Abstract:
A method for reconstructing computerized tomographic (CT) images of an object, including: scanning the object with a CT imaging system to acquire views that include measured projections of the object. Additionally, the method applies an iterative algorithm to minimize errors between the measured projections and reprojections of a reconstructed CT image, wherein at each iteration, projection errors become smaller causing the reconstructed CT image to become further refined.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to a digital image processing method for tomographic imaging. Specifically, the present invention relates to methods for reconstructing an underdetermined image from incomplete data.  
       BACKGROUND OF THE INVENTION  
       [0002]     In at least one conventional 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 a medical patient or other imaging object. The x-ray beam, after being attenuated by the object, impinges upon an array of radiation detectors. The intensity of the attenuated x-ray beam radiation received at the detector array is dependent upon the attenuation of the x-ray beam passing through the imaging object, such as the medical patient&#39;s body. Each detector element of the array produces a separate electrical signal that is a measurement of the x-ray beam&#39;s attenuation at the detector location. Separate attenuation measurements from all the detectors are acquired to produce a transmission profile.  
         [0003]     In conventional third generation CT systems, the x-ray source and the detector array are rotated with a gantry within the imaging plane and around an imaging object so that the angle at which the x-ray beam intersects the imaging 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”, which are used to control the brightness of a corresponding pixel on a cathode ray tube display.  
         [0004]     At least one known CT imaging system is available that combines a gantry rotation rate of 0.8 s with a data acquisition system (DAS) sampling rate of 1230 Hz. As a result, a projection sampling rate of 984 views per gantry rotation is obtained. Theoretical, experimental, and clinical investigations have shown that, from a standpoint of aliasing, this sampling rate is near a lower limit. It is desirable to increase the scan rate to at least 0.5 s per gantry rotation to reduce motion artifacts and to reduce imaging times, but to do so would require a higher sampling rate. Hardware limitations limit maximum sampling rates, however. For example, hardware and software limitations may limit a DAS sampling rate to 1408 Hz. For 0.5 s per scan, 704 views per gantry rotation would be obtained in such a system, yielding a 28.5% reduction in the number of available views, and hence data, as compared to other CT imaging systems that provide 984 views per gantry rotation. If proper compensation is not performed, view aliasing artifacts, such as streaks, will result in reconstructed images. Radiologists object to such aliasing artifacts. In sum, when the number of views acquired per gantry rotation is too low, insufficient data results, thereby, causing objectionable image artifacts.  
         [0005]     U.S. Pat. No. 6,285,732, issued to Hsieh on Sep. 4, 2001, and incorporated herein by reference, teaches methods and apparatus for reducing aliasing artifacts in computerized tomographic imaging using adaptive, non-uniform view interpolation within a selected view range. Additionally, in U.S. Pat. No. 6,285,732, Hsieh teaches a method of weighting the views to compensate for the non-uniform interpolation, and filtering and backprojecting the views to generate an image of the imaging object that he says reduces view aliasing artifacts “without clinically unacceptable reduction in spatial resolution.” 
         [0006]     In practice, because view interpolation inherently results in some reduction in spatial resolution, it remains desirable to provide a method and a system for CT imaging that reduces view aliasing artifacts, without employing view interpolation and its inherent limitations.  
       SUMMARY OF THE INVENTION  
       [0007]     The above need is met, according to the present invention, by providing a method for reconstructing computerized tomographic (CT) images of an object, includes scanning the object with a CT imaging system to acquire views that include measured projections of the object. Additionally, an iterative algorithm is applied to minimize errors between the measured projections and reprojections of a reconstructed CT image. At each iteration, projection errors become smaller, causing the reconstructed CT image to become further refined.  
