METHOD AND SYSTEM FOR MOTION COMPENSATION IN CT RECONSTRUCTION

Description

[0001] The invention relates to a method and a system for motion compensation in CT reconstruction, i.e. the reconstruction of layer images in computed tomography (CT), in particular taking into account a re-binning process.

[0002] Movement during image acquisition in a CT scan causes artifacts that can seriously degrade image quality and reduce the diagnostic value of the resulting images. This movement leads to inconsistency in the acquired data and thus to artifacts such as blurring, streaking, or ghosting.

[0003] This movement is often a patient movement. Patient movements can be involuntary movements such as organ movements or tremors, but also voluntary movements, for example, in uncooperative patients, in emergencies, or in pediatric imaging. However, the artifacts can also be caused by movements of the scanner itself, for example, in mobile CT systems with a movable or sliding gantry.

[0004] The ideal solution to this problem would be to completely eliminate any form of motion during scanning, but unfortunately, this is usually not a realistic option. Therefore, a solution is needed that can compensate for motion-induced artifacts and improve image quality.

[0005] A frequently used method for motion compensation in CT reconstruction is that of Schäfer et al. ("Motion-compensated and gated cone beam filtered back-projection for 3-D rotational X-ray angiography," in IEEE Transactions on Medical Imaging, vol. 25, no. 7, pp. 898-906; July 2006). The method proposed there is based on the assumption that the motion present during the CT scan is known. Motion correction is applied in the reconstruction process during the backprojection step. Each voxel (three-dimensional image point) of the volume to be reconstructed is virtually shifted according to the motion present at the moment of the acquisition. This method includes the reconstruction algorithm of Feldkamp, ​​David, and Kress ("Practical cone-beam algorithm," J. Opt. Soc. Am. A 1, 612-619; 1984). The method of Schäfer et al.is frequently used as a motion compensation method after new motion estimation methods for CT scans were proposed, such as by Bruder et al. ("Compensation of skull motion and breathing motion in CT using data-based and image-based metrics, respectively", Proc. SPIE 9783, Medical Imaging 2016: Physics of Medical Imaging, 97831E; March 22, 2016).

[0006] Another method for motion compensation in CT reconstruction is based on partial angle reconstruction (see J. Hahn et al. "Motion compensation in the region of the coronary arteries based on partial angle reconstructions from short-scan CT data. Medical physics, 44(11); 2017). In this method, motion compensation is performed separately on several partial angle reconstructions, which are incomplete reconstructions from a subset of the data. The complete motion-compensated reconstruction is obtained by combining the motion-compensated partial angle reconstructions. The motion compensation itself is very similar to the method of Schäfer et al., by moving the voxel volume according to the present motion.

[0007] However, the disadvantage of the reconstruction methods is that when combined with reconstruction algorithms that include a re-binning step, artifacts remain that reduce the quality of the motion compensation result.

[0008] JANG SEOKHWAN ET AL: "Head Motion Correction Based on Filtered Backprojection in Helical CT Scanning", IEEE TRANSACTIONS ON MEDICAL IMAGING, IEEE, USA, Vol. 39, No. 5, November 15, 2019, pages 1636-1645, XP011785806, discloses a method for head motion correction in a helical CT scan.

[0009] It is an object of the present invention to provide a method and a corresponding system for motion compensation in CT reconstruction, with which the disadvantages described above are avoided and, in particular, also enables optimal motion compensation after re-binning.

[0010] This object is achieved by a method according to patent claim 1, a system according to patent claim 10, a control device according to patent claim 11 and by a computed tomography system according to patent claim 12.

[0011] The inventive method for motion compensation in CT reconstruction comprises the following steps: Providing projection images of a CT scan, creating intermediate images, wherein the intermediate images are created from a rebinning of columns of the projection images, calculating slice images by back-projecting the intermediate images onto predetermined voxels of the slice images, wherein for each intermediate image and for each voxel, based on a predetermined movement profile (with movement data) of the voxels, the following steps are carried out during the recording of the projection images: a) selecting an initial movement state based on the intermediate image, b) calculating a reference voxel position of the voxel from its original voxel position and from the movement profile (i.e., with the movement data of the movement profile) for the initial movement state, c) calculating a column image position at which the voxel would be imaged at the reference voxel position in the intermediate image,d) Determination of a changed motion state of the voxel based on the calculated column image position, e) Calculation of a changed voxel position of the voxel from its original voxel position and the motion profile for the changed motion state, f) Calculation of a changed image position at which the voxel would be imaged at the changed voxel position in the intermediate image, g) Use of an image value of the intermediate image at the changed image position for the backprojection.

[0012] Projection images from a CT scan can be obtained by acquiring the images with a CT scanner, by simulating CT images, or by accessing a database containing previously acquired (or simulated) projection images. The term "projection images" does not refer to previously reconstructed images, but rather to images created by projecting an X-ray beam through an object under examination onto a detector. These are preferably raw data from a CT scan, but can also be preprocessed data, for example, where noise reduction has been applied.

[0013] The projection images are often acquired with a conical beam while the X-ray source and detector move along a circular or spiral trajectory. However, this is essentially irrelevant to the invention.

[0014] Intermediate images are created from the projection images using rebinning. These intermediate images are also projection images, but for clarity, the term "intermediate images" is used to indicate that these images are merely used as an intermediate stage in the reconstruction process. It should be noted that this step can also occur before the projection images are downloaded from a database. Thus, a recording can occur, the projection images can be rebinned, and the resulting intermediate images can be temporarily stored in a database.

