Patent Publication Number: US-9895124-B2

Title: X-ray CT apparatus and image reconstruction method

Description:
TECHNICAL FIELD 
     The present invention relates to an X-ray CT apparatus and an image reconstruction method, and in detail, to an image reconstruction method suitable for an X-ray CT apparatus using an X-ray tube device that can irradiate X-rays from a plurality of focal spots. 
     BACKGROUND ART 
     An X-ray CT apparatus is an apparatus in which an X-ray tube device and an X-ray detector are oppositely disposed to rotate around an object, irradiates X-rays from a plurality of rotation angle directions (views) to detect the X-ray transmitted through the object for each view, and generate a tomographic image of the object based on the detected projection data. In the recent years, an FFS (Flying Focal Spot) X-ray tube device having a function to irradiate X-rays to a plurality of spots by shifting an X-ray focus has been developed. In the FFS X-ray tube device, an X-ray focal spot can be shifted to a plurality of positions by electromagnetically moving a position of an electronic beam entering the anode (target). Hence, a plurality of projection data whose X-ray irradiation paths are different can be acquired from the same rotation angle direction (view), which can improve spatial resolution of the X-ray CT apparatus (the FFS method). 
     By the way, there is a problem that spatial resolution around the center of the entire effective field of view is improved while the spatial resolution deteriorates in the peripheral portion other than the central portion in an image reconstructed using the conventional FFS method. On the contrary to this, a BFFS (Balanced Flying Focus Spot) method is suggested in the patent literature 1, which homogenizes and improves the spatial resolution of the peripheral portion by setting an optimal focal movement distance based on the number of views to be scanned during one rotation (an angle difference between adjacent views) and a distance between the X-ray tube device and the rotational center. 
     CITATION LIST 
     Patent Literature 
     
