Patent Publication Number: US-2019180481-A1

Title: Tomographic reconstruction with weights

Description:
BACKGROUND 
     Non-invasive imaging technologies allow images of the internal structures or features of a patient to be obtained without performing an invasive procedure on the patient. In particular, such non-invasive imaging technologies rely on various physical principles (such as the differential transmission of X-rays through the target volume, the reflection of acoustic waves within the volume, the paramagnetic properties of different tissues and materials within the volume) to acquire data and to construct images or otherwise represent the observed internal features of the patient. 
     In some imaging techniques such as computed tomography (CT), positron emission tomography (PET), single photon emission tomography (SPECT), magnetic resonance imaging (MM), etc., it may be desirable to employ an iterative reconstruction approach, as opposed to direct or analytic reconstruction approaches, to reconstructing the images. Such iterative approaches are computationally intensive and time-consuming but may allow data to be acquired at a lower dose, relying on the iterative processing to provide images of a useful quality. 
     However, such iterative approaches have limitations in addition to their computational intensity. For example, conventional CT iterative tomographic reconstruction (IR) uses statistical weights to modulate the importance of each sinogram ray for benefits in dose efficiency and image quality. However, because these weights are assigned in the sinogram-domain ray-by-ray, they apply globally to all image locations along the full length of the ray. Similarly, in IR methods for other imaging technologies such as PET, SPECT, MRI, and so forth, the weight assigned to each measured value applies globally to all image locations contributing to that measurement. 
     While this provides the radiation dose and image quality benefits noted, it prevents differential treatment of sub-regions within the image, such as adaptive weighting of the measurements for individual pixel locations or sub-regions of the image. This may run counter to the needs of a given examination, where in many instances individual sub-regions in the image may benefit from different treatment of the same measurement to achieve the best image quality. 
     BRIEF DESCRIPTION 
     In one aspect of the present approach, a tomographic iterative reconstruction method is provided. In accordance with this embodiment, a set of projection data of a scanned region is accessed or acquired. A reconstruction operation is iteratively performed to reconstruct an image of the region. As part of each reconstruction operation, a weight factor is applied to each projection measurement. The respective weight factors are determined based on both a respective projection measurement position and a reconstructed pixel location. The image is displayed or stored. 
     In a further aspect of the present approach, an image reconstruction system is provided. In accordance with this aspect, the image reconstruction system includes a memory encoding processor-executable routines for iteratively reconstructing an image and a processing component configured to access the memory and execute the processor-executable routines. The routines, when executed by the processing component, cause acts to be performed comprising: acquiring or accessing a set of projection data of a scanned region; iteratively performing a reconstruction operation to reconstruct an image of the region; as part of each reconstruction operation, applying a weight factor to each projection measurement, wherein the respective weight factors are determined based on both a respective projection measurement position and a reconstructed pixel location; and displaying or storing the image. 
     In an additional aspect of the present approach, one or more non-transitory computer-readable media encoding processor-executable routines are provided. In accordance with this aspect, the routines, when executed by a processor, cause acts to be performed comprising: acquiring or accessing a set of projection data of a scanned region; iteratively performing a reconstruction operation to reconstruct an image of the region; as part of each reconstruction operation, applying a weight factor to each projection measurement, wherein the respective weight factors are determined based on both a respective projection measurement position and a reconstructed pixel location; and displaying or storing the image. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: 
         FIG. 1  is a block diagram depicting components of a computed tomography (CT) imaging system, in accordance with aspect of the present disclosure; 
         FIG. 2  depicts algorithmic steps of a conventional iterative reconstruction, in accordance with aspect of the present disclosure; 
         FIG. 3  graphically depicts an example of an image region split into differing sub-region each reconstructed using different amounts of sinogram data, in accordance with aspect of the present disclosure; 
         FIG. 4  depicts algorithmic steps of an iterative reconstruction, in accordance with aspect of the present disclosure; 
         FIG. 5  depicts algorithmic steps of a further iterative reconstruction, in accordance with aspect of the present disclosure; 
         FIG. 6  depicts algorithmic steps of an additional iterative reconstruction, in accordance with aspect of the present disclosure; 