[0015] During rebinning of projection images, the columns of the projection images are assigned to different intermediate images. In the following, the coordinates of the columns are indicated by "p" and the coordinates of the rows by "q." For a conical X-ray beam, a projection image is acquired with a beam cone. The individual pixels (essentially bins) on a detector thus receive intensity information from the rays of the X-ray source, with different detector pixels detecting rays from different angles due to the conical shape of the X-ray beam. However, some commonly used reconstruction methods require a parallel beam geometry. Other projection methods may require different beam geometries.

[0016] To convert them into parallel "recorded" intermediate images, from a large number of projection images (recorded at different positions of the measuring apparatus), those rays are selected that were parallel to rays of other projection images during the recording. Since the detector and X-ray source rotate during the recording, but the recording positions (in space) are known, the angle in space for each ray can be calculated from its recording position and the respective image position. In parallel projection, the bins would not be the individual pixels, but the individual columns of the projection images. For example, in a simple example, the first intermediate image could be formed from the values ​​of the rows p = 1 from the first projection image, p = 2 from the second projection image, etc. For the second intermediate image, this would then be, for example, p = 2 from the first projection image, p = 3 from the second projection image, and so on.In this way, parallel projection images are obtained in which the column image position (p-coordinate) simultaneously corresponds to a time course, since the lines originate from different recordings at different recording times and thus also correspond to a certain state of movement.

[0017] Optionally, the intermediate images can be filtered after rebinning. For example, convolution can be performed. During a preferred convolution step, the projection images are filtered for a better reconstruction result. Instead of (or in addition to) convolution, multiplication in Fourier space can also be performed.

[0018] The intermediate images are subjected to a Fourier transformation and multiplied by a matched filter in Fourier space. This can be more efficient than convolving the intermediate images. This type of filtering is essentially state-of-the-art.

[0019] Now, the computation of tomographic images is carried out by backprojecting the intermediate images. This is known in the art (see, for example, the above-mentioned paper by Schäfer et al. or the paper by Stierstorfer et al. mentioned below). However, during this computation, special motion compensation steps are also performed, which take rebinning into account. During the computation, voxels (three-dimensional image points or volume pixels) are considered that correspond to the area in which the object was examined or to an image point of the tomographic images to be reconstructed. Voxel values ​​thus ultimately reflect the image points of the reconstructed tomographic images, with each pixel of a tomographic image corresponding to a voxel of a layer of the acquired volume.

[0020] During backprojection (known per se), the intermediate images are used to calculate the actual slice images. The goal of the backprojection step is to reconstruct the voxel volume representing the patient or scanned object, which is formed from the aforementioned voxels. This is achieved by considering each voxel individually for each intermediate image (after rebinning and, if necessary, filtering). For each voxel, a ray is calculated that passes through the voxel and the corresponding position in the intermediate image. The information from the corresponding position in the intermediate image is then used for backprojection. Once this has been done for all voxels in the volume, the process is repeated for the next intermediate image until all intermediate images have been considered. The invention determines exactly which value from the intermediate image is used for backprojection.

[0021] Each voxel has a voxel position, which can be a three-dimensional coordinate or a three-dimensional vector. In the following, we will refer to a coordinate, which includes a vector. As previously stated, the voxels represent volume elements of the recorded object and thus lie in a virtual space that corresponds to the recording area. The voxel position is therefore a position in this virtual space.

[0022] For motion compensation during the calculation, a known motion profile is required. This relates to the acquisition area (the area where the object was located during acquisition) and thus to the movement of the voxels. Since the voxels are defined by their respective voxel positions, the motion profile relates to the change in the respective voxel positions of the voxels. For this purpose, the motion profile includes motion data for the individual voxels, or rather, the motion profile is a collection of motion data for the individual voxels.

[0023] The process of creating a motion profile is state-of-the-art. For example, a patient can be filmed by a camera during a scan, and the motion profile can be derived from the camera images. However, motion estimation methods for CT scans also exist, as described in more detail in the aforementioned study by Bruder et al. ("Compensation of skull motion and breathing motion in CT using data-based and image-based metrics, respectively").

[0024] Movement can be measured using sensors, e.g. motion sensors attached to the scanner to measure the movement of the scanner or 3D cameras to measure the movement of the patient.

[0025] Simply explained, the motion profile is designed to reproduce (with its motion data) the movement of each individual voxel over the acquisition time, or at least to interpolate it. Since this usually requires a very large amount of memory in practice (with 512 voxels per image axis, 30 acquisitions, and two bytes per voxel coordinate, the motion profile would be approximately 25 GB in size), the motion profile can also be based on approximations, subsamplings, and / or interpolations and / or contain predefined regions without motion. For example, it is sufficient if the movement of a few points on the walls of a heart is known, and the movement of the voxels in the heart volume is calculated based on these points, whereby only those voxels that lie within the movement range of the walls need to be taken into account. As will be explained in more detail below, the motion profile can be based on approximate values ​​or models for the movements.For example, rigid motion can be assumed, requiring only motion data for translation, rotation, and displacement of the center of rotation for the entire scanned object at a large number of time points (possibly every relevant time point). In this case, the entire volume moves at the same rate, and only one set of motion parameters is required for the entire volume instead of for each individual voxel. This approach therefore requires very little storage space.

[0026] Using the motion profile, the next reconstruction steps are then performed for each intermediate image and each voxel (with a known initial voxel position x). The goal is to assign the correct image information to the voxels (here, these are the voxels along the path of a ray, which is required for backprojection). While, as mentioned, the reconstruction of slice images from the intermediate images is known, the images of the voxels are often not located in the intermediate images where they should be (without movement) due to their movement. Therefore, in the current state of the art, without motion compensation, image content is sometimes assigned to the voxels that does not actually correspond to the image of these voxels. This leads to artifacts in the slice images and is undesirable.The following special steps for motion compensation essentially determine where in the intermediate images the image information of a voxel is likely to be found and use exactly this image information for the voxel.

