Computed tomography method utilizing a conical radiation beam

[0002] 1. Field of the Invention

[0003] The invention relates to a computed tomography method which includes the following steps:

[0004] generating a conical radiation beam which traverses an examination zone or an object present therein,

[0005] generating a relative motion, including a rotation about an axis of rotation, between the radiation beam and the examination zone or the object,

[0006] acquiring, during the relative motion, measuring data which is dependent on the intensity in the radiation beam to the other side of the examination zone,

[0007] reconstructing the spatial distribution of the absorption within the examination zone from the measuring data acquired by the detector unit.

[0008] The invention also relates to a computed tomography apparatus for carrying out the above method.

[0009] 2. Description of Related Art

[0010] A “conical” beam is to be understood to mean a beam of finite dimensions in two mutually perpendicular directions and is detected by a detector unit which is suitable for spatially resolved measurement in these two directions of the intensity of the beam which has been attenuated in the examination zone. A method of this kind is known from a publication by L. A. Feldkamp et al. “Practical Cone Beam Algorithms”, Journal of Optical Soc. Am. A, Vol. 1, No. 6/pp. 612-619, 1984.

[0011] It is a fundamental drawback of CT methods (CT=computed tomography) utilizing conical radiation beams that some voxels (volume elements) in the examination zone are only temporarily exposed to the radiation during the relative motion between the radiation source and the examination zone and that the absorption in these voxels cannot be reconstructed from the measuring data acquired by the detector unit. The part of the examination zone in which the spatial absorption distribution can be reconstructed, therefore, is always smaller than the part exposed to the radiation.

[0012] The known method utilizes a reconstruction algorithm for reconstructing the absorption within the rotationally symmetrical zone which is exposed to radiation during the entire relative motion and is shaped like a disc, the reconstruction in practice being limited to a plane slice within this zone. The known method is based on a circular relative motion.

[0013] However, there are also CT methods which involve a helical relative motion. In the case of such methods the absorption is not reconstructed in the voxels which are present in the radiation beam at the beginning or at the end of the relative motion.

[0014] Citation of a reference herein, or throughout this specification, is not to construed as an admission that such reference is prior art to the Applicant's invention of the invention subsequently claimed.

[0015] It is an object of the present invention to enlarge the zone in which the absorption distribution is reconstructed. This object is achieved according to the invention in that the method also includes the following steps for the reconstruction of the spatial distribution of the absorption:

[0016] a) defining at least one first and one second sub-volume within the overall volume traversed by the radiation beam,

[0017] b) reconstructing the spatial distribution of the absorption within the first sub-volume by means of a first reconstruction algorithm,

[0018] c) reconstructing the spatial distribution of the absorption within the second sub-volume by means of a second reconstruction algorithm which deviates from the first reconstruction algorithm.

[0019] The invention is based on the consideration that the known methods always utilize only one reconstruction algorithm for the reconstruction. For each voxel the absorption is then reconstructed by means of the same number of calculation steps of the same kind. Each reconstruction algorithm is subject to given secondary conditions (for example, the condition that all voxels in the volume to be reconstructed have been exposed to radiation during the entire relative motion) which are satisfied only in a part of the overall volume (the first sub-volume). These secondary conditions are adequate but not necessary for the reconstruction, i.e. there are additional voxels which do not satisfy this secondary condition but do satisfy less severe secondary conditions which are also adequate for a reconstruction, utilizing a different reconstruction algorithm, even if the signal-to-noise ratio could then be less attractive. These voxels are situated in another part of the overall volume (the second sub-volume).

[0020] The reconstruction zone can thus be enlarged by utilizing a hybrid reconstruction method involving a first reconstruction algorithm in a first sub-volume and a second reconstruction algorithm in a second sub-volume (other than the first sub-volume). The second reconstruction algorithm may include calculation steps of the same kind as the first algorithm, but a different number thereof. The term “different reconstruction algorithm” is to be broadly interpreted in this sense.

