Patent Application: US-21765008-A

Abstract:
the invention relates to a method for correcting truncation artifacts in a reconstruction method for computed tomography recordings . the projection images are recorded by an x - ray image detector being extended by determining the attenuation of the radiation outside the projection image for pixels . non - horizontal filter lines are extended by transaxial and axial artificial extension of the x - ray image detector for the purposes of truncation correction . the truncation correction for non - horizontal filter lines being carried out according to a method from at least one of the following groups : truncation correction takes place regardless of the specific location and orientation of the filter lines ; truncation correction takes place as a function of the specific position and orientation of the filter lines , with the filter lines themselves being retained ; and truncation correction takes place by introducing new modified filter lines , with filtering taking place along offset artificially extended filter lines .

Description:
fig8 shows the original projection with axial and transaxial truncation . in fig9 the x - ray image detector 4 has first been extended transaxially with the aid of hybrid correction , so that extension regions with attenuated transaxial continuation 17 result on both sides . in fig1 the x - ray image detector 4 has then been extended axially with the aid of hybrid correction , so that extension regions with attenuated transaxial continuation 18 result on both sides . the size of the extension regions can be configured freely in each instance and can be selected so that it is different for each detector side ( left , right , top , bottom ). further flexibility of the method means that steps b ) and c ) can be interchanged . fig1 shows the original projection with axial and transaxial truncation . in fig1 the x - ray image detector 4 has first been extended with the aid of hybrid correction so that extension regions with attenuated transaxial continuation 17 result on both sides . in fig1 the x - ray image detector 4 has then been extended axially by repeatedly copying and adding the first and last detector rows , so that extension regions with constant axial continuation 19 result on both sides . the size of the extension region can be configured freely in each instance and can be selected so that it is different for each detector side ( left , right , top , bottom ). the axial extension regions 19 should hereby be set so that no further filter lines are cut off . further flexibility of the method means that steps b ) and c ) can be interchanged . fig1 shows the original projection and a filter line f 3 , which is cut off axially on the left and transaxially on the right . curve 20 shows the corresponding projection profile p ( u ) for this filter line f 3 . in the supplemented curve 21 the profile has been continued on both sides by artificially generated projection values 22 by means of hybrid correction . the size of the extension region can be configured freely in each instance and can be selected so that it is different for each side of a filter line f 3 . fig1 shows the original projection , which has already been supplemented by extension regions with constant axial continuation 23 in the axial direction . in the curve 24 the projection profile p ( u ) of the filter line f 3 therefore only shows transaxial truncation . in the supplemented curve 25 the profile has been continued by artificially generated projection values 26 with the aid of hybrid correction . continuation 27 of the supplemented curve 25 results in the region of constant axial continuation 23 . the sizes of the extension regions for the x - ray image detector 4 and filter lines f 3 can be freely configured in each instance and can be selected so that they are different for each detector side ( top , bottom ) and for each side of a filter line f 3 . fig1 shows the original projection together with the projection of a water cylinder 28 . in the curve 29 the projection profile p ( u ) of the filter line f 5 only has transaxial truncation in this example . in the supplemented curve 30 the profile of the filter line f 5 has been continued by means of artificially generated projection values 31 , in that the filter line f 5 has been evaluated in this region along the projection of the water cylinder 28 . the corresponding projection values are artificially generated by computer - simulated x - ray beams . the center axis ( or rotation axis ) of the cylinder is oriented parallel to the z - axis of the reference coordinate system . the height of the cylinder is assumed to be infinite , so that only the point of intersection ( x , y , 0 ) of the center axis of the cylinder with the xy - plane and the radius r of the cylinder have to be determined . the three parameters ( x , y , r ) can be determined in that for example the measured projection values p ( u ) along the filter line f 5 and their first and second derivation in relation to u , p ′( u ) and / or p ″( u ) at a point u = u0 are determined . this gives the following equations for calculating ( x , y , r ): d ″( u 0 , x , y , r )* μ w = p ″ ( u 0 ). ( 3 ) here d refers to the sectional length of the x - ray beam with the water cylinder , d ′ and d ″ its first and second derivation in relation to u and μ w the attenuation coefficient of water . the procedure should be applied anew for each side of a filter line f 5 . the modified water cylinder correction differs from the original water cylinder correction in the use of cone - beam geometry . in the original method parallel beam geometry is used to generate the projection values , even though the original projections are acquired using cone - beam geometry . fig1 shows the original projection together with the original filter line f 3 and the modified filter line f 6 shown with a broken line . the curve 32 of the projection profile p ( u ) of the modified filter line f 6 only has transaxial truncation . in the curve 33 the profile has been continued with artificially generated projection values 34 with the aid of hybrid correction . the sizes of the extension regions for the filter lines can be freely configured in each instance and can be selected so that they are different for each side of a filter line . as a further variant it would be possible also to modify the filter line f 6 in the transaxial direction before the hybrid correction , for example by continuing this likewise horizontally as soon as it leaves the x - ray image detector 4 . the x - ray image detector 4 is artificially extended transaxially and axially . the extension is based on hybrid correction in each instance ( see example 1 ). the x - ray image detector 4 is artificially extended transaxially and axially . the transaxial extension is based on hybrid correction . the axial extension happens by means of constant continuation of the x - ray image detector 4 in the axial direction ( see also fig5 ), by repeatedly copying and adding the first and last detector rows ( see example 2 ). the filter lines are artificially extended in that the hybrid correction is carried out not along the detector rows as in the original method ( see also image 2 ) but along the filter lines ( see example 3 ). the filter lines are artificially extended , by constant continuation of the x - ray image detector 4 in the axial direction ( see also fig5 ) followed by hybrid correction along the filter lines ( see example 4 ). the filter lines are artificially extended , by carrying out a modified water cylinder correction along the filter lines ( see example 5 ). the filter lines are modified in such a manner that filtering takes place along offset filter lines . these are then artificially extended , by carrying out the hybrid correction along the offset filter lines ( see example 6 ). the filter part of the filtered backprojection consists of a one - dimensional linear filtering of the detector data . the data can be filtered by means of a convolution operation in real space . alternatively a convolution operation in real space can be replaced by a multiplication in reciprocal space . with single - row detectors it is clear that the whole detector row is dealt with in one filter step . in the case of multi - row detectors ( surface detectors ) data has to be found for the one - dimensional filter step . the data to be filtered is collected along one filter line . the data along one filter line can either be convoluted in real space or multiplied in reciprocal space . it should be noted that only the part of real space along a filter line is transformed to reciprocal space with a one - dimensional fourier transformation . these relationships are basic knowledge in specialist circles , so they have not been explained in the application . the selection of the filter lines is a function of the reconstruction problem and the reconstruction algorithm used . the frequently applied feldkamp algorithm described in [ 1 ] filters the detector data one - 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