WO2004019279A2 - Apparatus and method for reconstruction of volumetric images in a divergent scanning computed tomography system - Google Patents
Apparatus and method for reconstruction of volumetric images in a divergent scanning computed tomography system Download PDFInfo
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- WO2004019279A2 WO2004019279A2 PCT/US2003/026021 US0326021W WO2004019279A2 WO 2004019279 A2 WO2004019279 A2 WO 2004019279A2 US 0326021 W US0326021 W US 0326021W WO 2004019279 A2 WO2004019279 A2 WO 2004019279A2
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T11/00—2D [Two Dimensional] image generation
- G06T11/003—Reconstruction from projections, e.g. tomography
- G06T11/005—Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S378/00—X-ray or gamma ray systems or devices
- Y10S378/901—Computer tomography program or processor
Definitions
- the present invention relates generally to 2D and 3D computerized tomography (CT).
- CT computerized tomography
- this invention relates to methods and systems for reconstructing projection data which are neither equlinear or equiangular in nature.
- an x-ray fan beam and an equilinear or equiangular array detector are employed.
- Two-dimensional (2D) axial imaging is achieved. While the data set is complete and image quality is correspondingly high, only a single slice of an object is imaged at a time.
- a "stack of slices" approach is employed. Acquiring a 3D data set one slice at a time is inherently slow.
- motion artifacts occur because adjacent slices are not imaged simultaneously.
- dose utilization is less than optimal, because the distance between slices is typically less than the x-ray coUimator aperture, resulting in double exposure to many parts of the body.
- a cone-beam x-ray source and a flat 2D equilinear or curved 2D equiangular area detector are employed.
- An object is scanned, preferably over a 360-degree range, either by moving the x-ray source in a scanning circle around the object while keeping the 2D area detector fixed with reference to the source, or by rotating the object while the source and detector remain stationary. In either case, it is the relative movement between the source and object which affects scanning.
- the cone-beam geometry Compared to the 2D "stack of slices" approach for 3D imaging, the cone-beam geometry has the potential to achieve rapid 3D imaging of both medical and industrial objects, with improved dose utilization.
- cone-beam reconstruction when individual flat detectors are reconstructed independently. Simply combining separate reconstructed portions of the obj ect from independently processed projections results in an image characterized by discontinuous jumps between the various projections. Alternatively, one could first combine the discreet data sets from each detector into a new single data set that is then reconstructed. However, by simply combining the data into a larger data array and performing standard reconstruction techniques, the data elements in the new data set are not equally spaced. Thus, the resultant images will be distorted geometrically, or the dynamic range of the reconstructed data set will not represent the true transmission values of the object being imaged.
- the present invention relates to improved systems and methods for reconstructing projection data, including x-ray projection data for two-dimensional (2D) fan-beam and three-dimensional (3D) cone beam CT imaging, in which the geometry of the detectors is neither equilinear or equiangular, by reprojecting the actual measured data into a new virtual data array, which has an equilinear or equiangular geometry.
- multiple discreet projection data sets which, when combined, are neither equilinear or equiangular, are reprojected into a new virtual data set on an equilinear spaced detector on a line or plane, or an equiangular spaced detector array on an arc or cylinder.
- the resulting virtual projection data set can then be reconstructed using standard backprojection techniques and generate images which are geometrically correct, and represent the true x-ray transmission properties of the object being imaged.
- the projection data from two or more ID linear or 2D flat detector arrays are reprojected onto a single equilinear or equiangular virtual detector array prior to filtering and backprojecting the projection data.
- the projection data from two or more discrete detector positions are reprojected onto a virtual detector array having an equilinear or equilangular configuration, and the reprojected data is reconstructed to provide an image.
- the "virtual" detector array of the present invention is a data array comprising a plurality of pixels, having an equiliner or equiangular geometry, where the data values assigned to each pixel in the virtual array is based upon data from an actual detector or set of detectors having a non-equilinear and non-equiangular geometry.
- the present invention advantageously allows for the 2D and 3D tomographic reconstruction of objects.
- This invention enables divergent x-ray 2D fan beam or 3D cone beam tomographic reconstruction using a discrete number of ID linear or 2D flat detectors angled relative to one another by using a novel rebinning and reprojection technique onto virtual equilinear or equiangular detector arrays prior to performing standard filtered backprojection tomographic reconstruction techniques.