[0021] This invention includes an embodiment which can be used in the case of a circular trajectory (i.e. a trajectory where the relative motion between the radiation source and the detector unit on the one side and the examination zone on the other side is shaped as a circle). The criterion for assignment to the two sub-volumes is then given by the irradiation angle range (being the angular range covered in the relevant plane by the (parallel) projection of the rays from the radiation source to a voxel in a plane which is perpendicular to the axis of rotation, or is covered by the components of the vectors from the radiation source to the voxel in the plane of rotation of the radiation source). Voxels with an irradiation angle range of 360° (which voxels are exposed to radiation during the entire relative motion) are assigned to the first sub-volume and voxels with an irradiation angle range of at least 180° (but less than 360°) are assigned to the second sub-volume which bounds the first sub-volume to both sides and has sides extending perpendicularly to the axis of rotation.

[0022] The reconstruction of the absorption of the voxels in the first sub-volume is then performed by means of a first reconstruction algorithm which utilizes a reconstruction angle range of 360° (the reconstruction angle range is to be understood to mean the angular range covered by the (parallel) projections of the rays, used for the reconstruction, from the radiation source to a voxel in a plane which is perpendicular to the axis of rotation). For example, the algorithm described in the previously mentioned publication can be used as the reconstruction algorithm. For the second sub-volume use can be made of a reconstruction algorithm for which a reconstruction angle range of 180° suffices; as is known, CT methods involving a plane fan-shaped radiation beam also utilize reconstruction algorithms which operate with a reconstruction angle range of only 180°.

[0023] This invention includes two alternatives for the reconstruction of the absorption in these voxels. In conformity with a first alternative, measuring data is taken into account only from an irradiation angle range of exactly 180°. In conformity with a second alternative, all measuring data is taken into account which has been determined for rays through the relevant voxel, but the contributions by rays whose projection passes through the voxel from 180° offset directions are weighted in such a manner that their overall weight equals that of a single ray (i.e. a ray for one direction for which no ray occurs in the opposite direction). In this case the reconstruction is equivalent to a reconstruction with a reconstruction angle range of 180°, but a more attractive signal-to-noise ratio is obtained.

[0024] When the part of the examination zone that can be reconstructed by means of a circular trajectory does not suffice, the examination zone can be scanned along two adjacently situated circular scanning paths. This invention also includes an embodiment which is suitable for such a case. A (disc-shaped) intermediate zone which constitutes a third sub-volume then exists symmetrically with respect to the two circles along which the relative motion takes place. Whereas the absorption of the voxels in the first and the second sub-volume can be reconstructed in the manner explained with reference to Claim 2, the third sub-volume can be reconstructed, for example by means of an ART method (ART=Algebraic Reconstruction Technique).

[0025] This invention also includes an embodiment for a helical relative motion between the examination zone and the radiation source or the detector unit wherein the helical relative motion (17) includes a rotation about an axis of rotation (14) and a displacement in the direction parallel to the axis of rotation, wherein an irradiation angle range of exactly (2N+1)π exists for voxels in the examination zone, and having the steps of assigning voxels which are covered by the radiation beam and are situated outside the conical radiation beam at the beginning and at the end of the helical relative motion to a first sub-volume, assigning voxels which are situated within the radiation beam at the beginning or at the end of the helical relative motion to the second sub-volume, and reconstructing the absorption distribution in the two sub-volumes by means of different reconstruction algorithms. German patent application 198 25 296.4 discloses a method of this kind in which an irradiation angle range of exactly (2n+1)π is obtained for (a part of) the voxels in the examination zone; therein n is an integer. The absorption in these voxels can be reconstructed by means of the known method. The absorption of voxels which are situated within the radiation beam at the beginning or at the end of the helical relative motion cannot be reconstructed by means of the reconstruction method disclosed in the cited document, because the irradiation angle range for these voxels is smaller than (2n+1)π. Therefore, the secondary condition for the reconstruction method disclosed in the cited document is not satisfied; however, there are voxels with an irradiation angle range of π or more. These voxels are assigned to the second sub-volume and their absorption can be reconstructed by means of the method which is known from PCT/SE 98/000029, provided that each time only the measuring data for an irradiation angle range of exactly 180° is taken into account.