         
         PTL 1: Japanese Unexamined Patent Publication No. 2010-35812 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     However, a sampling rate and a gantry rotation speed of a data collection device are limited due to hardware limitations. Therefore, in order to increase the number of views to be scanned during one rotation, the gantry rotation speed needs to be reduced. When the number of views is increased by reducing the rotational speed, motion artifacts are adversely increased in case of a fast-moving organ such as the heart. The faster movement of the organ such as the heart, the more such motion artifacts affect an image considerably, which is inconvenient for a radiologist performing image diagnosis. Therefore, there is a request to improve spatial resolution over the entire effective field of view without reducing the rotational speed in scanning a moving site as a target. 
     The present invention was made in view of the above problems, and the purpose is to provide an X-ray CT apparatus and an image reconstruction method that can improve spatial resolution of the entire effective field of view without reducing a rotational speed in the FFS method for improving spatial resolution by moving an X-ray focal spot to a plurality of positions to acquire projection data. 
     Solution to Problem 
     In order to achieve the above purpose, the first invention is an X-ray CT apparatus characterized by comprising an X-ray tube device for irradiating X-rays to an object from a plurality of focal spots, an X-ray detector disposed oppositely to the X-ray tube device for detecting transmission X-rays transmitted through the object, a rotary disk that is equipped with the X-ray tube device and the X-ray detector and rotates around the object, a focal shift X-ray controller for shifting the focal spot in the X-ray tube device to arbitrary positions, a focal shift projection data generation unit for generating focal shift projection data in combination with the transmission X-rays by each of the irradiated X-rays whose focal spots were shifted to a plurality of positions by the focal shift X-ray controller, a virtual view generation unit for generating a virtual view in the view direction of the focal shift projection data to generate up-sampled projection data using the virtual view, and a reconstruction computing unit for reconstructing an image using actual data of the focal shift projection data in the central region closer to the image center than a predetermined boundary in the image plane and using the up-sampled projection data in the peripheral region outside the boundary. 
     The second invention is an image reconstruction method characterized by including the steps of acquiring focal shift projection data that is projection data by each of the irradiated X-rays of which focal spot was shifted to a plurality of positions in the X-ray tube device, generating a virtual view in the view direction of the focal shift projection data to generate up-sampled projection data using the virtual view, and reconstructing an image using actual data of the focal shift projection data in the central region closer to the image center than a predetermined boundary in the image plane and using the up-sampled projection data in the peripheral region outside the boundary. 
     Advantageous Effects of Invention 
     The present invention can provide an X-ray CT apparatus and an image reconstruction method that can improve spatial resolution of the entire effective field of view without reducing a rotational speed in the FFS method for improving spatial resolution by moving an X-ray focal spot to a plurality of positions to acquire projection data. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is an overall configuration diagram of the X-ray CT apparatus  1 . 
         FIG. 2  is a flow chart explaining the entire process flow executed by the X-ray CT apparatus  1 . 
         FIG. 3  is a flow chart explaining the flow of the virtual view generation process (A). 
         FIG. 4  is a schematic diagram showing the procedure of the virtual view generation process (A). 
         FIG. 5  is a flow chart explaining the flow of the virtual view generation process (B). 
         FIG. 6  is a schematic diagram showing the procedure of the virtual view generation process (B). 
         FIG. 7  is a flow chart explaining the flow of the virtual view generation process (C). 
         FIG. 8  is a schematic diagram showing the procedure of the virtual view generation process (C). 
         FIG. 9  is a flow chart explaining the flow of the virtual view generation process (D). 
         FIG. 10  is a schematic diagram showing the procedure of the virtual view generation process (D). 
         FIGS. 11( a ) and 11( b )  are diagrams explaining the up-sampling method using counter data,  FIGS. 11( c ), 11( d ), and 11( e )  are diagrams showing interpolation between two points, interpolation between four points, and interpolation by the TV method respectively. 
         FIG. 12  is a diagram explaining the up-sampled projection data  518  that is partially different in the number of views. 
         FIG. 13  is diagrams explaining a change of spatial resolution in the central region  604  and the peripheral region  603  of an image. 
         FIG. 14  is a flow chart explaining the flow of the reconstruction computing process. 
         FIG. 15  is a diagram showing modes of the projection data to be used for the reconstruction computing process of  FIG. 14 . 
         FIG. 16  is a diagram explaining the reconstruction computing process of the second embodiment. 
         FIG. 17  shows an example of a weighting factor to be applied in the reconstruction computing process of the second embodiment. 
         FIG. 18  is a flow chart explaining the flow of the reconstruction computing process of the second embodiment. 
         FIG. 19  shows an example of a weighting factor to be applied in the reconstruction computing process of the third embodiment. 
         FIG. 20  is a flow chart explaining the flow of the reconstruction computing process of the third embodiment. 
         FIG. 21  is a schematic diagram explaining an ROI set in the reconstruction computing process of the fourth embodiment and projection data to be used for each region. 
         FIG. 22  is a flow chart explaining the flow of the reconstruction computing process of the fourth embodiment. 
         FIG. 23  shows an example of synthesizing an image reconstructed using projection data up-sampled by the number of views different depending on the distance from the image center in the reconstruction computing process of the fifth embodiment. 
         FIG. 24  shows an example of synthesizing an image by weighting so as to smooth the region near the boundary in the example of  FIG. 23 . 
         FIG. 25  shows an example of expanding the number of regions in the example of  FIG. 24  to N. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, referring to the attached diagrams, suitable embodiments of the present invention will be described in detail. 
     First Embodiment 
     First, referring to  FIG. 1 , the overall configuration of the X-ray CT apparatus  1  will be described. 
     As shown in  FIG. 1 , the X-ray CT apparatus  1  is provided with the scan gantry unit  100  and the operation console  120 . 
     The scan gantry unit  100  is a device for irradiating an X-ray to an object and detecting the X-ray transmitted through the object and is comprised of the X-ray tube device  101 , the rotary disk  102 , the collimator  103 , the X-ray detector  106 , the data collection device  107 , the gantry controller  108 , the bed controller  109 , and the focal shift X-ray controller  110 . 
     The rotary disk  102  is provided with the opening  104 , and the X-ray tube device  101  and the X-ray detector  106  are disposed oppositely across the opening  104 . An object placed on the bed  105  is inserted in the opening  104 . The rotary disk  102  rotates around the object using the driving force to be transmitted through the driving transmission system from the rotary disk driving device controlled by the gantry controller  108 . 
     The operation console  120  is a device for controlling each part of the scan gantry unit  100  and acquiring projection data measured in the scan gantry unit  100  to generate and display an image. The operation console  120  is provided with the input device  121 , the image computing device  122 , the storage device  123 , the system controller  124 , and the display device  125 . 
     The X-ray tube device  101  is a flying focus X-ray tube device that can move a focal spot in the rotating anode (target). When the rotation axis direction of the X-ray CT apparatus  1  is set to the Z direction, the flying focus X-ray tube device deflects an electronic beam to be irradiated to the rotating anode (target) to the X or Y direction orthogonal to the Z direction. Hence, an X-ray focal spot is shifted, and X-rays of minutely different paths are irradiated from the same view position. 
     In the present embodiment, a focus moving direction by the X-ray tube device  101  is set to the rotation direction (channel direction) of the X-ray CT apparatus  1 . Also, the focal spots are set to spots shifted by “+σa” and “−σb” in the rotation direction (channel direction) from the reference focal spot. That is, the X-ray tube device  101  irradiates X-rays respectively from the first focal spot “+σa” moved in the positive direction of the channel direction and the second focal spot “−σb” moved in the negative direction. 