         FIG. 7  depicts an example of basis functions of sinogram weights, in accordance with aspect of the present disclosure; 
         FIG. 8  depicts an image generated using conventional iterative reconstruction; and 
         FIG. 9  depicts an image generated using an iterative reconstruction operation in accordance with aspect of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     One or more specific embodiments will be described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. 
     When introducing elements of various embodiments of the present disclosure, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Furthermore, any numerical examples in the following discussion are intended to be non-limiting, and thus additional numerical values, ranges, and percentages are within the scope of the disclosed embodiments. The term “pixel” is intended to include 2D pixels, 3D voxels, or in 4D or higher dimensional applications, the corresponding element of the reconstructed data. 
     One reconstruction technique used in CT imaging is iterative reconstruction. Use of iterative reconstruction techniques (in contrast to analytical methods) may be desirable for a variety of reasons, including image quality and/or reduced patient dose. As discussed herein, conventional iterative tomographic reconstruction (IR) uses statistical weights to modulate the importance of each sinogram ray for benefits in dose efficiency and image quality. However, because these weights are assigned in the sinogram-domain ray-by-ray, they apply globally to all image locations along the full length of the ray. That is, iterative reconstruction, is inherently “global” in that the whole object is modeled for reconstruction (regardless of the size of the clinical region of interest) to properly account for all absorption that contributes to the detector measurements in the forward model. Thus, individual pixel locations or sub-regions of the image cannot be differently weighted, such as based on spatial location, in conventional iterative reconstruction techniques. 
     In contrast, the present iterative reconstruction approach allows the use of varying sinogram weights in pixels or larger sub-regions in the reconstructed image. By way of example, the relative significance of each projection measurement may be determined based on both the measurement position and the location of the reconstructed pixel. Computationally, the significance of each projection based on these two factors is represented by a weight factor employed in the algorithmic computation. This approach can be applied to many CT imaging scenarios where flexible view-weighting in iterative reconstruction is needed. For example, this approach may be useful in wide-cone cardiac iterative reconstruction where conventional iterative reconstruction cannot achieve good temporal resolution while suppressing cone-beam artifacts at the same time. Further, the weights may vary over time in contexts where a time sequence of images are produced. 
     Thus, in such approaches, images may be reconstructed that have distinct regions which are each reconstructed using different weights, thereby improve the image quality of those regions relative to scenarios in which the same weighting is used across all regions. Likewise, to the extent that a region or regions may vary over time in a time-lapse or video context, different weighting may be applied in different regions of the image over time to improve image quality relative to conventional approaches where the same weighting is used throughout the image(s). Images and/or videos so produced can then be stored and/or displayed on a monitor, such as at the scan station or on a network-connected device, such as a workstation in a radiologist office. As regions of interest in the images may be presented with superior image quality relative to conventional images, such images and/or videos may improve the ability of a diagnostician to diagnose a condition and/or prescribe a treatment. 
     The approaches described herein may be suitable for use with a range of image reconstruction systems. However, to facilitate explanation, the present disclosure will primarily discuss the present reconstruction approaches in one particular context, that of a CT system. It should be understood that the following discussion may also be applicable to other image reconstruction modalities and systems as well as to non-medical contexts or any context where an image is reconstructed from projections or other forms of measurements. 
     With this in mind, an example of a computer tomography (CT) imaging system  10  designed to acquire X-ray attenuation data at a variety of views around a patient (or other subject or object of interest) and suitable for spatially-adaptive sinogram weighting in iterative reconstruction is provided in  FIG. 1 . In the embodiment illustrated in  FIG. 1 , imaging system  10  includes a source of X-ray radiation  12  positioned adjacent to a collimator  14 . The X-ray source  12  may be an X-ray tube, a distributed X-ray source (such as a solid-state or thermionic X-ray source) or any other source of X-ray radiation suitable for the acquisition of medical or other images. 
