fig1 shows an inventive ct system 1 with an x - ray tube 2 and an opposing multiline radiation detector 3 . the two are mounted on a gantry ( not visible here ) in a gantry housing 6 . for examination the patient 7 is pushed on a movable patient couch 8 along the system axis 9 , through the opening between detector 3 and radiation source 2 , while the radiation source 2 and detector 3 rotate around the system axis and scan the patient 7 . the ct system 1 is controlled by a control and arithmetic - logic unit 10 which has a memory 11 in which computer programs prg 1 to prg n are stored which during operation assume control of the system and also execute the inventive method with respect to scattered radiation correction and hardening correction . in fig2 a water layer with a thickness dh 2 o / cm and that has been penetrated by radiation is plotted on the abscissa and the curve 12 represents the relationship between this water layer thickness with irradiation by x - radiation with a beam potential of 120 kv in relation to the ratio , plotted on the ordinate , of scattered radiation to primary radiation s / p . as may be seen from this figure a ratio of 1 can be calculated even with a water thickness of about 25 cm . fig3 shows the dependency of the scattered radiation on the material sequence , based on the two materials water and bone . the coordinate relative to a central detector line is indicated on the abscissa while the scattered radiation intensity i s is plotted on the ordinate in arbitrary units . the curve 13 shows the characteristic of the primary radiation over the detector which turns out to be almost trapezoidal . the curves 14 and 15 show the scattered radiation produced by the primary radiation , the curve 14 reproducing a scattered radiation intensity profile which corresponds first of all to 20 cm water and then 5 cm bone during irradiation with 70 kv x - radiation , while the curve 15 corresponds to the intensity profile of the scattered radiation during irradiation of first of all 5 cm bone and then 20 cm water . the fundamental mathematical operators were generally formally stated in the introduction . the individual operations and variants thereof will be described in more detail hereinafter . fig4 schematically shows the inventive segmented , vectorized reprojection . the figure illustrates a measuring beam 22 which , issuing from an x - ray source 23 , penetrates a patient 7 en route to a detector 3 . on the one hand the patient has structures made of soft tissue 7 . 1 and structures made of bone tissue 7 . 2 . the measuring beam 22 thus penetrates a large number of voxels which comprise different material components . these voxels are consecutively numbered in the beam direction and denoted by the subscript j . they have the following meanings : f j = mean gray scale value in voxel j corresponding to the mean linear attenuation coefficient of the voxel , where α w or α k denote the mass attenuation coefficient in [ cm 2 / g ] in the case of a specific reference energy of the radiation that is to be advantageously selected . the soft part coverage and bone coverage in [ g / cm 2 ] required for the hardening correction and the scattered radiation correction then results in : the vector λ generally represents a combination of three vectors v w , v k , l , where : a single scalar variable can moreover be formed for example in the following way and is capable of at least sweepingly taking account of the dependency of the distribution of bone along the measuring beam relative to the distribution of soft tissue in the scattered radiation correction . the following variables are used for this purpose : the voxel coordinates of the centre of the voxel j along the measuring beam where j = 1 for designating the first voxel which belongs to the object , or of which the hu value corresponds to soft tissue or bone focal points of the “ soft part voxel ” or “ bone voxel ” along the measuring beam : the following scalar variable λ , which lies between − ½ and + ½ , estimates the relative asymmetry in the distribution of the bone along the measuring beam compared with the soft part focal point : the following procedure is proposed by way of example for the two - component hardening correction : theoretically the following applies to the polychromatic projection data , which constitutes logarithmized , standardized primary intensities (= primary attenuations ), at the spectrum q ( e ) in the case of two radiologically different materials with the mass attenuation coefficients α w ( e )=( μ w / ρ w )( e ) and α k ( e )=( μ k / ρ k )( e ) as a function of the mass coverage densities b w or b k [ g / cm 2 ] which penetrates the x - ray : the effective energy spectrum q ( e ) of the radiation can be assumed to be known . q ( e ) includes the emission spectrum of the x - ray tube , the effect of spectral filters and the energy - dependent detector response sensitivity . in other words , the function h ( b w , b k ) can basically be calculated in advance as a function of the mass coverage thickness ( b w , b k ) or it can be determined from experiments . the two - component hardening vector accordingly consists in estimating from an existing , if still incorrect , ct ( volumetric ) image by segmented reprojection the two mass coverages b w and b k and then converting the existing polychromatic projection values into idealized monochromatic values for a reference energy e ̂ that is to be stipulated . the idealized monochromatic projection values are h mono ( b w , b k )= α w ( e ̂) b w + α k ( e ̂) b k and the two - component hardening correction for a polychromatic projection value g ˜ is then by way of example a generalization of the “ folding model ” outlined in the already - cited document m . zellerhof , b . scholz , e .