     In the following description, projection data acquired using the FFS (Flying Focus Spot) method is referred to as FFS projection data. Particularly, projection data acquired using an X-ray irradiated from the above first focal spot is referred to as FFS (+) projection data, and projection data acquired using an X-ray irradiated from the above second focal spot is referred to as FFS (−) projection data. Also, projection data acquired using an X-ray irradiated from the reference focal spot without the FFS technique is referred to as FFS (without) projection data. 
     The X-ray tube device  101  is controlled by the focal shift X-ray controller  110  and continuously or intermittently irradiates an X-ray of a predetermined intensity. The focal shift X-ray controller  110  controls an X-ray tube voltage and an X-ray tube current to be applied or supplied to the X-ray tube device  101  according to the X-ray tube voltage and the X-ray tube current determined by the system controller  124  of the operation console  120 . The focal shift X-ray controller  110  controls alternate movement to the above first and second focal spots for each view according to the rotation of the rotary disk  102  for example. 
     The X-ray irradiation port of the X-ray tube device  101  is provided with the collimator  103 . The collimator  103  restricts an irradiation range of an X-ray emitted from the X-ray tube device  101 . For example, an X-ray becomes a cone-beam (cone or pyramid-beam) shape or the like. The opening width of the collimator  103  is controlled by the system controller  124 . 
     The transmission x-ray is irradiated from the X-ray tube device  101 , passes through the collimator  103 , is transmitted through an object, and then enters the X-ray detector  106 . 
     In the X-ray detector  106 , the X-ray detection element group is comprised of combinations of a scintillator and a photodiode, for example, approximately 1,000 pieces of the groups are arranged in the channel direction (circumferential direction), and approximately 1 to 320 pieces of the groups are arranged in the column direction (body-axis direction). The X-ray detector  106  is disposed oppositely to the X-ray tube device  101  across an object. The X-ray detector  106  detects an amount of X-rays irradiated from the X-ray tube device  101  and transmitted through the object and outputs the amount to the data collection device  107 . 
     The data collection device  107  collects an X-ray amount to be detected by each X-ray detection element of the X-ray detector  106 , converts the amount into digital data, and then sequentially outputs it to the image computing device  122  of the operation console  120  as transmission X-ray data. 
     The image computing device  122  acquires transmission X-ray data input from the data collection device  107  and generates projection data required for reconstruction after pre-processing such as logarithmic transformation and sensitivity correction. Because X-rays whose focal spots are alternately different for each view are irradiated from the X-ray tube device  101  when using the FFS method, the image computing device  122  generates FFS (+) projection data acquired using an X-ray irradiated from the first focal spot and FFS (−) projection data acquired using an X-ray irradiated from the second focal spot. 
     The image computing device  122  is provided with the virtual view generation unit  126  and the reconstruction computing unit  127 . 
     The virtual view generation unit  126  generates a virtual view for focal shift projection data (FFS (+) projection data and FFS (−) projection data) scanned using the FFS method and inserts the view to generate up-sampled projection data. The virtual view is a view to be computed and inserted in a view position that is not scanned actually. Projection data of the virtual view can be calculated by interpolating or estimating based on actually scanned projection data (hereinafter, referred to as actual data). The detail of virtual view generation will be described later. Projection data generated (up-sampled) by the virtual view generation unit  126  is referred to as up-sampled projection data 
     The reconstruction computing unit  127  reconstructs an image such as a tomographic image of an object using actually measured projection data (actual data of FFS (+) projection data and FFS (−) projection data) and up-sampled projection data generated by the virtual view generation unit  126 . 
     In the present embodiment, the reconstruction computing unit  127  reconstructs an image using actual data (FFS (+) projection data and FFS (−) projection data) and up-sampled projection data in consideration of spatial resolution of the image. Specifically, actual data of FFS (+) projection data and FFS (−) projection data is used for reconstructing an image in the central region in the image plane, which improves spatial resolution in the central region. Also, an image is reconstructed using up-sampled projection data in the peripheral region of the image, which improves spatial resolution. That is, spatial resolution deteriorates in the peripheral region when FFS projection data is used in the entire region of the image, but up-sampled projection data is used for the peripheral region in the present embodiment, which is intended to improve the spatial resolution in the peripheral region. The up-sampled projection data can increase the number of views without reducing a rotational speed to insert a virtual view by computation. Therefore, it is particularly suitable for the case of generating an image of a moving site. 
     Either of an analytical method such as a filter correction reverse projection method or a successive approximation method may be used as the image reconstruction process. 
     Image data reconstructed by the image computing device  122  (the reconstruction computing unit  127 ) is input to the system controller  124 , stored in the storage device  123 , and displayed on the display device  125 . 
     The system controller  124  is a computer provided with a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and the other. The storage device  123  is a data storage device such as a hard disk and stores a program, data, and the other for realizing functions of the X-ray CT apparatus  1  in advance. 
     The system controller  124  performs a scanning process according to the processing procedure shown in  FIG. 2 . In the scanning process, the system controller  124  sends control signals according to the scanning conditions set by an operator to the focal shift X-ray controller  110  of the scan gantry unit  100 , the bed controller  109 , and the gantry controller  108  in order to control the above respective units. The details of each process will be described later. 
     The display device  125  is comprised of a liquid crystal panel, a display device such as a CRT monitor, and a logic circuit for executing a display process in association with the display device and is connected to the system controller  124 . The display device  125  displays a reconstruction image output from the image computing device  122  as well as various information handled by the system controller  124 . 
     The input device  121  is comprised of, for example, a pointing device such as a keyboard and a mouse, a numeric keypad, various switch buttons, and the like and outputs various commands and information to be input by an operator to the system controller  124 . The operator interactively operates the X-ray CT apparatus  1  using the display device  125  and the input device  121 . The input device  121  may be a touch panel-type input device integrally formed with the display screen of the display device  125 . 
     Next, referring to  FIGS. 2 to 15 , the operations of the X-ray CT apparatus  1  will be described. 
       FIG. 2  is a flow chart explaining the entire scanning process flow executed by the X-ray CT apparatus  1  related to the present invention. 
     In the scanning process, the system controller  124  first receives inputs of scanning conditions and reconstruction conditions. The scanning conditions include X-ray conditions such as an X-ray tube voltage and an X-ray tube current, a scanning range, a gantry rotation speed, a bed speed, and the like. The reconstruction conditions include a reconstruction FOV, a reconstruction slice thickness, and the like. 
     After the scanning conditions and reconstruction conditions are input through the input device  121  or the like (Step S 101 ), the system controller  124  sends control signals to the focal shift X-ray controller  110 , the gantry controller  108 , and the bed controller  109  based on the scanning conditions. The focal shift X-ray controller  110  controls the electric power to be input to the X-ray tube device  101  based on the control signal input from the system controller  124 . Also, the focal shift X-ray controller  110  move an electronic beam irradiating to the rotating anode of the X-ray tube device  101  in a predetermined direction, by a predetermined distance, and at a predetermined timing in order to perform the FFS control that irradiates an X-ray by moving X-ray focal spots alternately. The gantry controller  108  controls the driving system of the rotary disk  102  according to the scanning conditions such as a rotational speed to rotate the rotary disk  102 . The bed controller  109  adjusts the bed to a predetermined scanning start position based on a scanning range. 
