reference is now made to fig1 which shows a ct scanner 20 , operative in accordance with a preferred embodiment of the present invention . scanner 20 comprises a bed 24 , supported by a base 26 , on which bed a subject 22 lies while his body is being imaged by the scanner . scanner 20 further comprises an x - ray tube 28 , which irradiates subject 22 , and a detector array 30 , which receives x - rays from tube 28 and generates signals responsive to the attenuation of the x - rays in passing through the subject &# 39 ; s body . preferably , array 30 comprises multiple , parallel rows of x - ray detector elements 23 . tube 28 and array 30 are mounted on an annular gantry 32 , so as to rotate about subject 22 . simultaneously , bed 24 is advanced through gantry 32 along axis 34 , which is generally parallel to the long axis of the subject &# 39 ; s body . scanner 20 as pictured in fig1 is of a type known in the art as a third - generation ct - scanner , characterized in that both tube 28 and detector array 30 rotate about subject 22 . it will be appreciated , however , that the principles of the present invention and the methods of image reconstruction to be described below are equally applicable to other types of ct scanners , for example , fourth - generation ct scanners , which include annular detector arrays that are generally rotationally stationary , while the x - ray tube rotates about the subject . scanner 20 may be configured so that axis 34 is substantially perpendicular to the plane of rotation of gantry 32 . additionally , axis 34 may preferably be angled relative to the gantry plane , for example , by swiveling bed 24 horizontally , in a direction indicated by arrow 33 , and / or by tilting gantry 32 about a generally horizontal tilt axis in a direction indicated by arrow 35 . preferably , the tilt and swivel angles are controlled by a system control unit 46 , which also regulates the rotation of the gantry and the advance of the bed . for clarity in the following discussion , we identify two sets of cartesian coordinate axes 38 in fig1 : rotating , gantry - fixed axes x , y , z , indicated by dashed arrows , and bed - fixed axes x ′, y ′, z ′, indicated by solid arrows . the z - axis is substantially the axis of rotation of gantry 32 and is fixed in space . the y - axis points from the center of rotation of the gantry to tube 28 and rotates therewith , and the x - axis is , therefore , generally parallel to the long axis of array 30 . the z ′- axis is parallel to bed axis 34 . axis y ′ points vertically upward , parallel to the swivel axis ( if any ) of bed 24 , and axis x ′ is thus generally horizontal . axis z ′ is angled relative to axis z by a two - dimensional angle θ , which takes into account both the tilt of gantry 32 and the swivel of bed 24 . the angle of rotation of the gantry φ is taken to be zero when tube 28 is at its uppermost rotational position . as tube 28 rotates and bed 24 advances , the tube describes a generally spiral path around axis 34 . preferably , bed 24 moves with substantially constant velocity , so that the spiral path has a constant pitch . at each “ view ,” i . e ., at each of a plurality of selected locations of tube 28 along this path , data acquisition circuitry 36 acquires a matrix of attenuation signals . the elements of this matrix are signals received from each detector element 23 of array 30 responsive to x - ray attenuation along a ray from tube 28 to the detector element . each such matrix may comprise a plurality of rows , wherein each such row corresponds to signals received at one of the plurality of views from one of the multiple rows of array 30 . for each view , data acquisition circuitry 36 performs signal normalization and logarithm operations , as are known in the art , to derive an x - ray attenuation value corresponding to each of elements 23 . image reconstruction circuitry 40 receives these values and performs interpolation and other data processing operations , as will be described below , to convert the views acquired during the helical scan into corrected , planar image slices at desired positions along the z - axis . these planar image slices may then be used to reconstruct three - dimensional or other ct images of the body of subject 22 , using methods known in the art . preferably , these images are stored in image memory 42 , displayed by display unit 44 , and may be otherwise printed and / or processed as is known in the art . the data and / or images may also be stored for later reconstruction and or display . fig2 a schematically represents the positions and detection areas of detector elements 23 in array 30 in two views , labeled “ view 1 ” and “ view 2 .” the two views are acquired at the same effective rotational angle of gantry 32 , i . e ., at rotation angles φ = 0 ° and φ = 360 °, respectively . ( the same results apply for φ = 180 ° and φ = 540 °. in the description that follows and in the claims , two views will be said to be acquired at the same effective rotational angle when they are acquired at gantry positions separated by an integer number of full , 360 ° rotations , for the case of 360 ° reconstruction , or by an integer number of half , 180 ° rotations , for 