Patent Publication Number: US-7583780-B2

Title: Systems and methods for improving a resolution of an image

Description:
BACKGROUND OF THE INVENTION 
     This invention relates generally to imaging systems and more particularly to systems and methods for improving a resolution of an image. 
     A computed tomography (CT) imaging system typically includes an x-ray source that projects a fan-shaped x-ray beam through a patient to an array of radiation detectors. The beam is collimated to lie within an xy plane, generally referred to as an “imaging plane”. Intensity of radiation from the beam received at the detector array is dependent upon attenuation of the beam by the patient. Attenuation measurements from a plurality of detector cells of the detector array are acquired separately to produce a transmission profile. 
     The x-ray source and the detector array are rotated within a gantry and around the patient to be imaged so that a projection angle at which the beam intersects the patient constantly changes. A group of x-ray attenuation measurements, which is analog projection data, from the detector array at one gantry angle or one projection angle is referred to as a “view”. A “scan” of the patient includes a set of views made at varying projection angles, during one revolution of the x-ray source and detector array. 
     To reduce a total scan time used to acquire multiple slices, a helical scan may be performed. Helical scan techniques allow for large volumes to be scanned at a quicker rate using a single photon source. To perform the helical scan, a table on which the patient rests, is moved along a z-axis about which the gantry rotates while analog projection data for a prescribed number of slices is acquired. The helical scan generates a single helix. The helix mapped out by the beam yields analog projection data from which images in each prescribed slice may be reconstructed. In addition to reducing scan time, the helical scan provides other advantages such as better use of injected contrast, improved image reconstruction at arbitrary locations, and better three-dimensional images. An example of the helical scan includes a multi-slice helical scan. In the multi-slice helical scan, the detector array extends along the z-axis. Typically, in the multi-slice helical scan, the detector array contains multiple rows, with each row corresponding to a different position along the z-axis, and a different measured slice. In an axial scan, analog projection data is processed to construct an image that corresponds to a two-dimensional slice taken through the patient. For discrete slices, iterative reconstruction of a full field of view may be performed to increase image quality. 
     For continuous scans, a scan pattern in which a position of the patient along the z-axis varies linearly with a rotation of the gantry is produced. During data acquisition, the continuous scan pattern is subject to quantization, and a discrete set of projection views is generated for a limited number of positions of the x-ray source around the patient. Conventional direct image reconstruction techniques, such as two-dimensional or three-dimensional filtered back-projection, reconstruct image voxels from projection data by interpolating elements in the projection data to accumulate contributions from each projection angle into a plurality of image voxels, and thus make an image or an image volume with a single pass over the projection data. A classical resolution of the image generated by applying the filtered back-backprojection is based upon a size of the detector array, a size of a focal spot, a sampling rate of a data acquisition system (DAS) in sampling the analog projection data, and a kernel of a filter that filters the projection data during the filtered back-projection. In a typical scenario, the classical resolution is no finer than the size of a projection of each detector cell at an isocenter of the CT imaging system. By the Nyquist theorem, it is not necessary to sample at more than twice the limiting classical resolution. However, the image volume generated by the conventional direct image reconstruction techniques does not typically have a high spatial resolution. 
     BRIEF DESCRIPTION OF THE INVENTION 
     In one aspect, a method for reconstructing an image in a tomographic imaging system is described. The method includes improving a spatial resolution of the image by iteratively reconstructing the image. 
     In another aspect, an iterative reconstruction method for trading-off a performance of a tomographic imaging system is described. The method includes adjusting a noise and a resolution in a portion of an iteratively reconstructed image. 
     In yet another aspect, an iterative reconstruction method for adjusting a resolution of a tomographic imaging system is described. The method includes adjusting an in-plane resolution in an iteratively reconstructed image, and adjusting a cross-plane resolution in the iteratively reconstructed image. 
     In still another aspect, a method for improving a spatial resolution of an image is described. The method includes iteratively reconstructing the image and improving the spatial resolution of the image. The method improves the spatial resolution of the image by at least one of developing a forward projection function having a smooth curve and developing the image having a smooth curve. The development of the forward projection includes developing the forward projection by determining a set of projection values. The development of the image includes reconstructing the image by determining an inverse of the set of projection values. 
     In another aspect, a processor for improving a spatial resolution of an image is described. The processor is configured to iteratively reconstruct the image and improve the spatial resolution of the image. The processor is configured to improve the spatial resolution of the image by at least one of developing a forward projection function having a smooth curve and developing the image having a smooth curve. The development of the forward projection includes developing the forward projection by determining a set of projection values. The development of the image includes reconstructing the image by determining an inverse of the set of projection values. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an isometric view of an embodiment of a multi-slice CT imaging system implementing a method for improving a resolution of an image. 
         FIG. 2  is a block diagram of the CT imaging system of  FIG. 1 . 
         FIG. 3  is a diagram illustrating an embodiment of a method for improving a resolution of an image. 
         FIG. 4  is a diagram illustrating the method of  FIG. 3 . 