         [0008]     Another aspect of the invention provides a system for reconstructing computerized tomographic images, that includes: 
        a) means for acquiring a measured projection signal of a computerized tomographic image;     b) an iterative filter for processing the measured projections subsequent to a predetermined delay and yielding a reprojected reconstruction signal;     c) means for acquiring an initial reprojected reconstruction signal of a computerized tomographic image;     d) a time delay for delaying implementation of the initial reprojected reconstruction signal as an input to the iterative filter subject to the predetermined delay;     e) a switch for controlling the implementation of the initial reprojected reconstruction signal as an input to the iterative filter; and     f) a summation for comparing the measured projection signal with the reprojected reconstruction signal to yield projection errors that will provide feedback for altering the iterative filter in subsequent operations of the iterative signal estimation system.        
 
       ADVANTAGES  
       [0015]     Improved CT imaging is thus provided, in this embodiment, by reducing view aliasing artifacts without reducing spatial resolution, typically attributed to view interpolation. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0016]      FIG. 1A  is a prior art pictorial view of a CT imaging system.  
         [0017]      FIG. 1B  is a prior art block diagram of the system illustrated in  FIG. 1A .  
         [0018]      FIG. 2  is a prior art flowchart of an iterative algorithm to reconstruct an object from limited-angle data.  
         [0019]      FIG. 3  is an exemplary block diagram of the digital image processing method according to the present invention.  
         [0020]      FIG. 4A  is a general signal estimation system that models the method of the present invention.  
         [0021]      FIG. 4B  is a diagram illustrating the present invention in a signal estimation framework. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0022]     Referring to  FIGS. 1A and 1B , a prior art 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 as either a single slice or multi-slice configuration. Each detector element  20  produces an electrical signal (not shown) that represents the intensity of an impinging x-ray beam  16 , and hence the attenuation of the x-ray beam  16  as it passes through patient  22 . Gantry  12  and the components mounted thereon, rotate about a center of rotation  24 , during a scan to acquire x-ray projection data.  
         [0023]     A control mechanism  26  of CT system  10  governs rotation of gantry  12  and the operation of x-ray source  14 . The 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 provided as an input to a computer  36 , which stores the image in a mass storage device  38 .  
         [0024]     Computer  36  also receives commands and scanning parameters from an operator via console  40 , that has a keyboard (not shown). 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 .  
         [0025]     A majority of clinical aliasing artifacts occur in prior art CT system  10  when a dense object is located near an outer region of a field of view, because the view requirement is roughly proportional to the distance of an object from the CT isocenter. For example, shoulder bones  50  of patient  22  often produce aliasing streaks. The digital image processing method of the present invention reduces these artifacts while maintaining optimal spatial resolution. In fact, when the filtered backprojection technique employs a smoothing filter such a Hamming window, the present invention can yield an actual enhancement of spatial resolution.  
         [0026]     Thus, in one embodiment of the present invention, an object  22 , for example, a medical patient, is scanned with CT imaging system  10  to acquire views comprising projection samples of the object  22 . These views are further processed by image reconstructor  34  into images that are stored by computer  36  in storage device  38  for viewing on CRT display  42 . (Because design choices are available in which distributed processing of images in various CT imaging systems  10  is performed, it will be understood that the invention is not limited to embodiments in which all processing is performed by a discrete image reconstructor  34 ).  
         [0027]     The present invention reduces artifacts due to inadequate view sampling. Signal to noise ratio of the acquired views is assumed to be adequate. One way to address such artifacts would be to double the number of views by interpolation, but this approach leads to a reconstruction with significantly reduced spatial resolution. Previously cited U.S. Pat. No. 6,285,732 teaches a nonuniform view interpolation method that provides a good compromise between aliasing artifact reduction and reduction of spatial resolution. The present invention avoids view interpolation entirely and therefore does not compromise spatial resolution.  
         [0028]     The present invention is also applicable to a limited-angle tomographic reconstruction problem in which views can be measured only in a limited angular range. An iterative algorithm for limited-angle image reconstruction that is related to the present invention is reported by K. C. Tam and V. Perez-Mendez in J. Opt. Soc. Am., 71 (1981) 582-592. Said algorithm is also discussed by K. C. Tam as prior art in U.S. Pat. No. 5,053,958. This prior art iterative algorithm, shown here in  FIG. 2 , uses measured projections and a priori information on the object to estimate missing projections. Both measured projections and estimated missing projections are used in image reconstruction. In contrast to the prior art, the iterative algorithm of the present invention, as shown in  FIG. 3 , uses the measured projections and a priori information for image reconstruction.  