[0026] Finally, the invention also includes a computed tomography apparatus for carrying out the method according to the invention. A computer tomography apparatus accordingly to the invention includes a radiation source (S) for emitting a conical radiation beam which traverses an examination zone (13) or an object present therein, a two-dimensional detector unit (16) which is connected to the radiation source and serves for the acquisition of measuring data which is dependent on the intensity in the radiation beam to the other side of the examination zone, a drive device (2, 5) for realizing a relative motion, including a rotation about an axis of rotation (14), between the radiation source (S) and the detector unit (16) on the one side and the examination zone (13), or the object, on the other side, and a reconstruction unit (10) for the reconstruction of the spatial distribution of the absorption within the examination zone (13) from the measuring data acquired by the detector unit (16), characterized in that it performs the following steps for the reconstruction of the spatial distribution of the absorption: defining at least one first and one second sub-volume within the overall volume traversed by the radiation beam, reconstructing the spatial distribution of the absorption within the first sub-volume by means of a first reconstruction algorithm, and reconstructing the spatial distribution of the absorption within the second sub-volume by means of a second reconstruction algorithm which deviates from the first reconstruction algorithm.

[0027] The invention will be described in detail hereinafter with reference to the Figures. Therein:

[0028] FIG. 1 shows a computed tomography apparatus in which the invention can be carried out.

[0029] FIGS. 2A-2C show the position of the sub-volumes or individual voxels on the side of a sub-volume, FIG. 3 show a flow chart of a reconstruction method according to the invention.

[0030] FIG. 4 shows the geometrical conditions for a voxel within the second sub-volume.

[0031] FIGS. 5aand 5bshow the weighting factors assigned to the various radiation directions for the reconstruction of the absorption of a voxel.

[0032] FIG. 6 shows the geometrical conditions in the case of scanning of the examination zone along two mutually offset circular paths, and

[0033] FIG. 7 shows the geometrical conditions in the case of a helical relative motion.

[0034] The computed tomography apparatus shown in FIG. 1 includes a gantry 1 which is capable of rotation about an axis of rotation 14 which extends parallel to the z direction of the co-ordinate system shown in FIG. 1. To this end a motor 2 drives the gantry at a preferably constant but adjustable angular speed. A radiation source S, for example an X-ray source, is connected to the gantry. The source is provided with a collimator device 3 which forms a conical radiation beam 4 from the radiation produced by the radiation source, i.e. a radiation beam which has a finite dimension other than zero in the z direction as well as in a direction perpendicular thereto (i.e. in the x,y plane).

[0035] The radiation beam 4 traverses an examination zone 13 in which a patient may be accommodated on a patient table (both not being shown). The examination zone 13 is shaped as a cylinder which will be referred to hereinafter as the object cylinder 13. After having traversed the object cylinder 13, the X-ray beam 4 is incident on a two-dimensional detector unit 16 which is connected to the gantry 1 and comprises a number of detector rows, each of which comprises a plurality of detector elements. Each detector element provides a measuring value for a ray of the radiation beam 4 in each position of the radiation source. The detector unit 16 may be arranged on an arc of circle about the axis of rotation 14, but also on an arc of circle about the radiation source S; however, it may also be plane.

[0036] The angle of aperture of the radiation beam 4, denoted by the reference α_max(the angle of aperture is defined as the angle enclosed by a ray of the beam 4, situated at the edge in the x,y plane, with respect to a plane of the central ray which is defined by the radiation source S and the axis of rotation 14) then determines the diameter of the object cylinder 13 within which the object to be examined is situated during the acquisition of the measuring values. The examination zone 13, or the object or the patient table, can be displaced parallel to the axis of rotation 14 or to the z axis by means of a motor 5. The transport speed in the z direction is constant and preferably adjustable.

[0037] The measuring data acquired by the detector unit is applied to an image processing computer 10 which reconstructs therefrom the absorption distribution in a part of the examination zone 13 and, for example, displays it on a monitor 11. The two motors 2 and 5, the image processing computer 10, the radiation source S and the transfer of the measuring data from the detector unit to the image processing computer 10 are controlled by a suitable control unit 7.

[0038] When the motor 5 for the transport in the z direction stands still and the motor 2 rotates the gantry 1, a circular scanning motion is obtained for the radiation source S and the detector unit. The control unit 7, however, can also activate the motors 2 and 5 simultaneously so that the ratio of the displacement speed of the examination zone 13 to the angular speed of the gantry is constant.