[0027] To better understand the following explanations, it should be noted that a voxel's movement is essentially just a change in its voxel position during the acquisition time. Within this acquisition time, several projection images are acquired at different acquisition times, so that each projection image shows the voxel at its current voxel position. Each intermediate image also simultaneously shows a time course in its columns, since the rows originate from different projection images. Thus, the column image position (p-coordinate) essentially corresponds to a time coordinate, and each p-coordinate corresponds to a different voxel motion state.

[0028] Since the exact acquisition time is known for each P-coordinate of an intermediate image (it is known which projection image the image information at this P-coordinate originates from and when this projection image was acquired), the motion state at that point is also known. Using the motion state (or the acquisition time), the current voxel position can be calculated from the motion profile. Essentially, the terms "motion state" and "acquisition time" are synonymous for voxel positions, since a specific motion state existed at a specific acquisition time. For ease of understanding, it is assumed below that the voxel positions can be determined directly from the motion profile using a known motion state, although the same can of course also apply to a known acquisition time.It should be noted that the column image coordinate p of different intermediate images does not necessarily have to be identical to the motion state, since, for example, the center of the intermediate images corresponds to the same p-coordinates but usually to different motion states. However, since, as mentioned above, it is known from which projection images the image contents of the intermediate images originate, the respective motion state can be derived from each p-coordinate of each intermediate image and can thus be used as a "global parameter" for the p-coordinates.

[0029] In short: The motion profile comprises motion data for different motion states. For a known motion state, the desired motion data can be selected from the motion profile and used to calculate a voxel position according to steps b) or e). The motion data can also be present as functions of the motion state. For the simple case of a simple translation z(t) with the translation function z and the motion state t, a changed voxel position x' for a known motion state T could simply be calculated from x' = z(T).

[0030] To compensate for motion, an initial motion state is first selected based on the intermediate image, with different initial motion states preferably being selected for different intermediate images. This initial motion state can essentially be chosen arbitrarily, but is preferably located at the center of each intermediate image being viewed. By considering the centers of the intermediate images, simple and standardized calculations are possible. Although each intermediate image is viewed in a different motion state (the acquisition time of the central column image position is usually different for each intermediate image), this has no adverse effects on the result, since everything is ultimately traced back to the (stationary) original voxel volumes.

[0031] Regarding the term "center," it should be noted that there can be multiple reference systems that can define a "center" in the intermediate image. One such system is the image center. This would be located halfway between the columns. However, the detector does not always have to be symmetrically constructed. If the center is defined by the gantry's center of rotation, it is possible that the detector will stay to the left of this center for longer than to the right of it during an acquisition. This is then reflected accordingly in the p-coordinates of the intermediate images. In this case, the center is not necessarily in the center of the intermediate image, but can be shifted slightly to the left or right.

[0032] However, it is also particularly preferable to start from the respective image centers (half of the columns) of the projection images. These can be regarded as the centers of the intermediate images, i.e. the column in the intermediate image in which an image center of a projection image is present. At this particular point, the rotation angle of the gantry in the cone beam geometry is identical to the virtual rotation angle of the parallel beam geometry, and thus the motion states of the projection image and the corresponding intermediate image are identical at this point. As previously stated, this image center of the projection image does not necessarily have to be in the image center of the intermediate image. For the sake of simplicity and to facilitate an easier understanding of the invention, however, the center can be imagined in the image center of the projection image for the following explanations.

[0033] When calculating a reference voxel position (voxel position relative to the initial motion state) from the motion profile, this position is then calculated relative to the selected initial motion state. As mentioned above, the motion profile is designed accordingly.

[0034] For example, in a simple but memory-intensive implementation, the exact position of the voxel can be determined in a lookup table for the respective motion state (time of acquisition). However, the voxel position can also be calculated from a function across the motion states, including the calculation of the function for the respective motion state.

[0035] For example, the motion profile can specify that a translation z and a rotation R (R is, for example, a matrix) take place around a pivot point c. The motion state (indicated here with "t" to represent the proximity to a recording time) can therefore be present as a data set of functions z(t), c(t), and RT. A voxel position x M for the initial motion state T could then be calculated from the original voxel position x using the formula x M = RT (xc(T))+c(T)+z(T). It is assumed here that the voxel to be reconstructed moves in the same way as the patient or scanned object moved during the recording (possibly also due to errors in the scanner's motion sequence).

[0036] For a voxel at a voxel position x, its reference voxel position x M is calculated for the initial motion state. In the next step, it is calculated where the voxel (located at the reference voxel position) would be visible in the intermediate image.

[0037] In this regard, at least the column image position p, or the two-dimensional image position (p, q), is calculated at which the voxel would be imaged at the reference voxel position x M in the intermediate image. The position in the q-direction is unproblematic and has only minor relevance for the basic procedure. Since the beam path is known (this was the basis for rebinning), it is easy to determine where a beam with a previously known direction through this voxel would have struck the intermediate image. With a parallel-beam geometry, for example, the projection of the voxel onto the intermediate image would simply have to be considered.

[0038] However, it should be noted that each column image position p in an intermediate image corresponds to a specific acquisition time and thus to a specific "changed motion state," which no longer has to correspond to the initial motion state (and usually does not). At this changed motion state (at the determined column image position p), the voxel could have been at a different voxel position due to its movement.