     X-ray irradiation from the X-ray tube device  101  and transmission X-ray data measurement by the X-ray detector  106  are repeated along with the rotation of the rotary disk  102 . The data collection device  107  acquires the transmission X-ray data measured by the X-ray detector  106  at various angles (views) around an object and sends the data to the image computing device  122 . The image computing device  122  acquires the transmission X-ray data input from the data collection device  107  and performs pre-processing such as logarithmic transformation and sensitivity correction to generate projection data. Because scanning is performed by moving the X-ray focal spot to two positions using the FFS method in the present invention, the image computing device  122  generates FFS (+) projection data acquired by an X-ray irradiated from the first focal spot and FFS (−) projection data acquired by an X-ray irradiated from the second focal spot (Step S 102 ). 
     The image computing device  122  (the virtual view generation unit  126 ) performs the virtual view generation process using the FFS (+) projection data and FFS (−) projection data (these are collectively referred to as FFS projection data) generated in the process of Step S 102  (Step S 103 ). 
     In the virtual view generation process, the virtual view generation unit  126  inserts a virtual view in an actual data (performs up-sampling) so as to have the predetermined number of views in order to generate up-sampled projection data. The number of views may be a value predetermined according to the device specifications or may be a value set by an operator. Also, the number of views may be a value determined by an image quality index (particularly spatial resolution) and the other parameters set by the operator. The specific method of the virtual view generation process will be described later (refer to  FIGS. 3 to 12 ). 
     After generating up-sampled projection data in which a virtual view is inserted by the Step S 103  process, the reconstruction computing unit  127  of the image computing device  122  next performs the image reconstruction process based on the reconstruction conditions input in Step S 101  (Step S 104 ). Any type of algorithm may be used as the image reconstruction algorithm to be used in the image reconstruction process. For example, a reverse projection process such as the Feldkamp method may be performed, and a successive approximation method or the like may be performed. 
     Conventionally, spatial resolution of an image reconstructed using FFS projection data can become higher in the central region of the image and become lower than when projection data without FFS is used as getting closer to the periphery, compared to when the FFS projection data is not used (refer to  FIG. 13 ). Therefore, projection data up-sampled by a virtual view is used for a region of low spatial resolution (Low region: peripheral region) where FFS effects cannot be obtained, in the reconstruction computing process of Step S 104  of the present invention. In a region where FFS effects can be obtained (Hi region: central region), an image is reconstructed using actual data of the FFS projection data (refer to  FIGS. 13 to 15 ). The details of the reconstruction process will be described later. 
     After the image is reconstructed in Step S 104 , the system controller  124  displays the reconstructed image on the display device  125  (Step S 105 ), and then a series of the scanning processes ends. 
     Next, each mode of the virtual view generation processes (A) to (D) of Step S 103  will be described referring to  FIGS. 3 to 10 . 
     First, the virtual view generation process (A) will be described referring to  FIGS. 3 and 4 . 
     The image computing device  122  acquires the FFS (+) projection data  501  and the FFS (−) projection data  502  by moving a focus of the X-ray tube device  101  (Step S 201 ), and then acquires the FFS projection data  503  by alternately combining the FFS (+) projection data  501  and the FFS (−) projection data  502  in the view direction (Step S 202 ). Furthermore, the virtual view generation  504  is executed for the FFS projection data  503  (Step S 203 ) to acquire the up-sampled projection data  505 . The virtual view generation unit  126  outputs the up-sampled projection data  505  to the reconstruction computing unit  127  (Step S 204 ). 
     The virtual view generation process (B) will be described referring to  FIGS. 5 and 6 . 
     The image computing device  122  acquires the FFS (+) projection data  501  and the FFS (−) projection data  502  by moving a focus of the X-ray tube device  101  (Step S 301 ) and then executes the virtual view generation  504  for the FFS (+) projection data  501  and the FFS (−) projection data  502  respectively (Step S 302 ). Then, the FFS projection data  513  is acquired by alternately combining the up-sampled FFS (+) projection data  511  and FFS (−) projection data  512  in the view direction (Step S 303 ). The virtual view generation unit  126  outputs the up-sampled projection data  513  to the reconstruction computing unit  127  (Step S 304 ). 
     The virtual view generation process (C) will be described referring to  FIGS. 7 and 8 . 
     The image computing device  122  acquires the FFS (+) projection data  501  and the FFS (−) projection data  502  by moving a focus of the X-ray tube device  101  (Step S 401 ) and then executes the virtual view generation  504  for the FFS (+) projection data  501  and the FFS (−) projection data  502  respectively (Step S 402 ). Then, the up-sampled FFS projection data  513  is acquired by alternately combining the up-sampled FFS (+) projection data  511  and FFS (−) projection data  512  in the view direction (Step S 403 ). 
     The virtual view generation unit  126  further performs the missing data process  514  for the up-sampled FFS projection data  513  (Step S 404 ). 
     The missing data process is a process for alternately combining FFS (+) projection data and FFS (−) projection data in the view direction to fill missing data caused in the FFS projection data  513  acquired by interpolating and estimating the missing data using projection data or that in the vicinity adjacent in the view direction and the channel direction. The FFS (+) projection data and FFS (−) projection data acquired by moving a focal spot in the channel direction have different X-ray paths respectively. Therefore, the data to be acquired is twice the number of channels. When measuring projection data for each view during scanning by alternately moving focal spots, FFS (+) projection data is acquired in odd views, FFS (−) projection data is acquired in even views, and these data is combined alternately, which causes alternate missing data for each view in the FFS projection data  513 . 
     In the process of Step S 404 , the missing data process  514  is performed to fill such missing data. 
     After acquiring the up-sampled projection data  515  for which the missing data process  514  was performed in Step S 404 , the virtual view generation unit  126  outputs the up-sampled projection data  515  to the reconstruction computing unit  127  (Step S 405 ). 
     The virtual view generation process (D) will be described referring to  FIGS. 9 and 10 . 
     The image computing device  122  acquires the FFS (+) projection data  501  and the FFS (−) projection data  502  by moving a focus of the X-ray tube device  101  (Step S 501 ) and then executes the virtual view generation  504  for the FFS (+) projection data  501  and the FFS (−) projection data  502  respectively (Step S 502 ). Then, the up-sampled FFS projection data  513  is acquired by alternately combining the up-sampled FFS (+) projection data  511  and FFS (−) projection data  512  in the view direction (Step S 503 ). 
     The virtual view generation unit  126  further executes the virtual view generation  504  for the up-sampled FFS projection data  513  (Step S 504 ). The process of Step S 504  acquires the up-sampled FFS projection data  516 . The virtual view generation unit  126  outputs the up-sampled projection data  516  to the reconstruction computing unit  127  (Step S 505 ). 
     Here, the virtual view calculating method (up-sampling method) will be described referring to  FIG. 11 . Each up-sampling method shown in  FIG. 11  can be applied to any of the virtual view generation processes in Step S 203  of  FIG. 3 , Step S 302  of  FIG. 5 , Step S 402  of  FIG. 7 , and Steps S 502  and S 504  of  FIG. 9 . 
     The virtual view generation unit  126  (the image computing device  122 ) calculates projection data of the virtual view by interpolation or estimation for views (virtual views) to be inserted using projection data near the view or channel direction, data of the counter Ray (counter data), projection data near the view or channel direction of the counter data, or the like. 
     (Up-Sampling Method for Generating a Virtual View Using Counter Data) 
     In projection data acquired in one-rotation (2π) scanning, a virtual view can be generated using data of the counter Ray (hereinafter, the data of the counter Ray is referred to as the counter data). Referring to  FIGS. 11( a ) and 11( b ) , an example of generating a virtual view for the projection data acquired in one-rotation scanning using the counter data to double the number of the views will be described. 
     In the projection data of one rotation shown in  FIG. 11( a ) , Ray 31  and Ray 32  are counter to each other. That is, they are on the same X-ray irradiation path. The counter data at the points A 1  and A 2  of Ray 31  are respectively the points B 1  and B 2  of Ray 32 . The points B 1  and B 2  are the data of the adjacent channel on the actual view (2γm+π) as shown in  FIG. 11( a ) . The relationship between the points A 1  and B 1  on the projection data can be expressed in the following formula (1) using the function R (γ, θ) that uses parameters in which γ represents the channel direction and θ represents the view direction.
 