     The collimator  14  permits X-rays  16  to pass into a region in which a patient  18 , is positioned. In the depicted example, the X-rays  16  are collimated to be a cone-shaped beam, i.e., a cone-beam that passes through the imaged volume. A portion of the X-ray radiation  20  passes through or around the patient  18  (or other subject of interest) and impacts a detector array, represented generally at reference numeral  22 . Detector elements of the array produce electrical signals that represent the intensity of the incident X-rays  20 . These signals are acquired and processed to reconstruct images of the features within the patient  18 . 
     Source  12  is controlled by a system controller  24 , which furnishes both power, and control signals for CT examination sequences, including acquisition of 2D localizer or scout images used to identify anatomy of interest within the patient for subsequent scan protocols. In the depicted embodiment, the system controller  24  controls the source  12  via an X-ray controller  26  which may be a component of the system controller  24 . In such an embodiment, the X-ray controller  26  may be configured to provide power and timing signals to the X-ray source  12 . 
     Moreover, the detector  22  is coupled to the system controller  24 , which controls acquisition of the signals generated in the detector  22 . In the depicted embodiment, the system controller  24  acquires the signals generated by the detector using a data acquisition system  28 . The data acquisition system  28  receives data collected by readout electronics of the detector  22 . The data acquisition system  28  may receive sampled analog signals from the detector  22  and convert the data to digital signals for subsequent processing by a processor  30  discussed below. Alternatively, in other embodiments the digital-to-analog conversion may be performed by circuitry provided on the detector  22  itself. The system controller  24  may also execute various signal processing and filtration functions with regard to the acquired image signals, such as for initial adjustment of dynamic ranges, interleaving of digital image data, and so forth. 
     In the embodiment illustrated in  FIG. 1 , system controller  24  is coupled to a rotational subsystem  32  and a linear positioning subsystem  34 . The rotational subsystem  32  enables the X-ray source  12 , collimator  14  and the detector  22  to be rotated one or multiple turns around the patient  18 , such as rotated primarily in an x,y-plane about the patient. It should be noted that the rotational subsystem  32  might include a gantry upon which the respective X-ray emission and detection components are disposed. Thus, in such an embodiment, the system controller  24  may be utilized to operate the gantry. 
     The linear positioning subsystem  34  may enable the patient  18 , or more specifically a table supporting the patient, to be displaced within the bore of the CT system  10 , such as in the z-direction relative to rotation of the gantry. Thus, the table may be linearly moved (in a continuous or step-wise fashion) within the gantry to generate images of particular areas of the patient  18 . In the depicted embodiment, the system controller  24  controls the movement of the rotational subsystem  32  and/or the linear positioning subsystem  34  via a motor controller  36 . 
     In general, system controller  24  commands operation of the imaging system  10  (such as via the operation of the source  12 , detector  22 , and positioning systems described above) to execute examination protocols and to process acquired data. For example, the system controller  24 , via the systems and controllers noted above, may rotate a gantry supporting the source  12  and detector  22  about a subject of interest so that X-ray attenuation data may be obtained at one or more views relative to the subject. In the present context, system controller  24  may also include signal processing circuitry, associated memory circuitry for storing programs and routines executed by the computer (such as routines for executing image reconstruction techniques employing differential weighting as described herein), as well as configuration parameters, image data, reconstructed images, and so forth. 
     In the depicted embodiment, the image signals acquired and processed by the system controller  24  are provided to a processing component  30  for reconstruction of images in accordance with the presently disclosed algorithms. The processing component  30  may be one or more general or application-specific microprocessors. The data collected by the data acquisition system  28  may be transmitted to the processing component  30  directly or after storage in a memory  38 . Any type of memory suitable for storing data might be utilized by such an exemplary system  10 . For example, the memory  38  may include one or more optical, magnetic, and/or solid-state memory storage structures. Moreover, the memory  38  may be located at the acquisition system site and/or may include remote storage devices for storing data, processing parameters, and/or routines for image reconstruction as described herein. 
     The processing component  30  may be configured to receive commands and scanning parameters from an operator via an operator workstation  40 , typically equipped with a keyboard and/or other input devices. An operator may control the system  10  via the operator workstation  40 . Thus, the operator may observe the reconstructed images and/or otherwise operate the system  10  using the operator workstation  40 . For example, a display  42  coupled to the operator workstation  40  may be utilized to observe the reconstructed images and to control imaging. Additionally, the images may also be printed by a printer  44  which may be coupled to the operator workstation  40 . 