         FIG. 5  is a flowchart of an embodiment of a method for improving a resolution of an image. 
         FIG. 6  is a continuation of the flowchart of  FIG. 5 . 
         FIG. 7  shows an embodiment of a plurality of images showing an effect of applying an embodiment of a method for improving a resolution of an image. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Iterative reconstruction includes a method that forms an image by repeatedly adjusting an existing estimate according to a quality of a match between actual projection data and expected projection data from a current estimate of the image. The quality of the match may also be affected by consideration of a plurality of characteristics of an image, such as a smoothness of the image and/or satisfaction of a pre-established model. Multiple iterations are performed to create an image that best matches actual projection data based on a pre-defined criterion. A full set of reconstructed images is referred to as a three-dimensional reconstruction, since the set is formed into a three dimensional representation of a patient with each image pixel or picture element corresponding to a single voxel or volume element in the three-dimensional reconstruction. 
     Referring to  FIGS. 1 and 2 , an embodiment of a multi-slice transmission computed tomography (CT) imaging system  10 , utilizing a method of reconstructing an image of an anatomical region of a subject  12 , such as a medical patient or a phantom, is shown. CT imaging system  10  includes a gantry  14  that has a rotating inner portion  16  including an x-ray source  18  and a detector array  20 . X-ray source  18  and detector array  20  revolve with rotation of gantry  14 . X-ray source  18  projects a beam  32  of x-rays toward detector array  20 . X-ray source  18  and detector array  20  rotate about subject  12  placed on an operably translatable table  22 . Table  22  is translated along a z-axis, parallel to a z-direction, between source  18  and detector array  20  to perform a helical scan of the anatomical region, or stays in the same position along the z axis throughout an axial scan of the anatomical region. Beam  32 , after passing through subject  12 , within a patient bore  24 , is detected at detector array  20  to generate analog projection data that is used to create a CT image of the anatomical region. 
     X-ray source  18  and detector array  20  rotate about a center axis  30  that is parallel to the z-axis. Beam  32  is received by multiple detector cells  34  in multiple detector rows of detector array  20 . Detector array  20  includes multiple rows of detector cells  34  and multiple channels of detector cells  34 . The detector channels are parallel to a channel axis, which is parallel to a plane of gantry  24 . The detector rows are parallel to a row axis, which is parallel to the z-axis. Each detector row is displaced from all other detector rows in the z-direction along the z-axis about which gantry  24  rotates. Detector cells  34  generate analog projection data, which represent electrical signals corresponding to intensities of beam  32 . As beam  32  passes through subject  12 , beam  32  is attenuated. Rotation of gantry  14  and an operation of source  18  are governed by a control mechanism  36 . Control mechanism  36  includes an x-ray controller  38  that provides power and timing signals to x-ray source  18  and a gantry motor controller  40  that controls a speed or rotation and a position of gantry  14 . A data acquisition system (DAS)  42  samples analog projection data from detector cells  34  and converts the analog projection data from an analog form to digital signals to generate sampled and digitized projection data, which is actual projection data. An image reconstructor  44  receives actual projection data from DAS  42  and performs image reconstruction, such as the method for improving a resolution of an image, to generate the CT image. A main controller  46  stores the CT image in a mass storage device  48 . Examples of mass storage device  48  include a nonvolatile memory, such as a read only memory (ROM), and a volatile memory, such as a random access memory (RAM). Other examples of mass storage device  48  include a floppy disk, a compact disc—ROM (CD-ROM), a magneto-optical disk (MOD), and a digital versatile disc (DVD). 
     Main controller  46  also receives commands and scanning parameters from an operator via an operator console  50 . A display monitor  52  allows the operator to observe the CT image and other data from main controller  46 . Display monitor  52  may be a cathode ray tube (CRT) or alternatively a liquid crystal display (LCD). The operator supplied commands and parameters are used by main controller  46  in operation of DAS  42 , x-ray controller  38 , and gantry motor controller  40 . In addition, main controller  46  operates a table motor controller  54 , which translates table  22  to position the anatomical region in gantry  14 . 
     Each of x-ray controller  38 , gantry motor controller  40 , image reconstructor  44 , main controller  46 , and table motor controller  54  is not limited to just those integrated circuits referred to in the art as a controller, but broadly refers to a computer, a processor, a microcontroller, a microcomputer, a programmable logic controller, an application specific integrated circuit, and/or any other programmable circuit. X-ray controller  38 , gantry motor controller  40 , image reconstructor  44 , main controller  46 , and table motor controller  54  may be a portion of a central control unit or may each be a stand-alone component as shown. 
     Although the specific embodiment mentioned above refers to a third generation CT imaging system  10 , the method for iteratively reconstructing an image equally applies to fourth generation CT systems that have a stationary detector and a rotating x-ray source, to fifth generation CT systems that have a stationary detector and an electron-beam deflected x-ray source, future generations of CT systems involving multiple x-ray sources and/or detectors, and an emission CT system, such as a single photon emission CT system (SPECT) or a positron emission tomographic system (PET). 