[0039] In short: If a voxel is not imaged directly in the center of an intermediate image, a different motion state than the initial motion state existed at the same time and the voxel could have been located somewhere else at that "time".

[0040] Therefore, the changed motion state of the voxel is now determined based on the calculated column image position p. The changed motion state could be calculated directly from the column image position.

[0041] According to the calculation of the column image position p described above, the changed column image position p' is now calculated. In addition, however, the changed row image position q' is also calculated here, resulting in the two-dimensional coordinate (p', q'). The calculation of the changed row image position q' can again be done simply by calculating where a (known) ray through the voxel at the changed voxel position x' would strike the intermediate image at a given angle. However, it should be noted that if a conical beam geometry was present during acquisition, the conical shape in the q-direction is retained even with parallel rebinning.

[0042] Finally, in the intermediate image, the image value at the changed image position (p', q') is taken and used as the value for the backprojection (and assigned to the voxel or a group of voxels if necessary).

[0043] This is done for all voxels for one intermediate image, and then again for each voxel for another intermediate image until all relevant intermediate images have been processed.

[0044] Essentially, the process can be summarized as follows: instead of working with the first available voxel position, one iteration step is performed first. While this method may appear to be imprecise, because the voxel could have been located somewhere else at the "time" of the changed column image position p', it turns out that image quality can be significantly improved with just a single iteration step. Of course, further iterations are possible, as discussed below, although each iteration step naturally requires additional computational effort.

[0045] The present invention thus integrates motion compensation into the backprojection and is particularly advantageous for a weighted and filtered backprojection algorithm (WFBP algorithm) such as that presented by K. Stierstorfer et al. ("Weighted FBP - a simple approximate 3D FBP algorithm for multislice spiral CT with good dose usage for arbitrary pitch". Physics in Medicine & Biology, 49(11), 2209; 2004) and which can be advantageously used for CT reconstructions. However, the described motion compensation method is basically advantageous for any CT reconstruction method that uses rebinning and backprojection steps.

[0046] A system according to the invention for motion compensation in CT reconstruction comprises means for carrying out the method according to the invention. The system preferably comprises the following components: a data interface designed to receive projection images of a CT scan, a re-binning unit designed to create intermediate images, wherein the intermediate images are created from a re-binning of the columns of the projection images, a reconstruction unit designed to calculate slice images by means of a back-projection of the intermediate images onto predetermined voxels of the slice images.

[0047] The reconstruction unit comprises (in addition to the elements known in the state of the art for reconstruction) the additional components: a movement module designed to select an initial movement state for an intermediate image or to determine a changed movement state for a voxel based on its calculated column image position in an intermediate image, a positioning module designed to calculate a voxel position of the voxel from its original voxel position and the movement profile to a selected or calculated movement state, a mapping module designed to calculate a column image position and a row image position at which a voxel would be mapped in an intermediate image, an acquisition module designed to acquire an image value of the intermediate image at the changed image position for use for backprojection.

[0048] The data interface is known in the art. It can be a network data interface, for example, and be designed to receive images via a PACS (Picture Archiving and Communication System). However, the data interface can also be a data bus of a CT system, via which captured projection images from a CT scan are transmitted.

[0049] The re-binning unit is used to create the intermediate images by means of re-binning, as described in more detail above, e.g. images with parallel beam guidance.

[0050] A reconstruction unit is essentially known in the art and is used to calculate the tomographic images. The reconstruction unit used here comprises the elements of a conventional reconstruction unit plus the additional modules listed above, which are described in more detail below.

[0051] The motion module is characterized by the fact that it specifies a motion state. A motion state can be determined using two modes, for which the motion module can (but does not necessarily have to) have two sub-modules.

[0052] The first mode is the selection of a motion state. This occurs based on a user specification, a preset, or the currently used intermediate frame. For example, the selection can be made by selecting a motion state that corresponds to a specific column position p of an intermediate frame (e.g., its center). However, a motion state can also be selected that is linked to a specific recording time. The corresponding sub-module could be called the "motion selection module."

[0053] The second mode is the determination of a voxel's motion state based on a calculated column image position p. This simply requires a specification of the column position and the selection of a motion state associated with this column position (of the relevant intermediate image). The corresponding sub-module could be called the "motion position module."

[0054] Basically, a simple motion module can have an assignment table or assignment function by means of which an image coordinate of each intermediate image can be assigned a corresponding motion state.

[0055] The positioning module maintains contact with the motion profile, e.g., through communication with a database or a memory area. The motion profile contains information about the movements of voxels, e.g., in the form of functions or tables, and the positioning module is designed to retrieve this information and, in particular, to write it to a predefined memory area.

[0056] The calculation of a voxel position can be performed as described above. The positioning module can calculate both the reference voxel position and the modified voxel position, since the calculation principle is the same. However, it can also have two sub-modules for calculating these values ​​separately.

[0057] The mapping module calculates the image positions as described in more detail above. Regarding the reference voxel position, only the column image position of the voxel in the intermediate image is necessary; however, its line image position can also be calculated additionally. For the modified voxel position, both the column image position of the voxel in the intermediate image and its line image position must be calculated so that the appropriate image information can be assigned to the voxel later.

[0058] The mapping module can have two sub-modules for separate calculation of the sizes.

[0059] The transfer module can achieve the transfer of the image value of the intermediate image simply by copying the image information at previously calculated image coordinates and writing it into a data set for backprojection.

[0060] These modules can be included in a control device of the CT system. A control device according to the invention for controlling a computed tomography system is designed to carry out a method according to the invention and / or comprises a system according to the invention.