     Further, the processing component  30  and operator workstation  40  may be coupled to other output devices, which may include standard or special purpose computer monitors and associated processing circuitry. One or more operator workstations  40  may be further linked in the system for outputting system parameters, requesting examinations, viewing images, and so forth. In general, displays, printers, workstations, and similar devices supplied within the system may be local to the data acquisition components, or may be remote from these components, such as elsewhere within an institution or hospital, or in an entirely different location, linked to the image acquisition system via one or more configurable networks, such as the Internet, virtual private networks, and so forth. 
     It should be further noted that the operator workstation  40  may also be coupled to a picture archiving and communications system (PACS)  46 . PACS  46  may in turn be coupled to a remote client  48 , radiology department information system (RIS), hospital information system (HIS) or to an internal or external network, so that others at different locations may gain access to the raw or processed image data. 
     While the preceding discussion has treated the various exemplary components of the imaging system  10  separately, these various components may be provided within a common platform or in interconnected platforms. For example, the processing component  30 , memory  38 , and operator workstation  40  may be provided collectively as a general or special purpose computer or workstation configured to operate in accordance with the aspects of the present disclosure. In such embodiments, the general or special purpose computer may be provided as a separate component with respect to the data acquisition components of the system  10  or may be provided in a common platform with such components. Likewise, the system controller  24  may be provided as part of such a computer or workstation or as part of a separate system dedicated to image acquisition. 
     As discussed herein, the system  10  of  FIG. 1  may be used to conduct a computed tomography (CT) scan by measuring a series of projection images from many different angles around a patient  18  or object. The projection images acquired at different view angles can be combined into a sinogram, which collects the multiple views into a single data set. A reconstruction algorithm processes the sinogram to produce a space-domain image representing the patient  18  or object. 
     There are multiple methods for image reconstruction. For example, iterative reconstruction techniques are used to produce images of high quality while reducing the required radiation dose. An example of a conventional iterative reconstruction approach is depicted in  FIG. 2  as a block diagram showing a simplified representation of an iterative reconstruction algorithm. The objective of such an iterative reconstruction approach is to produce the reconstructed images  100  that would result in estimated sinograms  102  that best match the set of measured sinograms  104  collected from a CT scan. On each iteration of the algorithm, a forward model  108  takes the geometry and other characteristics of the CT system, and computes the estimated sinogram  102  that would be produced by the current reconstructed image estimate  100  of the unknown object or patient. The forward model  108  is essentially simulating the attenuation of X-rays as they pass from the X-ray source, through the patient and into the detector of the CT system based on the current reconstructed image estimate. The estimated sinogram  102  is compared against the measured sinogram  104  from the CT scan. In the depicted example, the comparison of the estimated sinogram  102  and the measured sinogram  104  takes the form of determining a difference, i.e., error sinogram  116 , such as by subtracting the estimated sinogram  102  from the measured sinogram  104 . The significance of the error sinogram at different positions can be further weighted by the weighting factors  126 . Based on this weighted comparison, a backprojection  112  is calculated. The backprojection can further incorporate image statistics  120  so that the generated updated reconstructed estimate  100  conforms to or approaches the desired regularity condition of the scanned subject. The image statistics  120  may be based on a regularization function or prior distribution function image statistics and may reflect desired properties of the reconstructed image in different locations within the image and under various scan conditions. 
     With respect to the backprojection step  112 , in conventional iterative reconstruction approaches the statistical weights  126  are determined on a ray-by-ray basis, to reflect noise levels of each sinogram measurement. The statistical weights  126  are inherently “global” for all pixel locations along the full length of the ray, which does not allow flexible adjustments of the weights as a function of pixel locations in the image domain. 
     This can be understood from the aspect that iterative reconstruction is typically based on a single cost function of all image pixel variables. Iterations are performed of the algorithm until the cost function reaches a specified threshold, such as being minimized. As a simplified example, consider iterative reconstruction based on the weighted least-squares cost function: 
     