         [0029]     The advantage of the algorithm in  FIG. 3  versus  FIG. 2  is that the reconstruction of the present invention is driven toward consistency with the measured projections, whereas the reconstruction of the prior art is not. Consistency of the prior art reconstruction depends on the accuracy of the filtered backprojection technique, whereas consistency of the reconstruction of the present invention can be achieved even with an approximate backprojection technique. For this reason, when the filtered backprojection technique employs a smoothing filter such as a Hamming window, the reconstruction from the algorithm in  FIG. 2  will be blurred, but the reconstruction from the algorithm in  FIG. 3  will not.  
         [0030]     The algorithm in  FIG. 2  will now be described in greater detail. Referring to steps  51 - 53 , the measured projections in a limited angular range are acquired. A complete set of projections of the object is comprised of these measured projections plus the missing projections at inaccessible view angles, which are set to zero initially. The object density is reconstructed by filtered backprojection. The initial estimate of object density, steps  54  and  55 , is corrected by the a priori information on the object, namely the extent and location of the object, the known upper bound of object density, and that there is no negative density. The image of the object is corrected, pixel by pixel, by resetting to zero those pixels outside the known extent of the object, resetting to the upper bound those pixels with density exceeding the upper bound, and resetting to zero those pixels with negative density. After a test for convergence of the data is made, steps  56  and  57 , the missing projections of the interim object density in the missing views are calculated.  
         [0031]     A second iteration begins and the first estimate of the missing projections are now provided as well as the measured projections. A filtered backprojection operation is done on the whole set of projections in order to reconstruct the object. The object density is corrected by the a priori information, the second estimate of the missing projections is calculated, and so on. Typically the reconstructed image of the object converges after about 5 to 10 iterations and a final reconstructed object density or reconstructed image, step  58 , is output.  
         [0032]     The iterative method of the present invention will now be described. Referring to  FIG. 3 , measured projections  60  have been corrected for various well known errors such as variations in detector and channel gains, and are log adjusted, by taking the negative logarithm of the corrected data. The measured projections  60 , therefore, indicate the amount of attenuating material along the path of each detected x-ray beam. When these measured projections  60  are incomplete (e.g., limited view sampling or limited-angle acquisition), then an image constructed by filtered backprojection includes aliasing artifacts. The present invention&#39;s iterative process, shown in  FIG. 3 , reduces these aliasing artifacts while driving a reconstructed image  74  toward consistency with the measured projections  60 .  
         [0033]     Thus, in one embodiment of the present invention depicted in  FIG. 3 , there is provided an iterative method for refining a reconstructed image  74  from the measured projections  60 , each iteration of the method including the operations of calculating projection errors  62 ; constructing an image of projection errors  64 ; reprojecting the image of projection errors  66 ; updating the reconstruction  68 ; reprojecting the reconstruction  70 ; and testing for convergence  72 .  
         [0034]     From a signal processing point of view, the method of the present invention can be modeled as a general signal estimation system, as shown in  FIG. 4A . Referring to  FIG. 4A , a reference signal  82  and a corrupted signal  84  are given to a signal estimation system  80  that attempts to remove noise from the corrupted signal  84  through iterative filtering  88 . An estimated signal  85  output from the iterative filtering  88  is compared in step  90  with the reference signal  82 , resulting in an error signal  86 . The error signal  86  is used as feedback information to alter the filtering mechanism in iterative filtering  88  in order to drive the estimated signal  85  toward the reference signal  82 . In the context of tomographic image reconstruction, the reference signal  82  corresponds to the measured projections  60  (shown in  FIG. 3 ), the error signal  86  corresponds to the projection errors  62  (shown in  FIG. 3 ), and the estimated signal  85  corresponds to the reprojected reconstruction  70  (shown in  FIG. 3 ). When the iterative process starts, corrupted signal  84  is an initial corrupted signal  81 , which could be zero. After a first iteration of filtering, a switch  87  connects the corrupted signal  84  to the estimated signal  85  through a delay  83 , such that the current corrupted signal  84  is the estimated signal  85  from the previous iteration.  