[0061] The computed tomography (CT) system according to the invention comprises a control device or a system according to the invention and is designed to carry out a method according to the invention. CT systems are known in the prior art.

[0062] A large part of the aforementioned components of the system or control device can be implemented wholly or partially in the form of software modules in a processor of a corresponding computer system. A largely software-based implementation has the advantage that even previously used control devices can be easily retrofitted by a software update in order to operate in the manner according to the invention. In this respect, the object is also achieved by a corresponding computer program product with a computer program that can be loaded directly into a computer system or a memory device of a control device of a computed tomography system, with program sections in order to carry out all steps of the method according to the invention when the program is executed in the computer system or control device. Such a computer program product can, in addition to the computer program, optionally contain additional components such as, for example,documentation and / or additional components may also include hardware components, such as hardware keys (dongles, etc.) for using the software.

[0063] A computer-readable medium, e.g., a memory stick, a hard disk, or another portable or permanently installed data storage device, can be used for transport to the computer system or control device and / or for storage on or in the computer system or control device. The computer unit can store the program sections of the computer program that can be read and executed by a computer system or a computer unit of the control device. For this purpose, the computer unit can, for example, have one or more cooperating microprocessors or the like.

[0064] Further, particularly advantageous embodiments and developments of the invention emerge from the dependent claims and the following description, wherein the claims of one claim category can also be developed analogously to the claims and description parts to form another claim category and, in particular, individual features of different embodiments or variants can be combined to form new embodiments or variants.

[0065] In a preferred method, the initial motion state corresponds to a column image position p that is substantially in the center of the intermediate image. This means that the column image position P is located no further than 5% of the total columns of the intermediate image from the center, preferably no further than 1% of the total columns.

[0066] A particularly preferred initial motion state corresponds to a column image position p, which corresponds to the column in the intermediate image that was exactly in the center of the image in one of the projection images.

[0067] Preferably, such an initial motion state is selected for each intermediate image, i.e. particularly preferably for each intermediate image an initial motion state corresponding to a column image position which lies exactly in the center of the respective intermediate image.

[0068] According to a preferred method, in addition to a column image position at which the voxel would be imaged in the intermediate image, a row image position is calculated at which the voxel would be imaged in the intermediate image.

[0069] Regarding the motion profile and the calculation of the voxel position, it should be noted in practice that on the hardware side, image reconstruction often involves two RAMs: a smaller, faster RAM and a larger, slower RAM. Calculations are usually performed in the fast RAM. It is advantageous to write data required for calculations to the fast RAM so that the calculations are not unnecessarily slowed down by access times to the slow RAM. Since, as mentioned above, the motion profile can be quite large, it is usually located in the slow RAM (or a non-volatile memory).It could therefore be advantageous to load a certain amount of motion data from the motion profile into the fast RAM for each intermediate frame and to interpolate movements that occur between these motion states from the downloaded motion data. This can save computing time. Experiments have shown that, in addition to the initial motion state, two additional motion states are sufficient for effective motion compensation.

[0070] According to a preferred method, during the backprojection of the intermediate images, motion data (regarding voxel movements) are preselected from the motion profile for a number of intermediate images, in particular for each intermediate image, for the initial motion state and for at least one earlier and at least one later motion state. Thus, for example, motion data are available for an initial motion state for a p-coordinate in the center of the intermediate image, and motion data are available for a motion state for a p-coordinate to the left and right of the center.

[0071] In this case, the changed voxel position x' of the voxel is preferably calculated based on these preselected motion data and the determined changed motion state by interpolating "suitable" motion data for this changed motion state. For this purpose, the motion data of the nearest motion states are preferably used.

[0072] The interpolation is therefore preferably based on those motion states that are closest to the changed motion state. This means that the distance of the respective next preselected motion states from the column image position p of the reference voxel position x M is determined, and the (preselected) motion data of the motion profile of the neighboring motion states are used to calculate the changed voxel position x'. The distance between the image positions of the motion states is preferably included in the form of a weighting. The closer the column image position p of the reference voxel position x M is to a neighboring motion state, the more its motion data is included in the calculation of the voxel position.

[0073] In short: Several motion states (e.g., three) are selected, the motion data for these motion states is determined from the motion profile, and for a new motion state between the selected motion states, the relevant motion data is interpolated from the motion data of the neighboring motion states. The voxel position is then calculated using this interpolated motion data.

[0074] For three motion states with the initial motion state at the center (p0) and two motion states at the two other P coordinates pmin and pmax, for a calculated column image position p, the closest P coordinates would be determined (e.g., pmin and p0), the distance from p to these would be determined (e.g., A1 to pmin and A2 to p0), and then a weighted calculation of the motion would be performed using the weighting factors a1 and a2 (e.g., a1=A1 / (A1+A2) and a2=A2 / (A1+A2)). A preferred procedure for the "new" motion state T2 and the two neighboring known motion states T and T1, and the motion data RT , R T1 , c(T), c(T1), z(T), and z(T1) for these two known motion states would be: Interpolate a rotation R T2 from RT and R T1 . Interpolate a pivot point c(T2) from c(T) and c(T1), e.g., c(T2) = a1 c(T1) + a2 c(T). Interpolate a translation z(T2) from z(T) and z(T1), e.g., z(T2) = a1 z(T1) + a2 z(T). Calculate the changed voxel position using the formula: x ′ = R T 2 x − c T 2 + c T 2 + z T 2

[0075] It should be noted that for a center that does not correspond to the center of the intermediate image, the outer regions Pmin (always negative) and Pmax (always positive) do not necessarily have to be distributed symmetrically around p=0 and pmin ≠ -pmax can apply.