[0039] FIG. 2A shows the radiation source S, being denoted by a dot, the detector unit 16, being symbolized by a line, and the radiation beam 4 in a first position relative to the axis of rotation 14 and in a position which is 180° offset with respect thereto and is denoted by the references S′, 16′ and 4′. FIG. 2A also shows the examination zone 13. For the sake of clarity the dimensions in the direction parallel to the axis of rotation are shown at a larger scale than those in the direction perpendicular thereto. The absorption in all voxels which are situated within the approximately disc-shaped sub-volume V₁of the examination zone 13 that is covered by the radiation beams 4 and 4′ and the radiation beams emitted in all other radiation source positions can be reconstructed by means of the previously mentioned Feldkamp reconstruction algorithm or by means of another reconstruction algorithm for circular trajectories. Because of the unusual shape of this sub-volume, however, reconstruction will be limited to the dotted plane zone which is denoted by the reference V₀in FIG. 2A. It appears that the zone V₀is small in comparison with the part of the examination zone which is traversed by radiation.

[0040] FIG. 2A also shows two sides which extend perpendicularly to the axis of rotation and intersect the peak of the sub-volume V₁. A voxel on one of the sides and at the edge of the examination zone 13 is denoted by the reference P₂.

[0041] FIG. 2B shows (rotated through 90° relative to FIG. 2A) the circular path along which the radiation source rotates about the axis of rotation 14 as well as the voxel P₂on the side. The part of the circular path wherefrom P₂does not receive radiation because the aperture of the radiation beam is not large enough in the direction of the axis of rotation is shown to be thinner than the part of the path wherefrom the voxel P₂receives radiation. The transitions between the two arcs of circle are denoted by the radiation source positions S₁and S₂. It appears that the heavy arc of circle extends symmetrically with respect to an angular position ψ_sin which a ray from the radiation source to the voxel P₂passes exactly through the axis of rotation 14.

[0042] FIG. 2B also shows that the radiation source must rotate through an angle Δβ of more than 180° from the position S₁to the position S₂, even though the irradiation angle range Δψ (being the angular range covered by the parallel projection of the rays from the radiation source to the voxel P₂on the x-y plane) corresponds to exactly 180°. This difference between Δβ and Δψ is less for voxels which are situated nearer to the axis of rotation 14. It can be demonstrated that all other voxels on the sides (outside V₁) which are not situated at the outer edge of the examination zone have an irradiation angle range Δψ of more than 180° but less than 360 °.

[0043] The irradiation angle range is also larger than 180° and smaller than 360° for the voxels lying between the sides and the outer sides of V₁. Because the absorption of voxels with an irradiation angle range of at least 180° can be reconstructed (in the case of CT methods involving a flat, fan-shaped radiation beam it is also possible to utilize reconstruction algorithms which operate with a reconstruction angle range of only 180°), this part of the examination zone (including its sides) is defined as the second sub-volume V₂.

[0044] FIG. 2C shows the radiation source positions S₁and S₂in a representation which has been rotated through 90° relative to the FIGS. 2A and 2B. This Figure shows the two rays from the radiation source positions S₁and S₂to the voxel P₂as well as the connecting line between these voxels. An angle which corresponds to the angle of aperture of the conical radiation beam exists between the two connecting lines and the voxel. In the representation of FIG. 2B, in which the two rays are projected onto the x,y plane, this has an effect as if they are offset exactly 180°.

[0045] FIG. 3 illustrates the execution of a reconstruction method whereby the absorption distribution can be reconstructed in a significantly larger part of the examination zone.

[0046] After initialization in the block 101, the gantry rotates at a constant angular speed. In the step 102 the X-rays are switched on and the measuring data then acquired by the detector unit 16 is stored in a memory of the image processing computer.

[0047] During the processing step 103 each measuring value is weighted (multiplied) by a factor which is proportional to the cosine of the angle enclosed by the ray, with which the relevant measuring value is associated, with respect to the central ray (the central ray is the ray which emanates from the radiation source S, intersects the axis of rotation 14 at right angles and is incident at the center of the detector unit 16).