- the present invention is particularly useful for medical imaging applications, as well as numerous industrial applications, such as testing and analysis of materials, inspection of containers, and imaging of large objects.
- Fig. 1 shows standard equilinear and equiangular geometries used in various generations of CT scanners
- Fig. 2 shows a standard equilinear detector geometry in which the detectors are arranged with constant spacing along a line or plane;
- Fig. 3 shows the radiation profile of an imaged object defined by an equilinear arrangement of detectors
- Fig. 4 shows a standard equiangular detector geometry in which the detectors are arranged with constant angular spacing along an arc or cylindrical surface;
- Fig. 5 shows the radiation profile of an imaged object defined by an equiangular arrangement of detectors;
- Fig. 6 shows three equilinear-spaced detector arrays positioned and angled relative to one another, resulting in a geometry that is neither equilinear nor equiangular;
- Fig. 7 shows the predicted radius of reconstructed object with three detector arrays generally positioned along an arc having a radius centered at the x-ray focal spot;
- Fig. 8 shows the predicted radius of reconstructed object with three ID linear or 2D flat plate detector arrays positioned along a straight line in an equilinear arrangement
- Fig. 9 is a flow chart diagram of the rebinning algorithm for reconstructing ID fan beam or 2D cone beam projection data which is neither equilinear or equiangular;
- Fig. 10 shows the proj ection of multiple angled detector array positions onto a single virtual flat equilinear detector array;
- Fig. 11 shows the projection of multiple angled detector array positions onto a single virtual curved equiangular detector array.
- a radiation source 13 projects radiation onto multiple one-dimensional linear or two-dimensional planar area detector arrays 14 that are angled generally along line or a circle.
- the detector arrays generate scan data from a plurality of diverging radiation beams, i.e., a fan beam or cone beam.
- the source and detectors are rotated around the object to be imaged, and a plurality of projection images is captured to computer memory for tomographic projection image processing.
- a single source produces a fan or cone beam which is read by a linear ID or 2D array of detectors, as shown on the left.
- the detectors occupy a ID arc to image fan beam data, or a 2D cylindriacal surface to image cone beam data.
- an equilinear detector geometry is more clearly defined.
- the detector elements in an array are arranged with constant spacing along a straight line or a flat plane.
- the angle between rays connecting the x-ray source point and the detector elements does not remain constant.
- a radiation absorption profile, or image is generated with varying amplitudes for a region between the banlc of detectors and the x-ray source, as shown in Fig. 3.
- Figs. 4-5 illustrate an equiangular detector geometry.
- the detector elements in an equiangular array are arranged with constant angular spacing along a circle or cylinder.
- the angle between rays connecting the x-ray source point and the detector elements remains constant, but the distance between detectors may change.
- Fig. 5 shows the radiation absorption profile for the region between the bank of detectors and the x-ray source. Each ray is identified by its angle, ⁇ , from the central ray, and the absorption profile is denoted by the function R ⁇ ( ⁇ ).
- One method for achieving a wide field-of-view is to use multiple ID or 2D detectors, arranged end-to-end and angled relative to one another, as shown in Fig. 6.
- Another technique is to use a single array, translated to discrete positions along an arc opposite the x-ray source, to obtain a large "effective" field of view. In either case, when one or more equilinear ID linear fan beam or 2D planar cone beam detector arrays are positioned and angled along an arc opposite the x-ray source, the resulting geometry is neither equilinear or equiangular. As illustrated in Fig.
- the projection of equally spaced detector elements, d,-, on the angled arrays do not project onto equally spaced detectors, p j3 located on lines, planes, or arcs.
- the process of reprojecting these elements onto a new virtual detector array which is coincident or parallel to the central detector array will result in projections that are not equidistant.
- the Fourier transform filtering is performed continuously along the axes of the angled arrays without resampling, the spacing of detector arrays cannot be assumed to be equal.
- Fig. 7 shows in more detail the result of filtering on non-equally spaced detectors.
- Fig. 8 illustrates this same calculation of the predicted radius of the reconstructed object assuming the same input parameters of focal length and detector length, but where the detector arrays are arranged in a plane to provide equilinear geometry.
- the predicted radius of the angled detector geometry is larger than that of the equilinear detector geometry, and the resultant images with the angled detector geometry will be distorted geometrically.
- the algorithm shown in Fig. 9 describes a method of reconstructing fan beam or cone beam x-ray projection data of an object, where the detector configuration is neither equilinear or equiangular.