180 ° reconstruction . for simplicity of explanation , array 30 is shown as having only two parallel rows 27 and 29 of detectors 23 , each row comprising m detector elements 23 , labeled d 11 . . . d 1m and d 21 . . . d 2m respectively . gantry 32 is assumed to be tilted by angle θ relative to bed 24 , while the swivel angle of bed 24 is substantially zero . it will be understood , however , that the principles of the method to be described below are equally applicable to multi - slice arrays having greater or lesser numbers of rows , and to configurations of scanner 20 in which bed 24 has a non - zero swivel angle . similarly , the method applies generally for any rotational angle θ of tube 28 , as will be shown below . in an exemplary embodiment of the invention , to acquire a matrix of attenuation signals for the first of the two views , view 1 , the bed 24 is advanced through gantry 32 so that array 30 is centered at a position marked z 1 in the figure . as the bed continues to advance in the positive z ′- direction , gantry 32 makes a complete , 360 ° revolution about the bed . the gantry returns to the rotational position that it held in view 1 when the array is centered at position z 2 , where the signal matrix for view 2 is acquired . because view 1 and view 2 are acquired at the same effective rotational angle φ = 0 , and zero swivel angle , the positions of rows 27 and 29 in the two views , as shown in fig2 a , are mutually substantially aligned . a planar image slice is to be reconstructed in a plane parallel to the rotation plane of gantry 32 , at the position marked z 0 . in the situation illustrated by fig2 a , there is no view acquired that includes a row 27 or 29 centered at z 0 . a corrected slice at this position is reconstructed by choosing and interpolating between a plurality of effective detection points around a periphery of the corrected slice , at a radial distance from the z - axis that is generally equal to the distance of the detection points in rows 27 and 29 of array 30 from the z axis . an effective attenuation value is determined at each of the points by interpolating between the x - ray attenuation data received from two or more elements 23 in different rows 27 and 29 and / or in different views , view 1 and view 2 . the effective attenuation at each of the plurality of points corresponds , in close approximation , to the attenuation that would be measured along a line in the x - y plane from x - ray tube 28 to the point . for example , to determine an effective attenuation value at a point 50 , which is located on the periphery of the slice at z 0 , at a displacement r along the x axis as shown , a weighted sum is taken of data input from element d 2i in view 1 and data input from its adjacent element d 1i in view 2 . generally the weighting factors for the two input elements will vary inversely with the relative distances of the respective centroids of the two elements from point 50 . these weighting factors will generally be the same , however , for all points ( at varying values of r ) along the periphery of the slice at position z 0 . if the fan beam data is rebinned into parallel beam data an adjustment of the weighting for different positions on the fan may be desirable . however , such adjustments generally quite small . in alternative embodiments of the present invention , greater numbers of input elements may be included in the weighted sum to determine the effective attenuation value at point 50 , so as to improve the quality of the image , using z - axis weighting or filtering methods known in the art . furthermore , the attenuation data from array 30 may be reformatted , as is known in the art , from the fan beam format in which the attenuation signals are received , as exemplified in fig1 to a parallel beam format , for the purpose of improving the quality of the resultant ct image . it will be understood that the methods described herein with reference to elements 23 and the unreformatted data received are preferably applied to such reformatted data samples . although point 50 at position z 0 is shown in fig2 a as being midway between rows 27 and 29 , it will be understood that the method described above may be applied to determine effective attenuation values at any z - position in between rows 27 and 29 or within the detection area of one of the rows . in the particular case in which the z - position of point 50 is substantially centered within one of the rows , the effective attenuation value at the point is preferably derived directly from the attenuation data in that row . alternatively , the effective attenuation value may be calculated by taking a weighted average of the data in the row within which point 50 is centered with data from neighboring rows on either side thereof . fig2 b schematically represents the positions of detector elements 23 in the same configuration of scanner 20 as in fig2 a , i . e ., with tilt angle θ . two views , labeled view 1 ′ and view 2 ′, are acquired in the manner described above regarding view 1 and view 2 , with tube 28 taken to be at rotational angles φ = 90 ° and φ = 450 °, respectively . viewed from this substantially horizontal view angle , the z - axis of gantry 