[Formula 1]
 
 R   A1 (−γ m ,0)= R   B1 (γ m ,2γ m +π)  (1)
 
     Also, the relationship between the channel and the view at the points A 1  and B 1  can be expressed in the following formulas (2) and (3). 
     
       
         
           
             
               
                 
                   
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     Hence, the point A 1  A 2  in the virtual view  41  between the points A 1  and A 2  can be calculated in the following formulas (4) and (5) as the point B 1 B 2  calculated from the points B 1  and B 2  on the actual view (2γm+π). 
     
       
         
           
             
               
                 
                   
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     Using the similar procedure, a point adjacent by one pixel (the point C 1 C 2  of  FIG. 11( b ) ) in the virtual view  41  is calculated from the counter data, which can generate channel data (the point V 41   b ) by linear interpolation shown with a double circle of  FIG. 11( b ) . This operation is repeated to calculate each channel data of the virtual view  41 . Channel data at each point can be similarly calculated using the counter data for the other virtual views  41 ,  42 , and the subsequent views. 
     In the virtual view generation method (up-sampling method) using counter data, each channel data of virtual views is calculated based on the counter data (actual data) having biological information (measurement data transmitted through an object) closest to channel data to be estimated (the points shown with double circles). The counter data having the closest biological information means a Ray that has the closest transmission path among the measured Rays and enters from the opposite direction. The above counter data is characterized by obtaining a Ray selectively and calculating a virtual Ray γ estimated from the selected Ray to generate a virtual view. By using this method, only the number of views can be up-sampled while the number of channels is not changed. Although channel data of virtual views is calculated using an average value of two points of counter data in case of double sampling, the channel data may be calculated by linear interpolation between two points or non-linear interpolation in case of N-times sampling. Also, this method enables up-sampling in the channel direction to be performed simultaneously. 
     Additionally, the virtual view generation method is not limited to the up-sampling method using the counter data as described above. The method to be used may be the two-point interpolation that simply interpolates the adjacent views each other as shown in  FIG. 11( c ) , the four-point interpolation that interpolates using the adjacent views and the channel data as shown in  FIG. 11( d ) , or the interpolation by the TV (Total Variation) method as shown in  FIG. 11( e ) . 
     Also, the number of views of up-sampled projection data may be set to the arbitrary number of views including a decimal value such as 1.5 times of actual data. For example, when the number of views is increased partially in the view direction, the number is in multiples of a decimal value. The object  2  has a cross section with a shape close to an ellipse as shown in  FIG. 12( a ) . Therefore, as shown in  FIG. 12( b ) , the up-sampled projection data  518  in multiples of a decimal value can also be generated by increasing the number of partial views such as making the number of views dense in a view equivalent to the long diameter of an ellipse. 
     Next, the reconstruction computing process in Step S 104  of  FIG. 2  will be described referring to  FIGS. 13 to 15 . 
     As described above, spatial resolution of an image to be reconstructed using FFS projection data can become higher in the central region of the image and become lower than when projection data without FFS is used as getting closer to the periphery, compared to when the FFS projection data is not used (refer to  FIG. 13 ). 
       FIG. 13( b )  is the graph  606  showing the relationship between a distance from the center O and spatial resolution in the tomographic image  601  shown in  FIG. 13( a ) . Compared to when using projection data without FFS, spatial resolution (indicated by an index) is higher in a region inside the boundary  605  (hereinafter, referred to as the central region  604 ) in a distance from the image center O to the point P 0  when FFS projection data is used. On the other hand, spatial resolution (indicated by an index) is lower compared to when using projection data without FFS in a region (hereinafter, referred to as the peripheral region  603 ) outside the boundary point P 0  (the boundary  605  shown in  FIG. 13( a ) ). 
     Therefore, spatial resolution of the peripheral region  603  is improved by performing image reconstruction for data of the central region  604  already having sufficient spatial resolution using FFS projection data (actual data) that is not up-sampled and performing image reconstruction in the peripheral region  603  using projection data that is up-sampled by virtual view generation. 
     Hence, spatial resolution can be improved in the central region  604  while prevented from being affected by data generation, and the number of views is improved in the peripheral region  603  without reducing a rotational speed by generating a virtual view, which can improve the spatial resolution. 
     The procedure for the reconstruction computing process will be described referring to the flow chart of  FIG. 14 . 
     First, the reconstruction computing unit  127  obtains the boundary point P 0  of spatial resolution (Step S 601 ). The boundary point P 0  is a distance from the scanning center of a position where spatial resolution acquired by FFS projection data and that acquired by projection data without FFS are reversed. This boundary point P 0  is calculated by experimental data in advance and stored in the storage device  123  or the like. 
     As an evaluation index of spatial resolution, MTF (Modulation Transfer Function) is used. For example, the above boundary point P 0  may be calculated for each different spatial resolution evaluation index such as MTF50%, 10%, and 2% in order to allow an operator to select it. Since required image quality is different according to the examination and the diagnostic purpose, it desirable that required spatial resolution can be selected according to the balance with the other image quality (such as noise). 
     Alternatively, a boundary point to be the gravity center may be calculated from the boundary point P 0  obtained by a plurality of spatial resolution indexes such as MTF50%, 10%, and 2%. 
     The reconstruction computing unit  127  uses actual data of FFS projection data in the central region  604  on the central side from the boundary point P 0  and up-sampled projection data that up-sampled FFS projection data in the peripheral region  603  on the outside of the boundary point P 0  in order to perform reconstruction computation (Step S 602 ). 
     As the up-sampled projection data to be used in the peripheral region  603 , up-sampled projection data generated by any method of the above virtual view generation processes (A) to (D) may be used. That is, the up-sampled projection data that may be used is the up-sampled projection data  505  generated in the virtual view generation process (A) shown in  FIGS. 3 and 4  as shown in  FIG. 15( a ) , the up-sampled projection data  513  generated in the virtual view generation process (B) shown in  FIGS. 5 and 6  as shown in  FIG. 15( b ) , the up-sampled projection data  515  generated in the virtual view generation process (C) shown in  FIGS. 7 and 8  as shown in  FIG. 15( c ) , or the up-sampled projection data  516  generated in the virtual view generation process (D) shown in  FIGS. 9 and 10  as shown in  FIG. 15( d ) . 