     Additionally, although the methods for iteratively reconstructing an image are described in a medical setting, it is contemplated that a plurality of technical effects of the methods 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 non-destructive testing system, a baggage scanning system for an airport, other transportation centers, government buildings, and office buildings. The technical effects also accrue to micro PET and CT systems, which are sized to study lab animals as opposed to humans. 
       FIGS. 3 and 4  are diagrams and  FIGS. 5-6  are flowcharts illustrating an embodiment of the method for iteratively reconstructing an image. A source  302  illustrates a virtual representation of x-ray source  18 , a detector plane  304  illustrates a virtual representation of a plane of detector array  20 . The plane of detector array  20  faces x-ray source  18 . Detector plane  304  includes a plurality of detector elements  306 ,  308 ,  310 ,  312 , and  314  and each detector element of detector plane  304  is a virtual representation of detector cell  34 . Image reconstructor  44  receives a position of x-ray source  18  from experimental data, such as a change in a shadow of a wire, and generates the virtual representation of x-ray source  18 . A change in a location of source  302  is received from the experimental data. As an example, a location of source  302  is determined by placing the wire between x-ray source  18  and detector array  20 . The wire is fixed with respect to x-ray source  18  and not fixed with respect to detector array  20 . A change in a location of the shadow of the wire formed on detector array  20  provides a change in a location of source  302 . 
     Image reconstructor  44  also receives a position of detector array  20  from a position encoder that detects the position with respect to x-ray source  18 . The virtual representations of x-ray source  18  and detector array  20  can be generated by image reconstructor  44  from positions of x-ray source  18  and detector array  20  with reference to an xyz coordinate system illustrated in  FIG. 1 . A position of source  302  changes to match a change in a position of x-ray source  18  and a position of detector plane  304  changes to match a change in a position of the plane of detector array  20 . A distance between source  302  and detector plane  304  is proportional to a distance between x-ray source  18  and the plane of detector array  20 . 
     An optimization problem in the method for iteratively reconstructing an image, for a particular view angle, is expressed as 
     
       
         
           
             
               
                 
                   
                     
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     where r represents an image volume  318  that is reconstructed by applying the methods for improving a resolution of an image and that represents the anatomical region of subject  12 . Image volume  318  is an example of the image volume r. Image volume  318  includes a value representing an x-ray density, such as a CT number measured in Hounsfield units, of an image voxel  320 . Although image voxel  320  is cubical in shape, in an alternative embodiment, an image voxel within image volume  318  is of other shape, such as spherical, elliptical, cylindrical, parallelepiped, trapezoidal, or alternatively, polygonal. In an alternative embodiment, the image volume  318  includes a plurality of values representing x-ray densities of image voxel  320  and of a plurality of image voxels  322 ,  324 ,  326 ,  328 ,  330 , and  332  representing the anatomical region. In an alternative embodiment, image voxel  320  is located parallel to image voxel  322  along one of the x, y, and z-axis. In another alternative embodiment, image voxel  322  may be located at a periphery of image volume  318 . In equation (1), p represents actual projection data. In equation (1), F(r) represents a forward projection function or forward projection model of r onto detector plane  304 . The forward projection F(r) transforms r in a manner imitative of CT imaging system  10 . 
     In equation (1), U(r) is a regularization function that penalizes local image voxel differences. An example of U(r) includes a convex function, such as a square of a difference between a CT number of image voxel  320  and a CT number of image voxel  328  adjacent to image voxel  320 . 
     Moreover, in equation (1), D is a distortion measure of a mismatch between actual projection data p and the forward projection function F(r) of an estimate of an image. Examples of the distortion measure D include a non-negative convex function, a negative logarithm of a probability density function, and other penalty functions. As another example, the distortion measure D is expressed in a weighted quadratic form in an equation (2) represented as 
                       r   ^     ⁡     (   r   )       =       arg     ⁢       min   r     ⁢     {           (     p   -     F   ⁡     (   r   )         )     T     ⁢     W   ⁡     (     p   -     F   ⁡     (   r   )         )         +     U   ⁡     (   r   )         }                 (   2   )               
where W is a weighting function and T is a transpose operation. An example of the weighting function includes a diagonal matrix having a plurality of diagonal elements that are inverses of the actual projection data. In an alternative embodiment, any one of equations (1) and (2) does not include U(r). In another alternative embodiment, equation (2) does not include the weighting function W and includes (p−F(r)) instead of W(p−F(r)).
 
     An example of a relationship between r and p includes a linear relationship, such as p=Ar+n, where A is a matrix of values of detector element contributions of detector plane  304 , n represents a set of at least one noise value representing a random fluctuation, such as a variance, in p about a mean of actual projection data. During each iteration of equation (1), image reconstructor  44  calculates a perturbation of r which decreases a value of {circumflex over (r)}(r) in equation (1) with each iteration. Image reconstructor  44  computes, during a current iteration, the forward projection function F(r) and the regularization function U(r) from a value of {circumflex over (r)}(r) calculated during a prior iteration, which is prior to the computation of the forward projection function F(r) and the regularization function U(r). Image reconstructor  44  substitutes, during the current iteration, {circumflex over (r)}(r) in place of r in equation (1). During the prior iteration, image reconstructor  44  generates {circumflex over (r)}(r) from image volume  318  reconstructed, by filtered back-projection, from actual projection data p. In an alternative embodiment, during the prior iteration, image reconstructor  44  may generate {circumflex over (r)}(r) from image volume  318  having a value selected by the operator via operator console  50 . A quality of {circumflex over (r)}(r) depends strongly on a degree to which the forward projection function F(r) mirrors a physical reality of CT imaging system  10 . 