         [0035]      FIG. 4B  depicts the method of the present invention within the framework of a signal estimation system  100 , but with tomographic image reconstruction descriptors. Part numbers less than  100  in  FIG. 4B  correspond to identical part numbers shown in  FIG. 3 . As shown in  FIG. 4B , the measured projections  60  and the reprojected reconstruction  70  (through a delay  103  and a switch  107 ) are given to an iterative filtering process including operations ( 62 ,  64 ,  66 ,  68  (all shown in  FIG. 3 )) that attempts to remove error from the reprojected reconstruction  70 . The reprojected reconstruction  70  output from the iterative filtering process including operations ( 62 ,  64 ,  66 ,  68  (all shown in  FIG. 3 )) is compared in step  110  with the measured projections  60 , resulting in the projection errors  62 . The projection errors  62  are used as feedback information to alter the filtering mechanism in the iterative filtering process including operations ( 62 ,  64 ,  66 ,  68  (all shown in  FIG. 3 )) in order to drive the reprojected reconstruction  70  toward the measured projections  60 . For the first iteration of the process, an initial reprojected reconstruction  101 , which could be zero, is used instead of the delayed reprojected reconstruction  70 . Operational details of the iterative process are given next.  
         [0036]     Before the iterative process begins, it is useful to define an image mask of the object. In a preferred embodiment, the mask is constructed using measured data, such as from a separate optical scan of the object. If no separate measurements are made, however, then the mask can be constructed from the measured x-ray projections in a process utilizing unfiltered backprojection within a loop over all views. This process includes the steps of backprojecting the unfiltered measured projections  60  for the current view; calculating the result of the comparison (pixel&lt;=noise) for this backprojection, thereby identifying as TRUE the pixels through which x-rays pass without attenuation; and updating the mask (set initially to FALSE) by a logical OR operation with these TRUE pixels. After all views have been included, the mask is inverted by a logical NOT operation, so that pixels inside the object are TRUE, and pixels outside the object are FALSE. If a more accurate image mask is required, U.S. Pat. No. 4,888,693, assigned to General Electric Company, teaches a method to estimate the object boundary with greater accuracy by fitting curves to the edges of the projection data to more precisely determine end points between attenuated and unattenuated x-rays.  
         [0037]     Referring again to  FIG. 3 , the projection errors  62  are the measured projections  60  minus the reprojected reconstruction  70  (which is initially set to zero). The image of projection errors  64  is constructed by filtered backprojection, and in the preferred embodiment, pixels outside the object are reset to zero using an image mask of the object. The reprojected image of projection errors  66  is calculated by integrating along the path of each detected x-ray beam. The reconstruction  68  is updated as a linear combination of the current reconstruction  68  (which is initially set to zero) and the image of projection errors  64  using the coefficients c1 and c2, respectively, that yield the least squares projection errors  62 .  
         [0038]     To compute coefficients c1 and c2, projection data are loaded into three columns: col1 includes the reprojected reconstruction  70  (which is initially set to zero); col2 includes the reprojected image of projection errors  66 ; and col3 includes the measured projections  60 . For the first iteration, one can use c1=1 (which is arbitrary, since the reconstruction  68  is set to zero initially) and c2=((col3−col1)′*col2)/(col2′*col2). In another embodiment, one could instead use c=1 and c2=1 for the first iteration, which would yield an updated reconstruction  68  corresponding exactly to the image constructed by filtered backprojection of the measured projections. For subsequent iterations, one can use the least squares solution to the matrix equation [col1 col2]*x=col3, where x=[c1 c2]′. In another embodiment, one could instead use c1=1 (since c1 converges to unity) and c2=((col3−col1)′*col2)/(col2′*col2).  