     Also, the virtual view generation method of any of the up-sampled projection data  505 ,  513 ,  515 , and  516  may adopt the up-sampling method using counter data, interpolation with two points adjacent in the view direction, interpolation with four points adjacent in the view and channel directions, interpolation using the TV method etc., or the like as described above. 
     In the reconstruction computation, image reconstruction such as a reverse projection process may be performed after synthesizing actual data of FFS projection data with up-sampled projection data on projection data, or an image may be generated by synthesizing a portion corresponding to the central region  604  of an image reconstructed using the actual data of FFS projection data and a portion corresponding to the peripheral region  603  of an image reconstructed using the up-sampled projection data. 
     The reconstruction computing unit  127  outputs an image generated by the process in Step S 602  (Step S 603 ). The output destination is, for example, the storage device  123 , the display device  125 , and the like. 
     As described above, the X-ray CT apparatus  1  of the first embodiment up-samples focal shift projection data (FFS projection data) acquired by shifting an X-ray focal spot in the X-ray tube device  101  in the view direction. Then, in the image reconstruction computing process, an image is reconstructed using actual data of FFS projection data in the central region  604  closer to the scanning center than a predetermined boundary point P 0  and up-sampled projection data that up-sampled FFS projection data in the peripheral region  603  farther from the scanning center than the boundary point P 0 . 
     Because data up-sampled by a virtual view is used for the periphery of an effective field of view, there is no need to perform scanning by reducing a rotational speed to increase the number of views. Therefore, spatial resolution of the periphery is improved regardless of the rotational speed limit and the like due to hardware limitation, which can improve spatial resolution of the entire effective field of view. It is suitable to scan a moving site. 
     Second Embodiment 
     Next, the second embodiment of the present invention will be described referring to  FIGS. 16 to 18 . 
     The X-ray CT apparatus  1  of the second embodiment performs the joint process so that spatial resolution continues smoothly at the boundary point P 0  in the reconstruction computing process. 
     In the joint process, as shown in  FIG. 16 , both an image reconstructed by FFS projection data and an image reconstructed by up-sampled projection data are synthesized at a predetermined rate in a region of a predetermined range including the boundary point P 0  (hereinafter, referred to as the boundary region Q). In the central region  604   a  closer to the center than the boundary region Q, an image reconstructed by actual data of FFS projection data is used 100% similarly to the first embodiment. In the peripheral region  603   a  outside the boundary region Q, an image reconstructed by up-sampled projection data is used 100% similarly to the first embodiment. 
     That is, according to the distance from the center, an image reconstructed by FFS projection data and an image reconstructed by up-sampled projection data are synthesized while changing the weights each other. 
       FIG. 17  is a graph showing a weighting factor to be applied to a reconstruction image by up-sampled projection data. As shown in  FIG. 17 , the weighting factor W(P) changes according to the distance P from the center O. The weighting factor W(P) is “0” in the central region  604   a , a curve rising smoothly in the boundary region Q, and “1” in the peripheral region  603   a . Although the weighting factor to be applied to a reconstruction image by FFS projection data also changes according to the distance P from the center O, the weighting factor W(P) is “1” in the central region  604   a , a curve falling smoothly in the boundary region Q, and “0” in the peripheral region  603   a  on the contrary to that shown in  FIG. 17 . 
     The range of the boundary region Q is set arbitrarily, and it may be changed according to the desired spatial resolution of a desired region. 
     Also, although the weighting factor is shown in a smooth curve that depends on the distance P from the image center in the example of  FIG. 17 , it is not limited to this and may be shown in a straight line or bend line. 
     Also in the second embodiment, as shown in  FIGS. 16( a ) to 16( d ) , up-sampled projection data generated by any of the above virtual view generation processes (A) to (D) may be used for the peripheral region  603   a  and the boundary region Q. That is, the up-sampled projection data that may be used is the up-sampled projection data  505  generated by the virtual view generation process (A) shown in  FIGS. 3 and 4  as shown in  FIG. 16( a ) , the up-sampled projection data  513  generated by the virtual view generation process (B) shown in  FIGS. 5 and 6  as shown in  FIG. 16( b ) , the up-sampled projection data  515  generated by the virtual view generation process (C) shown in  FIGS. 7 and 8  as shown in  FIG. 16( c ) , or the up-sampled projection data  516  generated by the virtual view generation process (D) shown in  FIGS. 9 and 10  as shown in  FIG. 16 ( d ). 
     Also, the virtual view of any of the up-sampled projection data  505 ,  513 ,  515 , and  516  may be calculated using a method of interpolation between two points adjacent in the view direction ( FIG. 11( c ) ), interpolation between four points adjacent in the view direction and the channel direction ( FIG. 11( d ) ), or interpolation or estimation by the TV method etc. ( FIG. 11( e ) ) or using counter data ( FIGS. 11( a ) and 11( b ) ) as described above. 
     The number of views of up-sampled projection data is not limited to the double of actual data and may be more than the double. By partially increasing the number of views in the view direction, the arbitrary number of views including a decimal value such as 1.5 times may be set. 
     Referring to  FIG. 18 , the flow of the reconstruction computing process of the second embodiment will be described. 
     First, the reconstruction computing unit  127  obtains the boundary point P 0  of spatial resolution (Step S 701 ). The method of obtaining the boundary point P 0  is similar to the first embodiment (Step S 601  of  FIG. 14 ). 
     Next, the reconstruction computing unit  127  generates an image reconstructed using actual data of FFS projection data and an image reconstructed using up-sampled projection data for which the FFS projection data was up-sampled (Step S 702 ). 
     Next, the reconstruction computing unit  127  uses the image reconstructed by actual data of FFS projection data in the central region  604   a  closer to the center than the boundary region Q including the boundary point P 0  to generate a synthesized image using the image reconstructed by up-sampled projection data in the peripheral region  603   a  outside the boundary region Q. In the boundary region Q, weighted addition is performed for each image reconstructed in Step S 702  so as to be continuous spatial resolution (Step S 703 ). As described above, in the weighted addition, for example, an image generated by the up-sampled projection data is multiplied by a weighting factor of the shape shown in  FIG. 17 , an image generated by the actual data of FFS projection data is multiplied by a weighting factor of the shape opposite to the graph shown in  FIG. 17 , and these images are added. 
     The reconstruction computing unit  127  outputs an image generated by the process of Step S 703  (Step S 704 ). The output destination is, for example, the storage device  123 , the display device  125 , and the like. 
     As described above, the X-ray CT apparatus  1  of the second embodiment uses actual data of FFS projection data in the central region  604   a  close to the center in the image reconstruction computing process to synthesize each image generated using up-sampled projection data in the peripheral region  603   a  closer to the peripheral side than the boundary point P 0 . Additionally, in the predetermined boundary region Q, weighted addition is performed for each of the above images so that spatial resolution continues smoothly. 