     Image reconstructor  44  applies the forward projection function F(r) to image voxel  320  to generate a forward projection region including detector element  308  of detector plane  304 . As an example, the forward projection region is formed by forward projecting image voxel  320  smaller in size, such as an area, than the classical resolution. In an alternative embodiment, the forward projection region includes more than one detector element, such as, at least two of detector elements  306 ,  308 ,  310 , and  312 . In one embodiment, image reconstructor  44  adjusts  502 , such as increases or alternatively decreases, a size of image voxel  320  along at least one of a detector row axis  329  and a detector channel axis  331 . Detector row axis  329  is parallel to the z-axis and detector channel axis  331  is parallel to the plane of gantry  14 . Detector elements, such as detector elements  308  and  310 , are parallel to detector channel axis  331 . Detector elements, such as detector elements  306  and  308 , are parallel to detector row axis  329 . Image reconstructor  44  adjusts a size of image voxel  320  along detector channel axis  331  by adjusting, along at least one of the x-axis and the y-axis, the size of image voxel  320 . Image reconstructor  44  adjusts, such as decreases, along at least one of detector row axis  329  and detector channel axis  331 , a size of image voxel  320  compared to a size of the forward projection region. For example, image reconstructor  44  decreases a depth of image voxel  320  measured along detector row axis  329  to half a length of the forward projection region measured along detector row axis  329 . As another example, image reconstructor  44  decreases a width of image voxel  320  measured along detector channel axis  331  to a third of a width of the forward projection region measured along detector channel axis  331 . 
     Image reconstructor  44  adjusts, during the current iteration, a size of image voxel  320  to improve a spatial resolution, such as at least one of a cross-plane resolution and an in plane resolution, of image voxel  320  compared to a resolution of image voxel  320  during a prior iteration of equation (1) and compared to a convention reconstruction technique, such as filtered back-projection. For example, image reconstructor  44  adjusts a size of image voxel  320  along detector row axis  329  to improve a cross-plane resolution of image voxel  320 . As another example, image reconstructor  44  adjusts a size of image voxel  320  along detector channel axis  331  to improve an in-plane resolution of image voxel  320 . As yet another example, image reconstructor  44  adjusts a size of image voxel  320  along at least one of detector row axis  329  and detector channel axis  331  so that an in-plane resolution of image voxel  320  is equal to a cross-plane resolution of image voxel  320 . An in-plane resolution is a resolution in a plane along a radial direction in the plane and at an azimuth in the plane. Image reconstructor  44  adjusts a size of image voxel  320  so that all dimensions of image voxel  320  are different from a distance between image voxels  320  and  322 . 
     Image reconstructor  44 , in an alternative embodiment, determines or maps a number of detector elements that contribute to a resolution of image voxel  320  by forward projecting, at a projection angle from source  302 , image voxel  320  onto detector plane  304 . As an example, image reconstructor  44  forward projects a center  332  of image voxel  320  onto detector plane  304  to generate a forward projection point  334  and selects a pre-determined number, such as two or three, of detector elements, within detector plane  304 , along at least one of detector row axis  329  and detector channel axis  331 . In the example, the pre-determined number is received from the operator via operator console  50 . In the example, the detector elements that are selected are adjacent to detector element  308  that includes forward projection point  334 . In the example, alternatively, the detector elements that are selected are not adjacent to detector element  308  including forward projection point  334  but are apart from detector element  308  by a number of detector elements of detector plane  304 . As another example, image reconstructor  44  forward projects center  332  of image voxel  320  onto detector plane  304  to generate forward projection point  334  and selects a number of detector elements, within the forward projection region, that are located along at least one of detector channel axis  331  and detector row axis  329  and that have a size proportional to a size of image voxel  320 . In the example, the size, of detector elements, that is selected by image reconstructor  44  and that is proportional to the size of image voxel  320  includes a depth, along detector row axis  329 , of the detector elements. In the example, the depth is twice or alternatively thrice a depth along detector row axis  329  of image voxel  320 . A change in a number of detector elements within the forward projection region changes at least one of a size of the forward projection region and a shape of the forward projection region. As yet another example, image reconstructor  44  forward projects image voxel  320  onto detector plane  304  to generate a shadow of image voxel  320  onto detector plane  304  and selects, along at least one of detector row axis  329  and detector channel axis  331 , a number of detector elements falling within the shadow of image voxel  320 . The shadow of image voxel  320  has the same size, along detector row axis  329  and detector channel axis  331 , as that of a bottom surface  336  of image voxel  320 . Bottom surface  336  faces detector plane  304 . Alternatively, a size of the shadow of image voxel  320  along detector row axis  329  is at least equal to a size of bottom surface  336  along detector row axis  329 . In another alternative embodiment, a size of the shadow of image voxel  320  is at least equal to a size of bottom surface  336  along detector channel axis  331 . In the example, image reconstructor  44  selects detector elements that are within detector plane  304  and that lie within the shadow of image voxel  320 . As still another example, image reconstructor  44  forward projects image voxel  320  onto detector plane  304  by extending a plurality of rays from source  302  via a plurality of edges  339 ,  341 ,  343 , and  345  of image voxel  320  onto detector plane  304  to generate a forward projection surface on detector plane  304 . In the example, image reconstructor selects, along at least one of detector row axis  329  and detector channel axis  331 , a number of detector elements lying within the forward projection surface on detector plane  304 . As yet another example, image reconstructor  44  forward projects image voxel  320  onto detector plane  304  by extending a plurality of rays from source  302  via a plurality of points on edges  339 ,  341 ,  343 , and  345  of image voxel  320  onto detector plane  304  to generate a forward projection zone on detector plane  304 . In the example, image reconstructor  44  selects, along at least one of detector row axis  329  and detector channel axis  331 , a number of detector elements lying within the forward projection zone on detector plane  304 . Forward projection point  334  is the center of the forward projection region. In an alternative embodiment, forward projection point  334  is not the center of the forward projection region. 