32 is seen to be tilted with respect to the z ′- axis of bed 24 , and the positions of elements 23 of array 30 in the two views are mutually offset along the x - axis . moreover , since bed 24 has advanced along the z ′- axis direction relative to its position in view 1 and view 2 , the x - axis , coinciding with the plane of the image to be reconstructed , is shown in fig2 b as having shifted in the z ′- direction . for the purposes of the description that follows , we note further in fig2 b that elements 23 of array 30 are taken to have a common pitch p . each of the two rows 27 and 29 of array 30 has a respective longitudinal axis passing substantially through the centroids of the elements in the row , which axes are marked 5 θθ 2 a and 54 a respectively for view 1 ′, and 52 b and 54 b respectively for view 2 ′. bed 24 advances through gantry 32 at a velocity v , and the period during which the gantry makes a complete , 360 ° rotation is δt , so that between view 1 ′ and view 2 ′, array 30 advances by a distance δz ′ along the z ′- axis , as shown in fig2 b , given by δz ′= v · δt . in the plane of the gantry , the distance is δz = v · δt cos θ . fig3 is a flow chart illustrating a method for calculating effective attenuation values in a planar image slice in the x - y plane , generally perpendicular to the rotation axis of gantry 32 , in accordance with a preferred embodiment of the present invention . the key steps in this method involve taking a plurality of effective detection points in the periphery of the plane , as described above , and then selecting and calculating appropriate input data from elements 23 to determine the effective attenuation values at each of the plurality of points . the process of selecting and calculating the effective attenuation values is repeated at each of a plurality of gantry rotation angles φ . for each rotation angle , at least two attenuation signal matrices , from respective views at angles φ and φ + 360 ° ( or φ and φ + 180 ° in the case of 180 ° reconstruction ), are used in the calculation . in order to avoid the creation of image artifacts , for each angle it is generally necessary to select different input elements to correspond to each effective detection point and to determine appropriate weighting factors to use in interpolatively calculating the effective attenuation values at the points . for example , when φ = 90 °, as shown in fig2 b , image reconstruction circuitry 40 receives the coordinates of rows 27 and 29 in view 1 ′ and view 2 ′ from system control unit 46 ( shown in fig1 ). the circuitry compares the z - axis position of the plane for reconstruction , marked by the x - axis , with the positions of rows 27 and 29 to determine which of axes 52 a , 54 a , 52 b and 54 b is closest to the plane . in the case shown in fig2 b , axis 52 b in view 2 ′ is the closest . if two axes are equidistant from the plane , then either may be chosen as the closest , and the remainder of the calculation is substantially unaffected . next the circuitry determines which of the remaining row axes is the next closest to the point . for some rotation angles φ , the next closest axis is from the same view as the closest axis . such would be the case , for example , with regard to a plane passing through point 56 in fig2 b , for which axis 54 b is the next closest . the corrected attenuation value at point 56 is then determined simply by weighted interpolation between elements d 1 , k and d 2 , k , with the weighting factors dependent on the relative distances of axes 52 b and 54 b from point 56 . returning now to consider point 55 on the x - axis , the next closest axis after axis 52 b is axis 54 a of row 29 in view 1 ′. element d 2 , k + 2 in view 1 ′ is closest to point 55 in its detection area , but the border between this element and its neighboring element in array 30 , d 2 , k + l , is offset relative to the borders between element d 1 , k and its neighboring elements in view 2 ′. in order to avoid producing artifacts in the image that is reconstructed by circuitry 40 , an effective row element attenuation value is calculated by weighted interpolation between the attenuation values of elements d 2 , k + 1 and d 2 , k + 2 in view 1 ′. weighting factors for this interpolation are calculated based on the relative offset of elements 23 of array 30 between view 1 ′ and view 2 ′. this effective row element attenuation value is then combined by weighted interpolation with the value of the first input element ( in this case d 1 , k in view 2 ′) to compute the effective attenuation value at point 55 . the following formula is a general expression for calculating the effective row element attenuation value v eff for the case where the first element d 1 , k is from view 2 ′ and v eff is to be determined by interpolation among the attenuation values v 2 , i and v 2 , i + 1 received respectively from two elements d 2 , i and d 2 , i + 1 in view 1 ′: v eff = v 2 , k for m − 1 − δ z ′· sin θ / p ≦ k & lt ; m − 1 v eff = w m v 2 , m + w m + 1 v 2 , m + 1 for 0 ≦ k & lt ; m − 1 − δ z ′· sin θ / p where m = int [ k + δz ′· sin θ / p ], and w m and w m + 1 are interpolation weighting factors , and int ( x ) is the greatest integer in x . although for the specific case illustrated in fig2 b , θ = θ , where θ is the tilt angle of bed 24 , the formulas above may be generalized to include both the swivel angle of bed 24 and the tilt angle of gantry 32 by substituting : preferably , the weighting factors w m and w m + 1 are calculated for linear interpolation , for example by the following formulas : w m = δz ′· sin θ / p − int ( δ z ′· sin θ / p ) alternatively , the weighting factors may be calculated using a shift function , for example : w m = int { 0 . 