- p . rührnschopf , t . brunner : “ low contrast 3d reconstruction from c - arm data ”, proceedings of spie . medical imaging 2005 , vol . 5745 , pp . 646 to 655 will be given below . even with the same attenuation of the x - radiation , i . e . with the same standardized primary intensity p of the radiation , the scattered radiation depends on the material composition and the sequence in the beam path . the information on two material components , usually water and bone , and their position can be considered in all methods considered here . since the scattered radiation distribution is relatively smooth , the estimation model can be reduced to a highly simplified pixel grid in order to reduce calculation complexity . in the above - cited folding model the scattered radiation distribution is estimated using the following approaches : s ( x , y )=└ pe − p c ( p )┘** g ( x , y ) where p ( x , y ) is the estimation for standardized primary radiation distribution , and g ( x , y ) is a two - dimensional folding core which empirically describes the low - pass filtering ( smearing ) caused by the scattered radiation propagation . s ( x , y )=[ p q e − p c ( p )]** g ( x , y ) can be used , wherein the exponent q should be applied point - by - point to the function p = p ( x , y ). as a rule q & gt ;= 1 and can be empirically determined as a function of the mean path length , for example the mean of the variable b 0 ( p ) described below via the projection image . this more general approach corresponds to the first - mentioned approach when q = 1 . c ( p ) is a “ calibrating weighting function ” where : ca ( p )= c ( b 0 ( p ); u , f yz , a , . . . ). this weighting function describes the ratio of scattered intensity to primary intensity s / p for standard bodies , for example homogeneous plates or elliptical cylinders , as a function of the layer thickness ( b 0 ( p ) of water - equivalent material . this layer thickness can be clearly determined from the logarithmized primary attenuation p =− ln ( p ) based on the known hardening correction — a “ water correction . c also depends on the following physical acquisition parameters : potential u , radiation filter , collimated field size f yz of the detector , scattered radiation grid , air gap a , etc . c can in practice be calculated in advance by means of monte carlo calculations and be stored as a table or function . with fixed acquisition parameters c is only dependent on one variable , namely the water - equivalent layer thickness b 0 ( p ). using the weighting function c a simplified scattered radiation correction is obtained within the inventive iteration loop , a water - equivalent path length , derived from the estimated radiation attenuation and represented by p , and therefrom in turn a scatter fraction s / p via the tabulated weighting function c , being used and iteratively improved . the proposed generalization lies in the weighting function c being dependent not only on a material variable , the water layer thickness , but having to be worked out from at least three variables b w and b k and λ . in the simplest case λ is a parameter which describes the asymmetry of the position of the center of gravity of the bone compared with soft tissue in the beam path and the following applies : c = c ( b w , b k , λ ; u , f yz , a , . . . ). the current values of the two material thicknesses b w and b k and λ are re - produced with each iteration step . these may then be used as new input values in the multi - parameter weighting table c to obtain an iteratively improved estimation of the scattered radiation . fig5 can be used to describe a simple linear application of the parameter λ . this figure shows the dependency of the scatter fraction s / p on the position of a bone layer 5 cm thick relative to a water layer 20 cm thick . the ratio of scattered radiation to primary radiation s / p is plotted on the ordinate and the spacing of the bone layer from the base of the entire layer of water and bone penetrated by radiation is plotted on the abscissa . the value λ corresponding hereto is also plotted . the four curves 16 to 19 still differ in the x - ray spectra corresponding to the x - ray voltages of 70 kv and 120 kv and in the assumed bone density ( ρ k = 1 . 0 or 1 . 5 g / cm 3 ). the curve 16 corresponds to the scatter fraction characteristic at a radiation of 120 kvp and a bone density of 1 . 5 g / cm 3 . the curve 17 corresponds to the scatter fraction characteristic at a radiation of 70 kvp and a bone density of 1 . 5 g / cm 3 . the curve 18 corresponds to the scatter fraction characteristic at a radiation of 120 kvp and a bone density of 1 . 0 g / cm 3 . the curve 19 corresponds to the scatter radiation characteristic at a radiation of 70 kvp and a bone density of 1 . 