[0076] According to a preferred method, the following steps are performed at least once before using the image value for rear projection: Calculation of a changed column image position p' at which the voxel would be imaged at the changed voxel position x' in the intermediate image, determination of a changed motion state of the voxel based on the changed column image position p', calculation of a changed voxel position x' of the voxel from its original voxel position x and the motion profile for the changed motion state.

[0077] Thus, at least one new, changed voxel position is calculated iteratively. This takes into account the fact that each p-coordinate in an intermediate image simultaneously corresponds to an individual acquisition time and thus to an individual motion state.

[0078] According to a preferred method, when creating the intermediate images, the columns of the projection images are rebinned such that those columns of the projection images that were acquired with parallel X-ray beams in a plane orthogonal to the columns are used for an intermediate image. This is known in the prior art, but the method according to the invention is particularly well suited for such parallelized rebinning.

[0079] According to a preferred method, the intermediate images are filtered for a better reconstruction result, in particular by means of a convolution and / or a Fourier transform. In a preferred convolution, a filtered intermediate image is filtered by means of a predefined kernel, in particular a ramp filter such as ega Shepp-Logan kernel. In alternative filtering, the intermediate images are subjected to a Fourier transform and multiplied by a matched filter in Fourier space. Both the filtering and the Fourier transform are essentially known in the state of the art.

[0080] According to a preferred method (a particular iterative method), after calculating the slice images from the intermediate images, the following steps are performed: i) Reconstruction of comparison intermediate images from the slice images based on the motion profile, ii) Comparison of the comparison intermediate images with the intermediate images, iii) Creation of revised slice images based on the comparison, iv) Iterative repetition of steps i) to iii) with the most recently created slice images.

[0081] According to a preferred method, during the reconstruction of the intermediate comparison images, the pixels of the intermediate comparison images are determined for each pixel of each intermediate comparison image according to the following steps: Calculating a ray through the image voxels starting from a pixel of the intermediate comparison image, determining the motion data for a motion state corresponding to the image position in the intermediate comparison image from the motion profile, shifting the positions of the ray and image voxels relative to one another according to the motion data of the motion profile to the motion state, in particular wherein the ray is moved according to the motion data, accumulating values ​​of the image voxels along the ray with the relative shift of the ray and image voxels, adopting the accumulated values ​​for the position in the intermediate comparison image.

[0082] A pixel at position (p, q) in the intermediate image is to be filled with a value. To do this, a ray is calculated that passes through the image voxels and is absorbed accordingly. The value of the (correct) ray should then be an accumulation of values ​​from the image voxels along the ray. Now (as with backprojection) it is the case that the voxel volume may have been in different places at different times. However, since the column position p is known (it was chosen), the corresponding motion state is also known, and with it the corresponding motion data from the motion profile, which can either be derived directly from the motion profile or interpolated. The interpolation works in the same way as in backprojection.Using the corresponding motion data, the start and end points of the ray can then be shifted according to the motion (especially in the case of rigid motion) or, alternatively, the image voxels can be shifted (especially in the case of non-rigid motion). For this ray, which has moved (relative to the image voxels), the values ​​along the ray are accumulated and this value is written to the original position (p,q). This is explicitly not the new position of the ray, but rather the pixel with which it started, corresponding to the iteration through the pixels of the intermediate image.

[0083] Accordingly, in a preferred system, the reconstruction unit additionally comprises the following modules: a ray simulation module designed to calculate a ray through the image voxels starting from a pixel, a motion simulation module designed to determine the motion data of a motion state corresponding to the column image position in the comparison intermediate image from the motion profile and to shift the positions of the ray and image voxels relative to one another according to the motion data of the motion profile to the motion state, a simulation transfer module designed to accumulate values ​​of the image voxels along the ray with the relative shift of the ray and image voxels and to transfer the accumulated values ​​for the position in the comparison intermediate image.

[0084] This iterative motion compensation procedure can be incorporated into the reconstruction process, resulting in a motion-compensated voxel volume. If the forward projection step to obtain the intermediate comparison images were performed without considering motion, the resulting intermediate comparison images would also be motion-compensated. However, they are compared with the original (uncompensated) intermediate images. Thus, during the forward projection step, the same motion compensation calculations should be performed as during the back projection, only in the "other direction." In the forward projection, the motion removed in the back projection step is added back (all based on the motion profile). In the subsequent back projection step, the motion is compensated again.

[0085] In short, during forward projection, intermediate (comparison) images are calculated from the slice images. These intermediate (comparison) images are compared with the original intermediate images. The difference between the intermediate images is then backprojected, and the result is calculated with the previous slice images to achieve a more accurate result. The new, more accurate slice images are projected forward again, and so on.

[0086] Components of the invention are preferably provided as a "cloud service." Such a cloud service serves to process data, in particular using artificial intelligence, but can also be a service based on conventional algorithms or a service in which human evaluation takes place in the background. In general, a cloud service (hereinafter also referred to as "cloud") is an IT infrastructure in which, for example, storage space or computing power and / or application software is made available via a network. Communication between the user and the cloud takes place via data interfaces and / or data transmission protocols. In the present case, it is particularly preferred that the cloud service provides both computing power and application software.

[0087] In your preferred method, data is provided to the cloud service via the network. This comprises a computing system, e.g., a computer cluster, which typically does not include the user's local computer. This cloud can be provided, in particular, by the medical facility that also provides the medical technology systems. For example, the data from an image acquisition is sent via a RIS (radiology information system) or PACS to a (remote) computer system (the cloud). Preferably, the cloud computing system, the network, and the medical technology system represent a network in the data technology sense. The method can be implemented using a command constellation in the network. The data calculated in the cloud ("result data") are later sent back via the network to the user's local computer.