     Image reconstructor  44  selects at least one of a number of rows of detector elements along detector row axis  329  and a number of channels of detector elements along detector channel axis  331  by selecting detector elements of detector plane  304 . Image reconstructor  44  adjusts a size of detector element  308  to be greater than a size of detector cell  34 . For example, image reconstructor  44  increases a volume of detector element  308  to be greater than a volume of detector cell  34 . Alternatively, image reconstructor  44  adjusts a size of detector element  308  to be less than a size of detector cell  34 . For example, image reconstructor  44  increases a volume of detector element  308  to be less than a volume of detector cell  34 . Image reconstructor  44  applies a number of detector elements that are selected and that contribute to a resolution of image voxel  320  to reconstruct {circumflex over (r)}(r) in equation (1) and to improve a spatial resolution of {circumflex over (r)}(r) compared to the classical resolution generated by the filtered backprojection. 
     Image reconstructor  44 , in another alternative embodiment, determines  504  a plurality of values of detector elements that are within detector plane  304  and that are used to reconstruct image volume  318 . For example, image reconstructor  44  randomly assigns a value, such as a positive value or alternatively a negative value, to each detector element within the forward projection region, the forward projection surface, and the forward projection zone of detector plane  304 . As another example, image reconstructor  44  assigns a value to each detector element within the forward projection region and to each detector element lying within a forward projection area based on a distance  333  between center  332  of image voxel  320  and source  302  and on a distance  335  between source  302  and a center  337  of image voxel  322 . When distance  333  is greater than distance  335 , image reconstructor  44  assigns values to a number of detector elements within the forward projection area of image voxel  322  and the number of detector elements is higher than a number of detector elements within the forward projection region of image voxel  320 . An assignment of values to the higher number of detector elements within the forward projection area of image voxel  322  results in a resolution of image voxel  322  that is greater than a resolution of image voxel  320 . An increase in a resolution of image voxel  322  results in an increase in noise within image voxel  322  and a decrease in the resolution of image voxel  320  results in a decrease in noise within image voxel  320 . 
     Alternatively, when distance  335  is greater than distance  333 , image reconstructor  44  assigns values to a number of detector elements within the forward projection region of image voxel  320  and the number of detector elements is higher than a number of detector elements within the forward projection area of image voxel  322 . An assignment of values to the higher number of detector elements within the forward projection region of image voxel  320  results in a resolution of image voxel  320  that is greater than a resolution of image voxel  322 . An increase in a resolution of image voxel  320  results in an increase in noise within image voxel  320  and a decrease in the resolution of image voxel  322  results in a decrease in noise within image voxel  322 . 
     Image reconstructor  44  forms the forward projection area on detector plane  304  by forward projecting a ray from source  302  via image voxel  322  onto detector plane  304 . Image reconstructor  44  iteratively reconstructs image voxel  322  from the forward projection area by applying the systems and methods for improving a resolution of an image. For example, image reconstructor  44  iteratively reconstructs image voxel  322  from the forward projection area upon changing a number of detector elements within the forward projection area to improve a resolution of image voxel  322 . The forward projection area is separate from the forward projection region and does not include the forward projection region. Distance  333  between source  302  and center  332  determines a location of image voxel  320  within a field-of-view of x-ray source  18 . The field-of-view encompasses image volume  318 . Moreover, distance  335  between source  302  and center  337  of image voxel  322  determines a location of image voxel  322  within the field-of-view. 