     Hence, in addition to the effectiveness of the first embodiment, an image in which spatial resolution continues smoothly in the boundary region Q can be acquired. 
     Additionally, although weighted addition is performed to synthesize reconstructed images in the above reconstruction computing process, synthesized projection data may be reconstructed after synthesizing up-sampled projection data and actual data of FFS projection data on the projection data. In this case, the projection data to be used is that generated by performing weighted addition for up-sampled projection data and actual data of FFS projection data in a part corresponding to the boundary region Q. 
     Third Embodiment 
     Next, referring to the  FIGS. 19 and 20 , the third embodiment of the present invention will be described. 
     In the X-ray CT apparatus  1  of the third embodiment, it may be configured so that an image using actual data of FFS projection data and an image using up-sampled projection data are synthesized by changing weight over the entire image. 
       FIG. 19  is a graph showing the weighting factor W′(P) to be applied to a reconstruction image by up-sampled projection data in the third embodiment. This graph rises smoothly from “0” in a region close to the center and becomes “1” at the end of the peripheral region. That is, the graph has a shape in which a weighting factor changes according to the distance from the center O even in a region other than the boundary region Q. Thus, the graph shape of the weighting factor may be arbitrary, the weighting factor is changed so as to acquire desired spatial resolution in a desired region even in a region other than the boundary region Q. 
     Additionally, on the contrary to  FIG. 19 , a weighting factor to be applied to a reconstruction image by FFS actual projection data smoothly falls from “1” in the region close to the center and becomes “0” at the end of the peripheral region. 
     Although the weighting factor W′(P) is shown in a smooth curve that depends on the distance P from the image center in the example of  FIG. 19 , the weighting factor W′(P) is not limited to this and may be shown also in a straight line. 
     Referring to  FIG. 20 , the flow of the reconstruction computing process in the third embodiment will be described. 
     First, the reconstruction computing unit  127  obtains the boundary point P 0  of spatial resolution (Step S 801 ). The boundary point P 0  is obtained similarly to the first embodiment (Step S 601  of  FIG. 14 ). 
     Next, the reconstruction computing unit  127  generates an image reconstructed using actual data of FFS projection data and an image reconstructed using up-sampled projection data for which the FFS projection data was up-sampled (Step S 802 ). 
     The up-sampled projection data that may be used is that generated using any of the virtual view generation processes (A) to (D). 
     Next, the reconstruction computing unit  127  applies a weighting factor of a desired shape to each image and adds it (Step S 803 ). The weight is used for synthesizing an image reconstructed using actual data of FFS projection data and an image reconstructed using up-sampled projection data for which the FFS projection data was up-sampled at an appropriate rate so as to acquire desired spatial resolution in a desired region. 
     Then, the reconstruction computing unit  127  outputs an image generated by the process of Step S 803  (Step S 804 ). The output destination is, for example, the storage device  123 , the display device  125 , and the like. 
     As described above, the X-ray CT apparatus  1  of the third embodiment synthesizes an image reconstructed by actual data of FFS projection data and an image reconstructed by up-sampled projection data using a weighting factor that changes according to the distance from the scanning center in the image reconstruction computing process. 
     Hence, in addition to the effectiveness of the first embodiment, an image that becomes desired spatial resolution in a desired region in the image can be acquired. Also, a highly reliable image can be acquired in a desired region by increasing the weight of the actual data. 
     Fourth Embodiment 
     Next, referring to  FIGS. 21 and 22 , the fourth embodiment of the present invention will be described. 
     In the fourth embodiment, as shown in  FIG. 21 , the actual data  503  of FFS projection data is applied to the region of interest (ROI)  7  set by an operator and the central region  604 . Also, the up-sampled projection data  505  is applied to the peripheral region  603 . When the ROI  7  is in the peripheral region  603 , the actual data  503  of the FFS projection data is used for the range within the ROI  7 . 
     Referring to  FIG. 22 , the flow of the reconstruction computing process of the fourth embodiment will be described. 
     First, the system controller  124  and the region of interest (ROI)  7  are set (Step S 901 ). The setting of the ROI  7  is performed by an operator through the input device  121 . Next, the reconstruction computing unit  127  obtains the boundary point P 0  of spatial resolution (Step S 902 ). The boundary point P 0  is obtained similarly to the first embodiment (Step S 601  of  FIG. 14 ). 
     Next, the reconstruction computing unit  127  reconstructs an image using actual data of FFS projection data in the ROI  7  set in Step S 901  and the central region  604  or up-sampled projection data by a virtual view in the peripheral region  603  excluding the ROI  7  (Step S 903 ). 
     The up-sampled projection data that may be used is that generated using any of the virtual view generation processes (A) to (D). 
     The reconstruction computing unit  127  outputs an image generated by the process of Step S 903  (Step S 904 ). The output destination is, for example, the storage device  123 , the display device  125 , and the like. 
     As described above, the X-ray CT apparatus  1  of the fourth embodiment enhances the image reliability by reconstructing an image using actual data of FFS projection data in the ROI  7  and the central region  604 . Also, spatial resolution is improved using up-sampled projection data in the peripheral region  603  excluding the ROI  7 . Hence, it is possible to acquire an image whose reliability is high in a ROI to be diagnosed and the image center and whose spatial resolution of the periphery is improved. 
     Also in the fourth embodiment, the joint process shown in the second embodiment may be performed in the boundary region Q, and weighted addition may be performed for an image by FFS projection data and an image by up-sampled projection data using a weighting factor of a desired shape shown in the third embodiment. 
     Fifth Embodiment 
     Next, referring to  FIGS. 23 to 25 , the fifth embodiment of the present invention will be described. 
     As shown in  FIG. 23 , in the fifth embodiment, the reconstruction computing unit  127  synthesizes images reconstructed using FFS projection data of the number of respectively different views (the number of up-sampling) for the region  1002  from the center O to the distance P 1 , the region  1003  from the distance P 1  to the distance P 2 , and the region  1004  from the distance P 2  to the distance P 3  within the reconstruction image  1001 . For example, the number of views V 1  is set for actual data of FFS projection data in the region  1002 , FFS projection data up-sampled to the number of views V 2  is used in the region  1003 , and FFS projection data up-sampled to the number of views V 3  is used in the region  1004 . 
     When each image before synthesis of the regions  1002 ,  1003 , and  1004  is set as ξ(V 1 ), ξ(V 2 ), and ξ(V 3 ), the image ξ(V) after synthesis can be expressed in the following formula (6).
 