       
         
           
             
               
                 
                   
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     The statistical weights, denoted by the matrix W, have the same dimension as the sinogram y, while x is the image to be estimated and A is the system matrix. In a conventional approach, there is no room to adjust the weights for different sub-regions of the image x. 
     This unavailability of spatially-dependent sinogram-weighting or view-weighting in iterative reconstruction techniques is in contrast to its availability in analytical reconstruction approaches, such as filtered backprojection (FBP). In these analytical approaches, the reconstruction at each spatial location can be carried out by a closed form equation and the reconstructions at different spatial locations may be carried out with computations that are independent of each other. Thus, differential weighting may be applied. 
     However, iterative reconstruction is based on minimizing a cost function that considers all pixel jointly is intrinsically “global”, and thus not suitable in conventional approaches for differential weighting of the sinogram measurements in sub-regions or pixels in the reconstructed image. This may prove problematic, however, in certain CT imaging scenarios that would benefit from spatially-adaptive weights to optimize image quality and reduce various artifacts. For example, in a wide-cone cardiac CT context, the coronary arteries are subject to motion and it may be useful to use a relatively small portion of the acquired data, such as masked by a Parker window, to reduce the inconsistency in the sinogram data and reduce motion artifacts in the reconstructed image. However, in non-cardiac regions of the same scan that are not subject to motion, such as the spine and abdomen, it may instead be desirable to use all available data to maximize dose efficiency and reduce cone beam artifacts. 
     Another example where spatially-adaptive weights may be useful in in the helical CT context in which the patient is linearly displaced in the image bore while the gantry rotates. Due to small inconsistencies caused by patient motion and/or system inaccuracy, pin wheel (hurricane, HAR) artifacts may be present in the reconstructed image if all sinogram data are used in the iterative reconstruction process. To reduce the pin wheel artifacts, it may be desirable to use less than the full data in image regions that are prone to pin wheel artifacts. However, in regions where the pin wheel artifacts are less noticeable, such as the center of the image, it may be desirable to use the full data to maximize dose efficiency. 
     In a further example, spatially-adaptive weighting may be useful in various other contexts that may lead to artifacts or deficiencies in the image that may be spatially localized. For example, spatially-adaptive weighting may be useful to address localized issues related to scatter, low-signal, metal artifacts (such as due to metal implants or device in the scan area) and so forth. In such contexts, by using spatially-adaptive weighting, some X-rays could be weighted less or more in certain image sub-regions of the image. 
     With the preceding in mind, the present iterative reconstruction approach employs spatially-adaptive sinogram weighting. This weighting may take various forms. For example, in one implementation, the weight factors may be determined by applying a pixel-dependent multiplicative factor to a conventional pixel-independent weight. In a further implementation, the weight factors are determined by a pixel-dependent temporal window function (such as is illustrated graphically in  FIG. 3 ). In another embodiment discussed herein, the weight factors may be determined by a linear combination of basis temporal window functions. 
     Turning to  FIG. 3 , an example is illustrated where different image regions  140 A,  140 B,  140 C are reconstructed with different amounts of sinogram data. As used herein, the different image regions  140  may, in certain embodiments, be based on or derived as temporal window functions that are pixel-dependent. That is, the reconstructed image may be segmented into multiple (i.e., two or more) sub-image regions that each use a different set of temporal windows. For example, in a chest image, half-scan weights may be applied in a cardiac region (to reduce artifacts due to motion in this region) and full-scan weights may be applied in a background region where little motion is expected. In such an approach, the temporal window(s) may be determined based on a first and last view index (such as may be associated with one of the arcs  142  discussed below). 
     The arcs  142 A,  142 B,  142 C of different lengths represent the portion of the X-ray source trajectory, and the corresponding sinogram data, that are weighted differently from one another based on corresponding image regions  140 . Among the three arcs of the X-ray source trajectory, the shortest one  142 A is used for the reconstruction of the inner-most sub-region, whereas the longest one  142 C is used for the reconstruction of the outer-most sub-region. This contrasts with the conventional iterative reconstruction, where different image regions would have the same sinogram weights. In this example, the projection measurement along the ray  146  is used for reconstruction in the sub-region  140 C, but not in sub-regions  140 B and  140 A. 
     Turning to  FIG. 4 , a flow-type diagram is provided of one implementation of the present iterative reconstruction approach with multiple backprojectors  162 , here a region-of-interest (ROI) backprojector  162 A and a background backprojector  162 B, employing different statistical weights  160 , here ROI weights  160 A and background weights  160 B. Thus, in this implementation, instead of using a single back projector as shown in  FIG. 2 , multiple backprojectors  162  are instead employed, each associated with a different set of sinogram weights  160 . In this manner, different weights  160  may be used in different image sub-regions, such as a region-of-interest and a background region. In this implementation, the backprojection only needs to be computed in the corresponding sub-region, therefore the computational cost would be less than performing the backprojection operation in the entire reconstructed image. The different sub-image regions after the separate backprojection operations can be merged (block  164 ) by image-domain masks to generate the current reconstructed image estimate  110 . Smoothing of the mask boundaries can be employed for a smooth transition between the sub-regions. 
     Consistent with  FIG. 4 , the merged backprojection  164  is: 
     