     Image reconstructor  44  continues to determine a plurality of values of detector elements that are within detector plane  304  and that are used to reconstruct image volume  318 . As an example, image reconstructor  44  determines values of detector elements within the forward projection region by assigning values to the detector elements based on a distance, along at least one of detector row axis  329  and detector channel axis  331 , of the detector elements from forward projection point  334 . For instance, upon determining, by image reconstructor  44 , that a distance, along detector row axis  329 , between detector element  306  and forward projection point  334  is greater than a distance, along detector row axis  329 , between detector element  308  and forward projection point  334 , image reconstructor  44  assigns a lower value to detector element than  306  to detector element  308 . As another instance, upon determining, by image reconstructor  44 , that a distance, along detector channel axis  331 , between detector element  310  and forward projection point  334  is greater than a distance, along detector channel axis  331 , between detector element  308  and forward projection point  334 , image reconstructor  44  assigns a lower value to detector element  310  than to detector element  308 . 
     Image reconstructor  44  further continues to determine a plurality of values of detector elements that are within detector plane  304  and that are used to reconstruct image volume  318 . As an example, image reconstructor  44  assigns a value to each detector element within the forward projection region and to each detector element lying within the forward projection area based on a distance  338  between center  332  of image voxel  320  and forward projection point  334  of the forward projection region and on a distance  340  between center  337  of image voxel  322  and a forward projection point  342  of the forward projection area. When distance  338  is greater than distance  340 , image reconstructor  44  assigns higher values to detector elements within the forward projection region than to detector elements within the forward projection area. Alternatively, when distance  340  is greater than distance  338 , image reconstructor  44  assigns higher values to detector elements within the forward projection area than to detector elements within forward projection region. Forward projection point  342  is the center of the forward projection area. In an alternative embodiment, forward projection point  342  is not the center of the forward projection area. Distance  338  between center  332  and the forward projection point  334  determines a location of center  332 , and distance  340  between center  337  and the forward projection point  342  of the forward projection area determines a location of center  337 . As still another example, image reconstructor  44  assigns a plurality of values to detector elements within the forward projection region based on a pre-defined curve. Image reconstructor  44  receives the pre-defined curve from the operator via operator console  50 . The pre-defined curve can be a function of at least one of a number of detector elements within the forward projection region, a size, along at least one of detector channel axis  331  and detector row axis  329 , of the forward projection region, and a size, along at least one of x, y, and z-dimensions, of image voxel  320 . The x-dimension is parallel to an x-axis, the y-dimension is parallel to a y-axis, and the z-dimension is parallel to the z-axis. The y-axis is perpendicular to the z-axis, and the x-axis is perpendicular to both the x-axis and the z-axis. Image reconstructor  44  assigns values of the pre-defined curve to detector elements that are within detector plane  304  and that coincide with the pre-defined curve. 
     Image reconstructor  44 , in an alternative embodiment, assigns values to detector elements within detector plane  304  to satisfy at least one two conditions. A first one of the conditions is that the forward projection function F(r) is a smooth curve that excludes high frequency components, such as impulses. Another example of the high frequency components includes a plurality of rapid local variations that do not correspond to a plurality of slow changes normally expected in the forward projection function F(r). A smooth curve is an example of the pre-defined curve. An example of the forward projection function F(r) is Ar+n. Upon setting, by image reconstructor  44 , of r=1 and n=0, image reconstructor  44  determines values of A to generate the forward projection function F(r) as a smooth curve. A second one of the conditions is that image volume  318  is a smooth curve. Upon setting, by image reconstructor  44 , n=0, image reconstructor  44  determines values of A −1  to generate the image volume  318  as a smooth curve that excludes the high frequency components. 
     Image reconstructor  44 , in another alternative embodiment, determines  506  a number of detector elements within detector plane  304  to achieve a uniform spatial resolution, along at least one of detector channel axis  331  and detector row axis  329 , across the field-of view. For example, image reconstructor  44  determines that a number of detector elements within the forward projection region is equal to the number of detector elements within the forward projection area. As another example, image reconstructor  44  determines that a number of detector elements, along detector row axis  329 , within the forward projection region, is equal to a number of detector elements, along detector row axis  329 , within the forward projection area. As yet another example, image reconstructor  44  determines that a number of detector elements, along detector channel axis  331 , within the forward projection region is equal to a number of detector elements, along detector row axis  329 , within the forward projection area. Image reconstructor  44  receives a request for uniform spatial resolution from the operator via operator console  50 . 
     Image reconstructor  44 , in yet another alternative embodiment, changes a number of detector elements within the forward projection region based on a trigger frequency of a scan conducted by CT imaging system  10 . The trigger frequency determines a discrete number of projection data views collected around subject  12  for a full rotation of the x-ray source  18  around subject  12 . As an example, as the trigger frequency to acquire actual projection data used to reconstruct image voxel  320  increases, a number of detector elements selected within the forward projection region decreases. As another example, as the trigger frequency to acquire actual projection data decreases, a number of detector elements selected within the forward projection region increases. 