[0048] In the step 104 the measuring values supplied by a detector row (situated in the x,y plane) and weighted in conformity with the step 103 are subjected to a high-pass filtering operation. When the detector unit 16 is a plane unit, such filtering is ramp-like, i.e. it has a transfer factor which increases linearly as a function of the spatial frequency. When the detector unit is shaped so as to be curved about the radiation source S or about the axis of rotation 14, it is known that such filtering must be modified.

[0049] After all measuring data has thus been processed in conformity with the steps 103 and 104, a voxel x, y, z within a selectable zone (field of view or FOV) is selected (step 105). In the step 106 the flow chart is branched, depending on whether the irradiation angle range Δψ for this voxel is smaller than 360° or not. For a predetermined geometry of the computed tomography apparatus, a look-up table can state, for each voxel in a co-ordinate system connected to the gantry, whether the condition Δψ=360° is satisfied or not.

[0050] If the condition is satisfied, i.e. if the relevant voxel has been present in the radiation beam throughout the rotation, the filtered data is backprojected in the step 107, the measuring data from all rays having passed the relevant voxel during the acquisition of the measuring data then being taken into account for this voxel. Each measuring value is then multiplied by a so-called “magnification factor” which is dependent on the distance between this voxel and the relevant radiation source position in which the measuring value has been acquired.

[0051] If not one ray passes exactly through the relevant voxel in a radiation source position, a ray (or a filtered measuring value) can be found for this radiation source position by interpolation of the measuring values of a plurality of rays.

[0052] After the contributions to the relevant voxel have thus been accumulated for all radiation source positions, it is checked in the step 108 whether all voxels in the region FOV to be reconstructed have been traversed. If this is not the case, the flow chart proceeds to the step 105.

[0053] The succession of steps 103 . . . 107 essentially corresponds to the reconstruction algorithm indicated by Feldkamp. However, this algorithm is only suitable for reconstructing the absorption for the voxels which are exposed to radiation in all radiation source positions or lie in the disc-shaped zone V₁which is rotationally symmetrically situated relative to the axis of rotation 14. The hybrid reconstruction method according to the invention, however, enables the reconstruction of the absorption distribution in a larger zone.

[0054] When it is certain that the voxel x, y, z is not present in the sub-volume V₁, i.e. that it is not struck by radiation in all radiation source positions, it is checked in the step 109 whether an irradiation angle range Δψ of at least 180° exists for the selected voxel (this fact may also be contained in a look-up table). If this is not the case, the absorption in the relevant voxel cannot be exactly reconstructed and the program proceeds to the check 108. However, if the irradiation range Δψ amounts to at least 180°, the absorption in this voxel is also reconstructed by means of the reconstruction algorithm to be described in detail hereinafter.

[0055] In the step 110 first the irradiation angle range Δψ is then defined; this range is used for the reconstruction of the absorption in the voxel. It is assumed that the selected voxel x, y, z is situated on the outer sides of the sub-volume V₂and at the edge of the examination zone 13, for example like the voxel P₂. In this case there is no other choice than to take into account the entire irradiation angle range Δψ between the radiation source positions S₁for the reconstruction, because it satisfies exactly the condition Δψ=180°.

[0056] The measuring values of all rays in the irradiation angle range Δψ through this voxel are weighted by a weighting factor w₀in the step 111. In conformity with FIG. 5a, illustrating the dependency of this weighting factor w on the irradiation angle ψ, w₀is independent of ψ; ψ₁and ψ₂are then the irradiation angles corresponding to the radiation source positions S₁and S₂(in a projection on the x,y plane). The weighting factor w₀is proportional to the value 1/N, where N is the number of radiation source positions on the arc of circle between S₁and S₂(and hence the number of rays passing through the relevant voxel). As a result, the further steps are executed independently of the value N or the angle Δβ completed by the radiation source on the arc of circle from S₁to S₂. As has already been described, the angles αβ and the number N are dependent on the distance between the relevant voxel and the axis of rotation 14.