       
         
           
             
               
                 
                   
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     where e i =w i (y i −[Ax] i ) denotes the conventionally weighted error sinogram at detector cell i, with w i  denoting the conventional sinogram-domain weight that typically reflect noise levels of measurement at cell i, and v i   ROI  and v i   BKGND  denote the weights for cell i in the ROI and the background, respectively. The weights v i   ROI  and v i   BKGND  can be designed independent of each other to optimize reconstruction quality. 
     In one embodiment of this iterative reconstruction approach, and the other iterative reconstruction approaches discussed herein, numerical optimization techniques such as a line search may be employed to ensures monotonic decrease of the cost function after each iteration until a specified threshold, such as cost function minimization, is reached. In addition, in these and other embodiments, a relaxation factor may be employed to improve convergence. Further, with respect to this and other embodiments, the statistically-weighted, backprojected error may be spatially filtered. Furthermore, with respect to this and other embodiments, ordered subsets, conjugate gradient, preconditioner, Nesterov&#39;s optimal gradient iteration, method of momentum, and other numerical optimization techniques can be used to improve the speed of convergence and reduce the computational overhead. 
     Turning to  FIG. 5 , it is illustrated that this implementation can be extended beyond two sub-regions to N sub-regions, with a different backprojector  162  (e.g., backprojectors  162 C,  162 D,  162 E, and so forth) and separate weights  160  (e.g., weights  160 C,  160 D,  160 E, and so forth) provided for each sub-region. 
     In the preceding implementation, each iteration or the algorithm employs multiple backprojection operations, which may incur computational overhead compared to the conventional approach shown in  FIG. 2  where only a single backprojection is used each iteration. Conversely, turning to  FIG. 6 , in a different implementation the computational overhead may be reduced in the case where the space-dependent sinogram weights, e.g., v ji , are binary (i.e., one or zero). In this circumstance, the multiple back projections can instead be implemented as a single selective backprojection operation  180  that allows the selection of different view ranges at different pixel locations (e.g., spatially-adaptive view ranges  182 ). For example, the backprojection operation at a given pixel location skips measurements (i.e., is selective) that are outside the temporal window function at the respective pixel location. The selective backprojection is defined as: 
     