     The regularization function U(r) imposes a constraint on image voxel  320  based on values of image voxels near image voxel  320 . For example, the regularization function U(r) penalizes a value of image voxel  320  based on a value of at least one of adjacent image voxels  324 ,  326 ,  328 ,  330 , and  332 . As another example, U(r) penalizes a value of image voxel  320  based on values of image voxels that are not adjacent to image voxel  320  and that lie a number, such as one or two, of image voxels apart from image voxel  320 . An example of a penalty on a value of image value based on values of image voxels near image voxel  320  includes that a value of image voxel  320  is not greater than an average of values of the image voxels near image voxel  320 . Another example of a penalty on a value of image voxel  320  based on values of image voxels near image voxel  320  includes that a value of image voxel  320  is not greater than a median of values of the image voxels near image voxel  320 . 
     Image reconstructor  44 , in still another alternative embodiment, adjusts  508  a number of image voxels, along at least one of detector row axis  329  and detector channel axis  331 , that are near image voxel  320  and that penalizes a value of image voxel  320  to improve a spatial resolution of image voxel  320 . As an example, image reconstructor  44  adjusts a number of image voxels that are along detector row axis  329  to penalize a value of image voxel  320 . As another example, image reconstructor  44  adjusts a number of image voxels that are along detector channel axis  331  to penalize a value of image voxel  320 . As yet another example, image reconstructor  44  changes U(r) based on at least one of a function of a position of image voxel  320  within the field-of-view and a size, measured along at least one of the x-axis, y-axis, and z-axis, of image voxel  320 . As yet another example, image reconstructor  44  changes U(r) based on a function of a magnitude of a difference between image voxel  320  and at least one of the image voxels near image voxel  320 . In an example, U(r)= 
     
       
         
           
             
               
                 
                   
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     where α is a scaling constant, such as a positive real number, p is an exponent parameter, such as a positive real number, and b ij  is a directional weighting coefficient, such as a positive real number, r i  represents a value of image voxel  320  at a location i within image volume  318  and r j  represents a value of an image voxel j within image volume  318  near image voxel  320 , and C is a neighborhood of the image voxels near image voxel  320  selected to penalize image voxel  320 . In the example, image reconstructor  44  changes α and b ij  based on a location of image voxel  320  within the field-of-view. 
     Image reconstructor  44 , in one embodiment, adjusts a number of image voxels that are near image voxel  320  and that penalize a value of image voxel  320 , and adjusts a number of image voxels that are near image voxel  322  and that penalize a value of image voxel  322 , to achieve the uniform spatial resolution, along at least one of a radial direction across the field-of-view, an azimuthal direction across the field-of-view, and a z direction across the field-of-view. For example, image reconstructor  44  determines that a number of image voxels that are near image voxel  320  and that penalize a value of image voxel  320  is equal to a number of image voxels that are near image voxel  322  and that penalize a value of image voxel  322 . In an alternative embodiment, image reconstructor  44  adjusts a number of image voxels that are near image voxels  320  and that penalize a value of image voxel  320  and adjusts a number of image voxels that are near image voxel  322  and that penalize a value of image voxel  322  to achieve an isotropic spatial resolution, along at least two of the radial direction, azimuthal direction, and z direction, across the field-of-view. Image reconstructor  44  receives a plurality of values of desired spatial resolutions along at least two of the radial direction across the field-of-view, azimuthal direction across the field-of-view, and z direction across the field-of-view from the operator via operator console  50 . In another alternative embodiment, image reconstructor  44  adjusts a number of image voxels that are near image voxel  320  and that penalize a value of image voxel  320  and adjusts a number of image voxels that are near image voxel  322  and that penalize a value of image voxel  322  to achieve a desired spatial resolution, along at least one of the radial direction, azimuthal direction, and z direction, across the field-of-view. Image reconstructor  44  receives the desired spatial resolution from the operator via operator console  50 . 
     Image reconstructor  44  can also change a number of detector elements within the forward projection region and a number of image voxels that are near image voxel  320  and that penalize a value of image voxel  320  to achieve a spatial resolution, such as the uniform spatial resolution, the desired resolution, and the isotropic resolution, along at least one of the radial direction across the field-of-view, azimuthal direction across the field-of-view, and z direction across the field-of-view. 
     In one embodiment, during a half scan or alternatively a full scan of the anatomical region, image reconstructor  44  assigns  510  a high amount of confidence or weight to a portion of actual projection data and the forward projection function F(r), where the portion and the forward projection function F(r) are generated when source  302  is at a first position and are used to iteratively reconstruct image voxel  320 . The high amount of confidence is higher than an amount of confidence that image reconstructor  44  assigns to a portion of actual projection data and the forward projection function F(r), where both the portion and the forward projection function F(r) are generated when source  302  is at a second position and are used to iteratively reconstruct image voxel  320 . For example, upon determining that image voxel  320  is iteratively reconstructed from a first set of actual projection data when x-ray source  18  is at a projection angle of zero degrees and is also iteratively reconstructed from a second set of actual projection data when source  302  is at a projection angle of ninety degrees and upon determining that source  302  is closer to image voxel  320  at the projection angle of zero degrees than at the projection angle of ninety degrees, image reconstructor  44  assigns a higher amount of confidence to the first set of actual projection data than to the second portion of actual projection data. The first position is closer to image voxel  320  than the second position. A position of image voxel  320  with respect to source  302  changes with a projection angle of source  302 . Image reconstructor  44  changes the distortion measure D that is applied to actual projection data p and to the forward projection function F(r) to change a confidence. For example, image reconstructor  44  increases the distortion measure D from a second power of (p−F(r)) to a third power of (p−F(r)) to increase a confidence. 
