-y plane when eqs. (1)-(3) are applied under a circular x-ray source trajectory, but is tangential to the source trajectory under a helical scan mode. Also, the linear grid on which the row-wise 1D filtering is accomplished is adjusted accordingly when techniques (c) through (e) are utilized. 
   Thus, in some configurations and referring to flow chart  100  of  FIG. 6 , a technical effect of the present invention is achieved by a user operating CT imaging apparatus  10  to scan an object  22  at  102  to collect projection data. The scanning can be performed, for example, by operating CT imaging apparatus  10  to scan an object  22  as described above. The projection data obtained from the scanning is then subjected to a row-wise fan-to-parallel beam rebinning at  104 . The rebinned data is then view-weighted using weights w(α,β,t(x,y)) at  106 , and the view-weighted data is then subjected to a row-wise 1D ramp filtering at  108  followed by a 3D backprojection at  110  to produce an image of object  22 . Configurations represented by the flow chart of  FIG. 6  reflect the transformations described by eq. (1) above. 
   In some configuration and referring to flow chart  200  of  FIG. 7 , after operating CT apparatus  10  to scan an object  22  at  102  to collect projection data and row-wise fan-to-parallel rebinning is performed at  104 , the rebinned data is subjected first to row-wise ramp filtering  108  and then the filtered data is subjected to view weighting at  200  using weights w(α,β). The weighted data is then used in a 3D backprojection at  110  to produce an image of object  22 . The view weighting at  200  is implemented after the row-wise 1D ramp filtering at  108  because the view weighting function w(α,β) is not dependent on t(x,y). This independence of t(x,y) (rather than the dependence on t(x,y) of weights w(α,β,t(x,y)) at  106  of flow chart  100  of  FIG. 6 ) results in significantly improved computational efficiency because all projection data under virtual 3D parallel sampling need be filtered only once. Examples of suitable view weighting methods include, but are not limited to, those described by C. R. Crawford and K. F. King in “Computed tomography scanning with simultaneous patient translation,” Med. Phys. 17(6), pp 967-982, 1990 and by J. Hsieh in “A general approach to the reconstruction of x-ray helical computed tomography,” Med. Phys. Vol. 23 (2), pp 221-229, 1996. A significant feature of configurations of the present invention that utilize 3D reconstruction methods using virtual 3D parallel sampling is that the 1D ramp filtering is adaptively implemented along the tangential direction of an x-ray source trajectory. 
   Exemplary configurations of the present invention described herein utilize a CT imaging apparatus and x-ray radiation. However, configurations of the present invention are not limited to CT imaging apparatus and x-ray radiation. For example, some configurations of the present invention employ other types of radiation, even, for example, ultrasound radiation. 
     FIG. 8  and  FIG. 9  provide a comparison of shading/glaring artifact suppression in axial views of an HBP phantom.  FIG. 8  is a reconstruction using a prior art helical FDK algorithm with horizontal 1D ramp filtering and shows, among other things, shading in region  302 .  FIG. 9  is a reconstruction of the same HBP phantom as  FIG. 8  utilizing a configuration of a 3D reconstruction method utilizing virtual 3D parallel sampling in which tangential 1D ramp filtering is inherently implemented.  FIG. 9  shows, among other things, a substantial reduction in the shading artifact in region  302 . 
     FIG. 10  and  FIG. 11  provide a comparison of shading/glaring artifact suppression in axial views of a Defrise phantom.  FIG. 10  is a reconstructed image using a prior art helical FDK algorithm with horizontal 1D ramp filtering. Considerable glare is noted at region  304 .  FIG. 11  is a reconstructed image of the same phantom as  FIG. 10 . However,  FIG. 11  is reconstructed using a configuration of a 3D reconstruction method utilizing virtual 3D parallel sampling in which tangential 1D ramp filtering is inherently implemented. The glare at region  304  is greatly reduced in  FIG. 11 . 
     FIG. 12  and  FIG. 13  provide a comparison of shading/glaring artifact suppression and geometric distortion in coronal reformatted views of a Defrise phantom.  FIG. 12  is a reconstructed image using a prior art helical FDK algorithm with horizontal 1D ramp filtering. The reconstructed image of  FIG. 12  shows considerable glare and shading at numerous locations, including locations  306 ,  308 ,  310 ,  312 ,  314 ,  316 ,  318 , and  320 .  FIG. 13  is a reconstructed image of the same phantom as  FIG. 12 . However,  FIG. 13  is reconstructed using a configuration of a 3D reconstruction method utilizing virtual parallel sampling in which tangential 1D ramp filtering is inherently implemented. A significant reduction in glare and shading artifacts is noted, including but not limited to the artifacts at locations  306 ,  308 ,  310 ,  312 ,  314 ,  316 ,  318 , and  320 . Geometric distortion is also reduced. 
     FIG. 14  and  FIG. 15  provide a comparison of shading/glaring artifact suppression and geometric distortion in sagittal reformatted views of a Defrise phantom.  FIG. 14  is a reconstructed image using a prior art helical FDK algorithm with horizontal 1D ramp filtering. The reconstructed image of  FIG. 15  shows considerable glare and shading at numerous locations, including locations  322 ,  324 ,  326 ,  328 ,  330 ,  332 ,  334 ,  336 ,  338 ,  340 ,  342 , and  344 . In addition, considerable geometric distortion is evident in various shapes, including but not limited to shape  346 .  FIG. 15  is a reconstructed image of the same phantom as  FIG. 12 . However,  FIG. 13  is reconstructed using a configuration of a 3D reconstruction method utilizing virtual parallel sampling in which tangential 1D ramp filtering is inherently implemented. A significant reduction in glare and shading artifacts is noted, including but not limited to the artifacts at locations  322 ,  324 ,  326 ,  328 ,  330 ,  332 ,  334 ,  336 ,  338 ,  340 ,  342 , and  344 . Additionally, geometric distortion is reduced, including but not limited to shape  346 . 
   It will thus be observed that configurations of the present invention significantly improve the suppression of shading and glaring artifacts resulting from inconsistencies in cone beam helical data acquisition in volumetric CT scanning systems as well as the speed of image generation. In addition, configurations of the present invention improve suppression of distortion resulting from inconsistencies in cone beam helical data acquisition in volumetric CT scanning systems. Furthermore, configurations of the present invention have improved noise characteristics and can provide better dose efficiency than other known scanning algorithms implementations including various exact CT reconstruction algorithm implementations. 
   In addition, row-wise fan-to-parallel rebinning to generate virtual 3D parallel sampling avoids design and manufacturing complexities of some known systems employing sequential triggering. The incorporation of a view weighting function in the reconstruction process enables various configurations of the present invention to handle partial scan (i.e., view angle range smaller than 360 degrees) and over scan (i.e., view angle range larger than 360 degrees) under both circular and helical x-ray source trajectories. Various configurations of the present invention also provide flexibility by implementing view weighting either before filtering or after filtering, or even in the process of 3D backprojection. 
   While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.