[Formula 4]
 
ξ( V )=ξ( V 1)+ξ( V 2)+ξ( V 3)  (6)
 
     The up-sampled projection data may be that generated using any of the virtual view generation processes (A) to (D) described in the first embodiment. 
     Also, as shown in the image  1001   a  of  FIG. 24 , the joint process may be performed so as to acquire continuous spatial resolution in the boundary portions between the region  1002  and the region  1003  and between the region  1003  and the region  1004 . The joint process is similar to the second embodiment. That is, the images ξ(V 1 ), ξ(V 2 ), and ξ(V 3 ) are reconstructed by projection data of each view number using the weighting factors W(V 1 ), W(V 2 ), and W(V 3 ) that change the spatial resolution continuously and smoothly before synthesizing the images in the boundary portions  1006  and  1007 . 
     The synthesized image ξ(V) can be expressed in the following formula (7).
 
[Formula 5]
 
ξ( V )= W ( V 1)ξ( V 1)+ W ( V 2)ξ( V 2)+ W ( V 3)ξ( V 3)  (7)
 
     Also, although there are three regions in the examples shown in  FIGS. 23 and 24 , the number is not limited to three and can be extended to n regions as shown in the image  1001   b  of  FIG. 25 . 
     The synthesized image ξ(V) can be expressed in the following formula (8).
 
[Formula 6]
 
ξ( V )= W ( V 1)ξ( V 1)+ W ( V 2)ξ( V 2)+ W ( V 3)ξ( V 3)+ . . . + W ( Vn )ξ( Vn )  (8)
 
     According to the fifth embodiment, up-sampled projection data of the number of views V 1  to Vn different depending on the distance P from the image center O can be used for synthesizing an image. Therefore, for example, spatial resolution can be increased by a desired amount in the peripheral region from the boundary point P 0  by appropriately increasing the number of up-sampling gradually as being farther from the image center O. Hence, spatial resolution can be uniformed over the entire image. Also, images of various qualities can be generated according to the diagnostic purpose by preferentially improving spatial resolution in a desired region. 
     Although the suitable embodiments of the X-ray CT apparatus related to the present invention are described above, the present invention is not limited to the above embodiments. It is apparent that a person skilled in the art could arrive at various modified examples or amended examples within the scope of the technical ideas disclosed in the present application, and it is understood that these naturally belong to the technical scope of the present invention. 
     DESCRIPTION OF REFERENCE NUMERALS 
       1 : X-ray CT apparatus 
       100 : scan gantry unit 
       101 : X-ray tube device 
       102 : rotary disk 
       103 : collimator 
       106 : X-ray detector 
       110 : focal shift X-ray controller 
       120 : operation console 
       121 : input device 
       122 : image computing device 
       123 : storage device 
       124 : system controller 
       125 : display device 
       126 : virtual view generation unit 
       127 : reconstruction computing unit 
       501 : FFS (+) projection data 
       502 : FFS (−) projection data 
       503 : FFS projection data (focal shift projection data) 
       505 ,  513 ,  515 ,  516 , and  518 : up-sampled projection data