5 + δ z ′· sin θ / p − int ( δ z ′· sin θ / p )} other weighting factors may similarly be used , such as , but not limited to utilizing more elements per row , depending , inter alia , on geometrical considerations in the ct scanner . similar formulas may be straightforwardly derived from the above equations for cases in which the first element ( i . e ., the element nearest to the point of interest in the planar corrected slice ) is in view 1 ′, and an effective row element attenuation value must be determined by interpolation between elements in the preceding view 2 ′. in other preferred embodiments of the present invention , effective row attenuation values are calculated for the row whose axis is nearest the plane of the planar corrected slice , as well as for the row whose axis is next - nearest the plane . in this case , for example , an effective row attenuation value for row 27 could be calculated with respect to point 55 by weighted interpolation between elements d 1 , k and d 1 , k − 1 in view 2 ′. the value would then be combined by weighted interpolation with the value of v eff determined for row 29 in view 1 ′, as described above , to calculate the effective attenuation value for point 55 . additionally or alternatively , in some preferred embodiments of the present invention , data from more than two rows may be combined by interpolation to determine effective attenuation values for a planar corrected slice . for example , data from both of rows 27 and 29 in both view 1 ′ and view 2 ′ could be thus combined , and data from additional views at φ =+ 360 · n ° ( or + 180 − n ° for 180 degree reconstruction ) could also be introduced , in determining the effective attenuation value for point 55 . in these preferred embodiments , the respective offset of each of the rows is taken into account , and interpolative weighting factors are calculated accordingly , based on the principles described above . it will be appreciated that although the above preferred embodiments have been described , for simplicity , in terms of a two - slice scanner , based on detector array 30 having two rows of elements 27 and 29 , the principles of the present invention are equally applicable to single - slice scanners , as well as to multi - slice scanners and arrays having three , four or more rows of elements . furthermore , the above preferred embodiments have been described with reference to 360 ° image reconstruction , in which the planar corrected slice is produced by interpolating between two views taken at adjacent positions of x - ray tube 28 , between which the tube has made a full circle of rotation around bed 24 . it will be appreciated , however , that the inventive principles described above may similarly be applied to 180 ° image reconstruction systems , as are known in the art . in such systems , the effective attenuation values are calculated from data acquired in two views that are 180 ° apart . generally , an additional offset is introduced between array elements 23 in the two views , and the formulas given above for calculating v eff are preferably corrected to account for this offset . it will also be appreciated that while the above preferred embodiments have been described with regard to medical ct imaging system 20 , which is pictured as a third - generation system , forming an image of the body of human subject 22 , the principles of the present invention may similarly be applied to fourth - generation and other types of ct imaging systems for medical and non - medical purposes . it will additionally be appreciated that the preferred embodiments described above are cited by way of example , and the full scope of the invention is limited only by the claims .
a method for reconstructing images of a subject in a variable - angle helical - scan ct scanner including an x - ray tube , a detector array , and a bed , the method comprising : angling the translation axis and the rotation axis at an acute angle relative to one another ; rotating the x - ray tube about the rotation axis while translating the bed along the translation axis through a plane of rotation of the tube , whereby the x - ray tube describes a helical path relative to the subject ; acquiring first and second views of the subject at the same effective rotational angle about the axis of rotation , said views comprising x - ray attenuation data received from elements of the array ; producing a planar corrected image slice by interpolation of the data in different views , wherein the data is generated by non - corresponding elements in the different views ; and repeating the above steps at respective positions at a plurality of rotational angles of the x - ray tube .