       
         
           
             
               
                 
                   
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     where S j  denotes the set of sinogram bins that should be used for pixel j. For each pixel, the backprojection operation restricts the range of summation to rays that belong to the set S j , and a single backprojection operation  180  suffices. Because S j  can vary across j, it becomes a way to realize space-variant sinogram weights in iterative reconstruction. 
     With the preceding in mind, the prior implementations may be generalized to a more flexible, spatially-adaptive backprojection, defined as: 
     
       
         
           
             
               
                 
                   
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     where the coefficient v ij  denotes a weight factor that depends on both sinogram and image locations. 
     Although this is a generalized form of sinogram weight, the computational cost for explicit generation and storage of v ij  may be prohibitive. With this in mind, in a further embodiment, the weight v ij  may be expressed as the linear combination of a small number of basis functions that can be computed on-the-fly as: 
     
       
         
           
             
               
                 
                   
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                   ) 
                 
               
             
           
         
       
     
     where v ki  denotes the kth basis function of the weights; α jk  denotes the coefficient of the kth basis function at pixel j; K denotes the number of basis functions. Typically, K is less than the number of sinogram bins, therefore this factorized form can reduce the overhead to explicitly store the full weights v ij . 
       FIG. 7  shows an example where each basis function represents a sinogram-domain window function that covers a narrow range of projection angles. Eight basis functions are shown, each corresponding to an angular range of π/8. A linear combination of these basis functions can form various sinogram weights. In particular, by a linear combination of these basis function, a view-range window can be generated at each image pixel location j. Should higher precision of these window function be needed, the number of basis functions, K, can be increased. 
     With respect to implementation, a study was conducted in which iterative reconstruction was implemented with spatially-adaptive sinogram weighting using multiple backprojectors having different respective sinogram weights. The approach was applied to wide-cone cardiac CT, with a trans-axial coverage of 16 cm. To improve the tradeoff between temporal resolution and cone-beam artifacts, short-scan sinogram weights were used for the heart region of the patient, while full-scan sinogram weights were used for the rest of the patient to reduce missing data in regions with high cone angles. Qualitative and quantitative evaluations of the resulting reconstructed images showed that the present approach achieved the same temporal resolution as a conventional short-scan, but prevented or limited artifacts in non-heart regions and maintained the consistent image quality in these regions as a conventional full-scan. 
     Results of this approach and a conventional iterative reconstruction are shown in  FIGS. 8 and 9 , with each figures respectively showing reconstructed images in edge slices with conventional sinogram weighting ( FIG. 8 ) and adaptive sinogram weighting as discussed herein ( FIG. 9 ). In edge slices, the conventionally reconstructed image shown in  FIG. 8  suffers from artifacts caused by missing data due to the short-scan weights, but the image reconstructed using spatially adaptive sinogram weighting does not exhibit the same artifacts. As may be appreciated, such artifact-reduced or artifact-free images may be stored and/or displayed (such as on the scanner itself or on a PACS system for remote or future viewing) and used in making diagnosis or treatment decisions by a reviewer. 
     Technical effects of the invention include the use of differing or varying sinogram weights in pixels or larger sub-regions in the reconstructed image. In certain implementations, this may take the form of applying spatially-adaptive sinogram weighting during an iterative reconstruction process to improve image quality. 
     This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.