- the algorithm describes a method for generating a new virtual equilinear or equiangular fan beam or cone beam detector array which is defined along a straight line or generally along an arc. For every pixel defined in the virtual detector array, the projection point in the original projection data is determined and the x-ray absorption amplitude for that point is calculated by interpolating the nearest neighbor pixels.
- standard filtered backproj ection and algebraic reconstruction techniques maybe performed to generate image data.
- the method consists of creating a single virtual detector array for each proj ection position, which is defined as being equilinear or equiangular, and reprojecting two more real detector arrays onto the virtual array. Once the real projection data is reprojected onto the virtual detector, the data is filtered and backprojected using standard tomographic reconstruction techniques;
- the projection angle index, iproj is first assigned the value 1.
- the x-ray source and detector array(s) are moved to a projection angle relative to the object being imaged. This can be accomplished by either moving the source and detector relative to a stationary object (preferably by moving the source and detector in a circle or arc around the object), or by keeping the source and detector stationary and rotating the object to the desired projection angle.
- the projection data can obtained for a plurality of projection angles (1...nproj), preferably at a plurality of equally spaced angles as the source/detector and object are rotated 360 degrees with respect to each other.
- a new virtual equilinear or equiangular array, P is allocated.
- the virtual array, P includes virtual pixels which are equally spaced in distance along a line or plane in the case of a virtual equilinear array, or equally spaced in angle along an arc or curved plane in the case of a virtual equiangular array.
- the real projection data, D from each real detector array (1...ndet) is acquired for the given projection angle, iproj.
- the real proj ection data is then reproj ected onto the virtual array, P, at step 107.
- the reprojection subroutine includes looping through each virtual pixel in the virtual array, P, (step 109), and for each virtual pixel, determining the real detector pixel, d, that is intersected by the line connecting the virtual pixel and the x-ray source (step 111).
- an interpolation technique then is applied to d and its nearest neighbors on the real detector array to compute an x-ray absorption amplitude value to be assigned to the virtual pixel, p (step 112). This process is repeated until absorption amplitude values have been assigned to each of the virtual pixels in the virtual array.
- data from the virtual detector array is then filtered at step 117 and backprojected at step 118.
- the filtering step which can be visualized as a simple weighting of each Fourier transformed projection in the frequency domain
- the backproj ection step which can be seen as the dual, or in a more strict mathematical sense, the adjoint, of projection.
- a projection value is backprojected, or smeared out, over the image points along the ray. This entire process is then repeated for each of the projection angles.
- a new equilinear virtual detector is allocated and defined along a one-dimensional line in the case that a fan beam geometry, or along a two-dimensional flat plane in the case of a cone beam geometry.
- the images are captured by the actual three-panel detector array, and then a new equiangular virtual detector is allocated.
- the equiangular virtual detector is an arc in the case of a fan beam geometry, and a curved cylindrical surface in the case of a cone beam geometry.
- the new virtual array assumes that detector elements are equally spaced in distance or angle, respectively.
- the projected position in the real detector arrays is computed and an interpolation technique is applied to nearest neighbors on the real array to compute the correct x-ray absorption amplitude of the object to be reconstructed.
- standard filtered backproj ection, algebraic reconstruction techniques, and other tomographic imaging algorithms may be applied to generate image data of an object.
- the real detector array comprises three fiat panel detectors arranged end-to-end, and angled to approximate an arc having a radius centered on the focal spot of the radiation source.
- the principles of the invention can be used with actual detectors having any number of detector elements, including both ID line detectors and 2D panel detectors, where the geometry of the actual detector is neither equilinear or equiangular.
- the principles of the present invention can be advantageously employed in a system where one or more detectors are movable to various discrete positions along a line or arc relative to the x-ray source, such as described in co-pending U.S. Patent Application No.
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AU2003262726A AU2003262726A1 (en) | 2002-08-21 | 2003-08-21 | Apparatus and method for reconstruction of volumetric images in a divergent scanning computed tomography system |
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US20070104308A1 (en) | 2007-05-10 |
AU2003262726A1 (en) | 2004-03-11 |
WO2004019279A3 (en) | 2004-03-25 |
US20110135054A1 (en) | 2011-06-09 |
US7903779B2 (en) | 2011-03-08 |
US7106825B2 (en) | 2006-09-12 |
US7965811B1 (en) | 2011-06-21 |
US20040179643A1 (en) | 2004-09-16 |
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