     Image reconstructor  44 , in an alternative embodiment, adjusts, such as increases, a number of detector elements within the forward projection region to improve a resolution of image voxel  320  that is deteriorated by a change in a size of a focal spot during acquisition of actual projection data used to iteratively reconstruct image voxel  320 . The size of the focal spot includes an area of the x-ray source  18  and beam  32  originates at the area. Further, in another alternative embodiment, image reconstructor  44  shifts a location, along at least one of detector row axis  329  and detector channel axis  331 , of forward projection point  334  to improve a resolution of image voxel  320  that is deteriorated by a change in a location of the focal spot during acquisition of actual projection data used to iteratively reconstruct image voxel  320 . 
     Image reconstructor  44 , in still another alternative embodiment, shifts a location of forward projection point  334 , along the z-axis, to improve a resolution of image voxel  320  that is deteriorated by an error in a measurement of a location, along the z-axis, of table  22  during acquisition of actual projection data used to iteratively reconstruct image voxel  320 . Image reconstructor  44 , in one embodiment, shifts a location of forward projection point  334  and/or adjusts, such as increases, a number of detector elements, along the z-axis, within the forward projection region to improve a resolution of image voxel  320  deteriorated by a sag of table  22 . 
     Image reconstructor  44 , in an alternative embodiment, shifts a location of forward projection point  334 , along detector channel axis  331 , of the forward projection region with a change in time and/or a change in a projection angle of source  302  to improve a resolution of image voxel  320  deteriorated by vibrations of gantry  14  that occur during acquisition of a portion of actual projection data used to reconstruct image voxel  320 . Projection angle of source  302  changes with a change in a location of x-ray source  18 . In another alternative embodiment, image reconstructor  44  adjusts at least one of a number of detector elements within the forward projection region and a location of forward projection point  334  of the forward projection region to improve a resolution of image voxel  320  deteriorated by at least one of a change in a size of the focal spot, a change in a location of the focal spot, a change in a location of table  22  along the z-axis, a sag of table  22 , and a plurality of vibrations of gantry  14  that occurs during acquisition of actual projection used to reconstruct image voxel  320 . 
       FIG. 7  shows an embodiment of a plurality of images  602 ,  604 ,  606 , and  608  created by applying a conventional method and the method for improving a resolution of an image. Images  602  and  608  are reconstructed from the same scan taken at low resolution detector settings. Images  604  and  606  are reconstructed from two separate scans taken at high resolution detector settings. Images  602 ,  604 , and  606  are reconstructed by applying Feldkamp-based reconstruction and image  608  is reconstructed by applying the method for improving a resolution of an image. It is evident that image  608  has better resolution than image  602 , and similar resolution compared to images  604  and  606 . 
     Although the systems and methods for improving a resolution of an image are described by using multi-slice CT imaging system  10 , the systems and methods are capable of being adapted for various imaging systems including, but not limited to magnetic resonance imaging (MRI) systems, optical scanning systems, CT systems, radiotherapy systems, X-ray imaging systems, ultrasound systems, nuclear imaging systems, magnetic resonance spectroscopy systems, and positron emission tomography (PET) imaging systems. It is also noted that image reconstructor  44  determines a position, with respect to source  302  and detector plane  304 , of any of image voxels within image volume  318 . It is also noted that in one embodiment, the operator controls image reconstructor  44  via operator console  50  to improve a resolution of an image and decides whether the resolution has been improved. 
     Technical effects of the systems and methods for iteratively reconstructing an image include improving a resolution of an image. Other technical effects include reducing a variance in a spatial resolution of image voxel  318  by achieving the uniform spatial resolution. An increase in a resolution of an image iteratively reconstructed by applying the system and methods for iteratively reconstructing an image results in a decrease in noise in the image. The variance in a spatial resolution of image volume  318  can be a function of a distance between an isocenter of gantry  14  and any of image voxels  320  and  322 . For example, spatial resolution of image voxel  320  decreases with an increase of distance of any of image voxels  320  and  322  from the isocenter. Distance between the isocenter and any of image voxels  320  and  322  changes due to at least one of a shallow angle of beam  32 , a finite integration time of DAS  42 , heel effects, and other factors. During the finite integration time, DAS  42  integrates a portion of actual projection data acquired at a projection angle. However, in reality, a portion that is within actual projection data and that is integrated is not acquired at an exact projection angle and therefore, an azimuthal blur is created within image volume  318 . Image reconstructor  44  reduces the azimuthal blur by selecting a number of detector elements within the forward projection region based on the DAS trigger frequency. 
     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.