[0057] Backprojection takes place in the step 112; the measuring values of the rays distributed across the irradiation angle range of 180° are then multiplied by the magnification factor which is dependent on the distance between the radiation source position associated with this ray and the voxel. The weighting, being independent of the irradiation angle ψ, and the multiplication by the magnification factor, being dependent on the irradiation angle ψ, can also be performed in a single step.

[0058] When the voxel to be reconstructed is situated within the sub-volume V₂(but outside the sub-volume V₁), for example like the voxel P′₂in FIG. 2A, the circumstances are slightly different in comparison with the case where a voxel is situated on the side and at the edge of the examination zone 13 (for example, like P₂). This is illustrated on the basis of FIG. 4 which shows the circumstances for the voxel P′₂(see FIG. 2A) in a representation which is analogous to that of FIG. 2B. This figure again shows the angular position ψ_s, and S₁and S₂are the radiation source positions which are symmetrically situated with respect thereto and wherefrom the rays to the voxel P′₂(more exactly speaking their projections on the x,y plane) are exactly 180° offset. FIG. 4 shows that to both sides of these radiation source positions there are further positions in the solid region wherefrom the voxel P′₂is irradiated. In this case there are the following possibilities for the steps 110 and 111:

[0059] a) A range which corresponds exactly to 180° is cut from the overall irradiation angle range ψ_i-ψ₀available, for example a range which is symmetrical relative to the symmetry position ψ_sand is characterized by the radiation source positions S₁and S₂or (see FIG. 5a) by ψ₁and ψ₂. The range cut out, however, need not be symmetrical to ψ_s. The weighting factor w₀₀, with which all measuring values are weighted in the same manner, is then again proportional to the value 1/N.

[0060] b) A second possibility consists in taking into account also the rays with an irradiation angle outside the range ψ₁and ψ₂and to weight these rays and a corresponding part of the radiation directions situated between ψ₁and ψ₂in such a manner that the rays through the voxel P′₂, whose projections in the x,y plane extend in exactly opposite directions, together are assigned the same weight as, for example the single ray characterized by the radiation angle ψ_sfor which no (180° offset) counterpart exists. Because the outer rays are thus taken into account with a weight which is less than that assigned to the rays at the center, this reconstruction is equivalent to a reconstruction with a reconstruction angle range of 180° (FIG. 5a).

[0061] The hybrid reconstruction method is terminated after the absorption has thus been determined for all voxels situated in the FOV as well as in the sub-volumes V₁and V₂.

[0062] Instead of using the Feldkamp algorithm, a different reconstruction algorithm may also be used for the reconstruction of the absorption of the voxels in the sub-volume V₁and V ₂. Similarly, the absorption distribution in the sub-volume V₂can be reconstructed by means of another reconstruction algorithm enabling the reconstruction from an irradiation angle range of less than 360°.

[0063] As is shown in FIG. 2A, the slice which is defined by the sub-volumes V₁+V₂and in which the reconstruction distribution can be reconstructed, is significantly wider than the slice V₀in which the absorption distribution can be reconstructed while utilizing exclusively the Feldkamp algorithm. When an FOV of a diameter smaller than the examination zone 13 is selected, the slice V₁+V₂may even be thicker. This is because it can be demonstrated that all points within the examination zone with an irradiation angle range Δψ=180° are situated on a convex surface F which is rotationally symmetrical relative to the axis of rotation 14. Such surfaces F, denoted by dashed lines in FIG. 2a, are tangent to the apex of the cone. Each slice within the surfaces, but also the volume which is bounded by the surfaces F, can be completely reconstructed. The voxels between the surfaces F and the cone defined by the sub-volume V₁are then assigned to the sub-volume V₂and the voxels inside the cone are assigned to the sub-volume V₁.

[0064] However, it may occur nevertheless that the overall volumes defined by the surfaces F are not adequate for many applications. In that case the examination zone can be scanned along two circles which are mutually offset in the direction of the axis of rotation. This is illustrated in FIG. 6 in which the references S_aand S′_adenote two 180° offset radiation source positions on the one circle and the references S_band S′_bdenote two 180° offset radiation source positions on the other circle. For reasons of clarity the detector units are not shown, but the resultant sub-volumes V₁and V₂are shown. The reconstruction for the sub-volumes V₁and V₂can again be performed as described with reference to FIG. 3.