0 g / cm 3 . the curves 20 and 21 show the corresponding values only for water without bone at 120 kvp and 70 kvp . the direction of irradiation is from above , i . e . with an abscissa value of 20 cm the bone layer is penetrated on top and is penetrated first by the radiation . the curves 16 to 18 are slightly bent but for simplification interim values can be obtained in a first approximation by a linear interpolation . an improved approximation can in principle be achieved by parabolic or cubic interpolation . if , for example , curve 17 is examined for 70 kv and ρ k = 1 . 5 g / cm 3 , actual values of l k = 5 cm , l w = 20 cm and b k / l k = ρ k = 1 . 5 g / cm 3 result from segmented reprojection . for − 0 . 5 & lt ;= λ & lt ;= 0 . 5 the scatter fraction s / p is then calculated by means of linear interpolation , so s ( λ ) is designated s + = s / p for the extreme position of the bone close to the source in front of water where λ =− 0 . 5 , s − = s / p for the extreme position of the bone close to the detector behind water where λ = 0 . 5 , and if b k / l k = ρ k is neither 1 . 5 nor 1 . 0 g / cm 3 but lies therebetween , s ( λ ) should be determined for ρ k = 1 . 5 and 1 . 5 g / cm 3 and then interpolated between the two results . to cover the diversity of possible bone - water combinations , series of monte carlo calculations can be carried out in advance to determine and tabulate s / p at least for the extreme values of s + and s − for combinations of water and bone thicknesses ( l w , l k ) or , more generally , water and bone coverages ( b w , b k ). alternatively a monte carlo method or an analytical scatter model may be used . basically it is also possible to directly calculate the scattered radiation distribution in each iteration step by a monte carlo method from the current voxeled volumetric image f ( n ) . however the monte carlo simulation is still very time - consuming even with today &# 39 ; s computers . a further possibility is the deterministic or analytical calculation of scattered radiation of the first order from the current voxeled volumetric image f ( n ) by taking overall account of the contribution of higher scatter orders known from the document y . kyriakou , t . riedel , w . a . kalender : “ combining deterministic and monte carlo calculations for fast estimation of scatter intensities in ct ”, phys . med . biol . 51 ( 2006 ), pp . 4567 to 4586 . but this analytical method is also relatively complex since multi - dimensional integrals have to be numerically evaluated . the scattered radiation correction algorithms s corr will be discussed hereinafter . these involve formulae ( subtractive or multiplicative ), as are mentioned for example in the document m . zellerhof , b . scholz , e .- p . rührnschopf , t . brunner : “ low contrast 3d reconstruction from c - arm data ”, proceedings of spie . medical imaging 2005 , vol . 5745 , pp . 646 to 655 . the subtractive form consists in the subtraction of the estimated scattered radiation intensity from the respective uncorrected , standardized intensity distribution p ( n + 1 ) ( x , y )= i ′( x , y )− s ( n ) ( x , y ), to avoid physically meaningless negative values a multiplicative scattered radiation correction can be used instead of the subtractive correction . the following applies in this connection : for the event s ( n ) ( x , y )& lt ;& lt ; i ′( x , y ) the multiplicative correction changes to the subtractive correction . explicit reference is made to the fact that with the above - given illustration only a combination of two different material components , in this case soft tissue (≅ water ) and bone , have been explicitly disclosed without limiting the generality . however , the mathematical formulization readily allows a generalization to more than two components , for example soft tissue , bone and contrast medium . according to the invention a different number of components may also be used in the hardening correction and scattered radiation correction . however it is more advantageous with the hardening correction , which is a local effect , to take account of the larger number of different material components and their position than it is absolutely necessary with the scattered radiation correction , which is a far - reaching effect . it is understood that the above - mentioned features of the invention can be used not only in the respectively given combinations but also in other combinations or alone without departing from the scope of the invention .
the invention relates to a method for combined bone hardening and scattered radiation correction in x - ray computed tomography of a heterogeneous object with a ct system comprising an x - ray source moved around an object , a flat detector with a large number of distributed detector elements which detect measuring beams from a focal point of the x - ray tube , and a control and arithmetic - logic unit — by iterative reconstruction and segmented vectorial reprojection calculation , wherein a scattered radiation correction and a radiation hardening correction are carried out in each iteration cycle for at least two different material components of the object being examined . the invention also relates to an x - ray ct system for carrying out this method .