[0088] The disclosed invention significantly improves the results of motion compensation for known motions, particularly in combination with the WFBP algorithm, compared to the prior art. After motion-compensated reconstruction, significantly fewer motion artifacts remain than, for example, in the method of Schäfer et al. when combined with the WFBP algorithm. The main difference is that the disclosed invention takes the rebinning process into account during motion compensation, resulting in a more accurate representation of the motion state present at each step, thereby reducing the remaining artifacts in the final result.

[0089] A significant reduction in motion artifacts improves image quality and thus the diagnostic value of the resulting images. Improving image quality in motion-affected CT scans is therefore highly desirable for clinical practice, as it enables greater accuracy in the diagnostic process.

[0090] Furthermore, the invention can avoid the need to repeat CT scans due to motion artifacts. Repeating CT scans results in increased dose to the patient, which is highly disadvantageous. Furthermore, re-acquiring scans is time-consuming and could consume urgently needed resources.

[0091] In projects involving mobile CT scanners, the disclosed motion compensation method could lead to an improvement in image quality, making the scanners more attractive for clinical practice.

[0092] The invention is explained in more detail below with reference to the accompanying figures using exemplary embodiments. In the various figures, identical components are provided with identical reference numerals. The figures are generally not to scale. They show: Figure 1 a roughly schematic representation of a computer tomography system with an embodiment of a control device with a system according to the invention for carrying out the method, Figure 2 a flow chart for a possible sequence of a method according to the invention, Figure 3 a supplemented flow chart for a possible sequence of an iterative procedure, Figure 4 a flowchart for a preferred iterative procedure, Figure 5 a schematic representation of a preferred system, Figure 6 an image of moving voxels, Figure 7 a re-binning, Figure 8 a selection of a motion state, Figure 9a result of the method according to the invention in comparison.

[0093] The following explanations assume that the imaging system is a computed tomography system. However, the procedure can also be used with other imaging systems.

[0094] Figure 1shows a roughly schematic view of a computed tomography system 1 with a control device 10 for carrying out the method according to the invention. The computed tomography system 1 conventionally comprises a scanner 2 with a gantry in which an X-ray source 3 rotates, each of which irradiates a patient, who is pushed into a measuring space of the gantry by means of a couch 5, so that the radiation strikes a detector 4 opposite the X-ray source 3. It is expressly pointed out that this exemplary embodiment is only one example of a CT and that the invention can also be used on any CT construction, for example with an annular, fixed X-ray detector and / or multiple X-ray sources.

[0095] Likewise, only those components of the control device 10 that are essential for explaining the invention are shown. Such CT systems and associated control devices are generally known to those skilled in the art and therefore need not be explained in detail.

[0096] A core component of the control device 10 is a processor 11, on which various components are implemented in the form of software modules. The control device 10 further comprises a terminal interface 14, to which a terminal 20 is connected, via which an operator can operate the control device 10 and thus the computed tomography system 1. A further interface 15 is a network interface for connection to a data bus 21 in order to establish a connection to a RIS (radiology information system) or PACS (picture archiving and communication system).

[0097] The control device 10 can control the scanner 2 via a control interface 13, ie, for example, the rotation speed of the gantry, the displacement of the patient bed 5, and the X-ray source 3 itself are controlled. The raw data RD are read from the detector 4 via an acquisition interface 12. Furthermore, the control device 10 has a memory unit 16 in which, among other things, various measurement protocols are stored.

[0098] An (image data) reconstruction unit 18 is implemented as a software component on the processor 11. This reconstruction unit 18 reconstructs the desired image data from the raw data RD obtained via the data acquisition interface 12. This reconstruction unit 18 modules the system 9 for motion compensation during CT reconstruction. The system 9 itself comprises: A data interface 6, which is designed here to receive the raw data RD (or the projection images B from the data acquisition interface 12).

[0099] A re-binning unit 7 designed to create intermediate images Z, the intermediate images Z being here, for example, as in Figure 7 shown can be created from a re-binning with a parallel beamline.

[0100] The reconstruction unit 8 additionally comprises the following modules: A motion module 30 designed to select an initial motion state MI for an intermediate image Z or to determine a changed motion state M for a voxel V based on its calculated column image position p, p' in an intermediate image Z. A motion state M, MI can therefore be determined using two modes. The first mode is the selection of a motion state MI. This occurs here, for example, based on a specification by the currently used intermediate image Z (see, for example, Figure 8). For example, the selection can be made by selecting a motion state MI that corresponds to the center of the intermediate image Z. The second mode is the determination of a motion state M based on a calculated column image position p. This simply requires a specification of the column position, and a motion state M is selected accordingly, which is linked to this column image position P (of the relevant intermediate image Z).

[0101] A positioning module 31 is designed to calculate a voxel position x', x M of the voxel V from its original voxel position x and the movement profile BP to a selected or calculated movement state MI, M. The positioning module 31 is in contact with a movement profile BP, which is present here in the storage unit 16. The calculation of a voxel position is described in more detail below. Figure 2described, wherein the positioning module 31 is able to calculate both the reference voxel position x M and the changed voxel position x'.

[0102] An imaging module 32 is designed to calculate a column image position p, p' and a line image position q, q' at which a voxel V would be imaged in an intermediate image Z. With respect to the reference voxel position xM, it is only necessary to calculate the column image position of the voxel V in the intermediate image Z, but its line image position q can also be calculated additionally. For the changed voxel position x', both the column image position p' of the voxel in the intermediate image Z and its line image position q' must be calculated so that the appropriate image information can later be assigned to the voxel V.