         [0039]     The reprojected reconstruction  70  can be calculated by integrating along the path of each detected x-ray beam. In the preferred embodiment, however, to save computer time, the reprojected reconstruction  70  is calculated as a linear combination of the current reprojected reconstruction  70  (which is set to zero initially) and the reprojected image of projection errors  66  using the coefficients c1 and c2, respectively. The test for convergence  72  is based on the root mean square of projection errors  62 . Upon convergence, the refined reconstructed image  74  is obtained.  
         [0040]     Comparing  FIGS. 2 and 3 , it would seem logical to take from  FIG. 2  steps  54  and  55  (in which the object density is corrected by the a priori information on the object), and insert these steps into  FIG. 3  between steps  68  and  70 . The updated reconstruction  68  would then be subjected to three corrections: (1) resetting to zero those pixels outside the known extent of the object; (2) resetting to the upper bound those pixels with density exceeding the upper bound; and (3) resetting to zero those pixels with negative density. Correction (1) can have no effect, because pixels outside the object are already zero for the preferred embodiment in which an image mask of the object is applied to the image of projection errors  64 . Correction (2) and (3) can result in small improvements to the refined reconstruction  74 ; however, including either of these corrections in the present invention prevents the use of the preferred method of computing the reprojected reconstruction  70  by linear combination. The reprojected reconstruction  70  must instead be calculated by integration, which takes more computer time. Moreover, including either of these two corrections in the present invention can sometimes lead to non-monotonic convergence of the root mean square of projection errors  62 . The test for convergence  72  must then allow for non-monotonic behavior without stopping prematurely. Thus, to save computer time and to ensure monotonic convergence, the preferred embodiment of the present invention does not make a priori corrections to the updated reconstruction  68 .  
         [0041]     From the preceding description of various embodiments of the present invention, it is clearly evident that one or more methods, apparatuses, and systems incorporating the present invention provide improved CT imaging by reducing view aliasing artifacts while maintaining optimal spatial resolution by driving the reconstructed image toward consistency with the measured projections.  
         [0042]     Although particular embodiments of the invention have been described and illustrated in detail, it is also clearly understood that the same is intended by way of illustration and example only and is not in any way solely limited to these disclosed illustrations and examples. 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 also be used with a helical scan. Accordingly, the spirit and scope of the invention are to be limited only by the terms of the appended claims and their legal equivalents.  
       PARTS LIST  
       [0000]    
       
           10  Computed tomography (CT) imaging system  
           12  Gantry representative of a “third generation” CT scanner  
           14  X-ray source  
           16  Beam of x-rays  
           18  Detector array  
           20  Detector elements  
           22  Object, for example a medical patient  
           24  Center of rotation  
           26  Control mechanism  
           28  X-ray controller  
           30  Gantry motor controller  
           32  Data acquisition system (DAS)  
           34  Image reconstructor  
           36  Computer  
           38  Mass storage device  
           40  Console  
           42  Cathode ray tube display  
           44  Table motor controller  
           46  Motorized table  
           48  Gantry opening  
           50  Shoulder bones  
           51  Measured projections  
           52  Complete set of projections  
           53  Density reconstructed by filtered backprojection  
           54  Density corrected by the a priori information  
           55  A priori information  
           56  Test for convergence  
           57  Missing projections  
           58  Reconstructed density  
           60  Measured projections  
           62  Projection errors  
           64  Image of projection errors  
           66  Reprojected image of projection errors  
           68  Updated reconstruction  
           70  Reprojected reconstruction  
           72  Test for convergence  
           74  Reconstructed image  
           80  Signal estimation system  
           81  Initial corrupted signal  
           82  Reference signal  
           83  Delay  
           84  Corrupted signal  
           85  Estimated signal  
           86  Error signal  
           87  Switch  
           88  Iterative filtering  
           90  Summation  
           100  Signal estimation system for tomographic image reconstruction  
           101  Initial reprojected reconstruction  
           103  Delay  
           107  Switch  
           110  Summation