[0065] Halfway between the circular paths there is situated a flat, slice-like sub-volume V₃which is bounded on both sides by the sides (FIG. 2a) belonging to the sub-volume V₂. At least the voxels which are situated at the outer edge of the examination zone in the sub-volume have an irradiation angle range of less than 180°.

[0066] The assignment to the sub-volumes V₂or V₁again takes place in dependence on the irradiation angle range Δψ. The assignment to the sub-volume V₃, however, takes place in dependence on the position, i.e. on the z co-ordinate of a voxel.

[0067] The reconstruction of the absorption distribution in the volume V₃is effectively performed by means of an ART method. ART methods are iterative methods where the voxels to be reconstructed are first assigned a suitable absorption value, after which the absorption values of voxels situated on the same ray are accumulated and compared with the measuring value acquired for the relevant ray. The difference is suitably distributed between the voxels situated on this ray. After the absorption distribution has thus been corrected in all voxels of the volume to be reconstructed, the described comparison with the acquired measuring data is repeated etc. The ART method enables an approximative reconstruction of the absorption also in the voxels with an irradiation angle range Δψ<180°.

[0068] The invention can be used not only for CT methods where a circular relative motion takes place, but also for CT methods where a helical relative motion occurs between the examination zone and the radiation source or the detector due to a displacement in the z direction.

[0069] In the case of a helical scanning motion it is in principle irrelevant whether the rotational and displacement motion are performed by the radiation source S and the detector unit 16 or by the examination zone (or the object present therein); only the relative motion is of importance. Therefore, in FIG. 7 it is assumed that the radiation source S (and the detector unit 16 which is connected thereto via the gantry 1 and is not shown in FIG. 7) moves upwards along the helical path 17, whereas the examination zone 13, as well as the object present therein (not shown in FIG. 7), are stationary.

[0070] According to a method of this kind which is described in the not previously published German patent application 198 25 296.4, the dimensions of the detector unit, the radiation beam emitted by the radiation source 4, the transport speed and the rotary speed are adapted to one another in such a manner that the detector unit detects exactly the rays which are coincident with the turns H₀and H₃of the helix 17. Because the two helix turns H₁and H₂are also present therebetween, they will be situated at a distance from one another which amounts to three times (generally (2N+1) times) the distance between two neighboring helix turns.

[0071] It can be demonstrated that in this case all voxels which enter the radiation beam after the beginning of the scanning of the examination zone and leave this beam before the end of the scanning operation will have been irradiated by the radiation source at an angle of exactly 3π (generally (2n+1)π)), thus enabling a very simple reconstruction with a very high image quality.

[0072] The foregoing does not hold for the voxels which are already present in radiation beam 4 at the beginning of the scanning motion and the voxels which are still present therein at the end of the scanning motion. The irradiation angle range is smaller for these voxels so that they cannot be reconstructed by means of the method described in the cited document.

[0073] However, a hybrid reconstruction can again be performed by assigning all voxels which are situated outside the radiation beam at the beginning and at the end of the helical relative motion to a first sub-volume whose absorption distribution is reconstructed in conformity with the reconstruction algorithm disclosed in the cited document. A part of the voxels that are present in the beam path at the beginning of irradiation, i.e. the voxels projected between the turns H₁and H₂by the radiation source, is irradiated from an angle range of more than 180°. Reconstruction can then be performed by assigning the voxels in this part to a second sub-volume and by reconstructing the absorption distribution therein by means of a method which is known from PCT/SE 98/000029, only the rays for an angle range of exactly 180° then being used for the reconstruction.

[0074] The voxels which are projected on the zone between the helix turns H₀and H₁at the beginning of irradiation are irradiated from a range of more than 2π (but less than 3π). These voxels can be assigned to a third sub-volume whose absorption distribution is reconstructed in that rays from a scanning angle range of 360° are used for each voxel therein.

[0075] All references cited herein are incorporated herein by reference in their entirety and for all purposes to the same extent as if each individual publication or patent or patent application was specifically and individually indicated to be incorporated by reference in its entirety for all purposes.