with initial reference to fig6 and 7 , a computed tomography ( ct ) imaging system 10 includes a gantry 12 representative of a “ third generation ” ct scanner . gantry 12 has an x - ray source 13 that projects a cone beam of x - rays 14 toward a detector array 16 on the opposite side of the gantry . the detector array 16 is formed by a number of detector elements 18 which together sense the projected x - rays that pass through a medical patient 15 . each detector element 18 produces an electrical signal that represents the intensity of an impinging x - ray beam and hence the attenuation of the beam as it passes through the patient . during a scan to acquire x - ray projection data , the gantry 12 and the components mounted thereon rotate about a center of rotation 19 located within the patient 15 . the path y ( t ) of the x - ray source 13 is thus a circular arc . the rotation of the gantry and the operation of the x - ray source 13 are governed by a control mechanism 20 of the ct system . the control mechanism 20 includes an x - ray controller 22 that provides power and timing signals to the x - ray source 13 and a gantry motor controller 23 that controls the rotational speed and position of the gantry 12 . a data acquisition system ( das ) 24 in the control mechanism 20 samples analog data from detector elements 18 and converts the data to digital signals for subsequent processing . an image reconstructor 25 , receives sampled and digitized x - ray data from the das 24 and performs high speed image reconstruction according to the method of the present invention . the reconstructed image is applied as an input to a computer 26 which stores the image in a mass storage device 29 . the computer 26 also receives commands and scanning parameters from an operator via console 30 that has a keyboard . an associated cathode ray tube display 32 allows the operator to observe the reconstructed image and other data from the computer 26 . the operator supplied commands and parameters are used by the computer 26 to provide control signals and information to the das 24 , the x - ray controller 22 and the gantry motor controller 23 . in addition , computer 26 operates a table motor controller 34 which controls a motorized table 36 to position the patient 15 in the gantry 12 . the above - described ct system is designed to rapidly perform a full - scan in which the x - ray source revolves in a circular arc completely around the subject being imaged . the present invention may be employed in such a ct system , but because the invention may also be employed in short - scans and super - short - scans , it is particularly useful when used with a c - arm x - ray system depicted in fig1 . referring particularly to fig1 , the c - arm x - ray system includes a c - arm 60 to which the two - dimensional detector 16 and the x - ray source 13 are mounted . here , again the patient 15 is positioned on a table 62 that extends between the source 13 and the detector 16 . the c - arm is rotationally mounted to a base 64 , and cone beam data is acquired by rotating the x - ray source 13 and detector 16 around a defined axis 66 . c - arm scanners are particularly useful in image - guided interventions and they are characterized by scans in which the x - ray source and detector are rotated over a very short arc . as shown best in fig1 a , in the preferred embodiment of the present invention the detector array 16 is a flat array of detector elements 18 , having n r ( e . g . 1024 ) elements 18 disposed along the in - plane ( x , y ) direction , and n z ( e . g . 1024 ) elements 18 disposed along the z axis . the x - ray beam emanates from the x - ray source 13 and fans out as it passes through the patient 15 and intercepts the detection array 16 . each acquired view is a n r by n z array of attenuation measurements as seen when the gantry is oriented in one of its positions during the scan . as shown in fig1 b , the object of the present invention is to reconstruct a set of 2d image slices 35 from the 3d array of acquired data produced by the x - ray cone beam during the scan . it can be seen that because the cone beam diverges as it passes through the patient 15 , the accurate reconstruction of the parallel image slices 35 is not possible with a straight forward fan beam filtering and backprojection process . the present invention enables an accurate reconstruction of the image slices 35 from this acquired cone beam data . in addition , the present invention enables the accurate reconstruction of image slices 35 even when the circular path of the x - ray source 13 is less than a complete circle . this reconstruction method is implemented in the image reconstructor 25 . referring particularly to fig1 , the cone beam projection data is received from the das 24 as a two - dimensional array of values which are preprocessed in the standard manner at process block 40 . such preprocessing includes correcting for known errors and offsets and calculating the minus log of the data to convert it to x - ray attenuation values . the preprocessed cone beam attenuation profiles g ( u , v , t ) are then modified by calculating the weighted derivative g ( u , v , t ) as indicated at process block 42 . this is performed as set forth above in eq . ( 16 ). the 1d hilbert filter of the weighted derivative of the cone beam data g ( u , v , t ) is then computed as set forth above in eq . ( 28 ) to produce filtered cone beam data sets q 1 ( ū , v , t ), q 2 ( ū , v , t ) and q 3 ( ū , v , t ) as indicated at process blocks 44 , 46 and 48 . as indicated by process blocks 50 , 52 and 54 these filtered cone beam data sets q 1 ( ū , v , t ), q 2 ( ū , v , t ) and q 3 ( ū , v , t ) are each backprojected as set forth above in eq . ( 27 ) and the backprojected data is summed as indicated at process block 56 to produce a 3d image f ( x ). the desired 2d image slices 58 are produced from the 3d image and output to computer 26 . the present invention is valid when the x - ray source arc covers an angular range of 180 °+ fan angle , namely a short scan mode . the backprojection segments t 1 , t 2 , t 3 is correspondingly changed for each image voxel . the present invention is also valid even if the source arc is shorter than 180 °+ fan angle . this is a super - short scan mode . a number of variations are possible from the preferred embodiment described above . the differentiations in preweighted data may be computed using a fast fourier transform ( fft ) method . also , the hilbert convolution process may be implemented using an fft method . parameters such as source to detector distance , source to isocenter distance , the source to image point distance may be measured in a geometrical calibration process and incorporate into the method . the convolution process may be implemented using either a horizontal detector coordinate or vertical coordinate . the convolution procedure may be numerically implemented by combining the convolution procedure in terms of horizontal coordinate and in terms of vertical coordinate . the present invention may be applied to a curved detector and circular source trajectory . it should be apparent to those skilled in the art that the convolution procedure may be numerically implemented by combining the convolution procedure in terms of horizontal coordinate and in terms of vertical coordinate . the present invention may also be applied to a curved detector and circular source trajectory . the present invention may be utilized to reconstruct an image for other clinical applications such as radiation therapy where an x - ray source and a flat - panel imager slowly rotates around the patient . while the invention is most advantageously applied to cone beam data sets , the present invention may also be utilized to reconstruct fan - beam ct images . this is the case of nz = 1 .
an image reconstruction method for cone beam x - ray attenuation data acquired over a super - short - scan , short - scan or full - scan includes backproejcting over three adjacent segments of the arc traversed by the x - ray source . each backprojection consists of a weighted combination of 1d hilbert filtering of the modified cone - beam data along both horizontal and non - horizontal directions .