[0103] An acquisition module 33 is configured to acquire an image value of the intermediate image Z at the modified image position p', q' for use in backprojection. The acquisition module 33 can acquire the image value of the intermediate image Z, for example, simply by copying the image information at previously calculated image coordinates p', q' and writing it into a data set for backprojection.

[0104] Figure 2 shows a flow chart for a possible sequence of an inventive method for motion compensation in CT reconstruction.

[0105] In step I, projection images B of a CT scan are provided, whereby a beam from the X-ray source 3 of the CT scanner 2 is directed to Figure 1 is radiated onto the detector 4 and a series of projection images B are recorded.

[0106] In step II, intermediate images Z are created, whereby the intermediate images Z are created from a rebinning of columns of the projection images B. Here, parallelized intermediate images Z are created from projection images B that were recorded with a conical beam.

[0107] In step III, layer images S are calculated by back-projecting the intermediate images Z onto predetermined voxels V of the layer images S, whereby the following steps are carried out for each intermediate image Z and for each voxel V based on a predetermined movement profile BP of the voxels V during the recording of the projection images B: In step IIIa, an initial movement state MI is selected based on the intermediate image Z. This can, for example, correspond to a coordinate exactly in the center (e.g. in the image center) of the intermediate image Z.

[0108] In step IIIb, a reference voxel position xM of voxel V is calculated from its original voxel position x and from the motion profile BP to the initial motion state MI. Voxel V may have moved to the original voxel position xM in the initial motion state MI. This movement is taken into account here.

[0109] In step IIIc, a column image position p is calculated at which voxel V would be imaged at the reference voxel position xM in the intermediate image Z. Here, the complete image position p, q is calculated, although the row image position q is not necessarily required. This can be done, for example, by projecting voxel V onto the intermediate image Z.

[0110] In step IIId, a changed motion state M of the voxel V is determined based on the calculated column image position p.

[0111] In step IIIe, a changed voxel position x' of the voxel V is calculated from its original voxel position x and the motion profile BP to the changed motion state M.

[0112] In step IIIf, a changed image position p', q' is calculated, at which the voxel V would be imaged at the changed voxel position x' in the intermediate image Z.

[0113] In step IIIg, an image value of the intermediate image Z at the changed image position p', q' is used for the back projection.

[0114] A dashed arrow indicates that steps IIId to IIIf can be repeated or repeated several times in the form of an iterative improvement of the result, with the changed column image position p' then forming the basis in step IIId.

[0115] Figure 3shows an expanded flow chart for a possible sequence of an iterative procedure, where after calculating the slice images S from the intermediate images Z according to Figure 2 The following steps are performed: In step IIIh, comparison intermediate images (ZV) are reconstructed from the slice images based on the motion profile (BP). This step is divided into four substeps.

[0116] In step IIIh 1< a ray is calculated through the image voxels VB starting from a pixel of the comparison intermediate image ZV.

[0117] In step IIIh 2<, the motion data for a motion state M is determined according to the column image position p in the comparison intermediate image ZV from the motion profile BP and the positions of the beam and image voxels VB are shifted relative to one another according to the motion data of the motion profile BP to the motion state M, in particular wherein the beam is moved according to the motion data.

[0118] In step IIIh 3< an accumulation of values ​​of the image voxels VB along the ray with the relative displacement of ray and image voxels VB takes place.

[0119] In step IIIh 4< the accumulated values ​​for the position p, q are transferred to the comparison intermediate image ZV.

[0120] In step IIIi, the comparison intermediate images ZV are compared with the intermediate images Z.

[0121] In step IIIj, revised slice images S are created based on the comparison.

[0122] Steps IIIh, IIIi and IIIj are repeated iteratively with the most recently created slice images S.

[0123] Figure 4 shows a flowchart for a preferred iterative procedure.

[0124] From the intermediate images Z (denoted by Z0 in the following formula), slice images S are generated using a backprojection Q as described above. This backprojection Q combines the convolution and the backprojection itself in one step. The first slice image S (in the formula f0) is iteratively improved with each pass (fk). A forward projection (in the formula P) calculates a comparison intermediate image ZV from a slice image S (according to P(fk)).

[0125] The difference between the comparison intermediate image ZV and the original intermediate image Z is then calculated: P(fk ) - Z0. The result is backprojected: Q(P(fk ) - Z0) and the result is subtracted from the previous slice image by a factor a: fk-aQ(P(fk ) - Z0). This yields the next slice image f k+1, and the steps are then repeated.

[0126] In forward projection, motion is inserted rather than removed as in back projection. Ideally, the slice image S is free of motion after motion-compensated back projection. In forward projection, for each intermediate comparison image ZV, the iteration is no longer through the voxels, but rather through the positions (p, q) of the intermediate comparison image ZV. For each position in the intermediate comparison image ZV, the corresponding ray through the corresponding voxel volume is calculated, and the values ​​of the voxel volume along the calculated ray are written to the position in the intermediate comparison image ZV.

[0127] Since the position in the intermediate comparison image ZV is known, the motion state M corresponding to the respective column image position p can be determined to include the motion. For example, this motion state M can be used to move the ray through the voxel volume instead of the entire voxel volume itself. In principle, however, both are possible. The values ​​along the newly calculated ray can now be written to the corresponding position in the intermediate comparison image ZV. This calculates an intermediate comparison image ZV that also contains the motion.

[0128] Figure 5 shows a schematic representation of a preferred system 9. A basic structure of the system 9 has already been described in Figure 1 shown, however, this preferred embodiment has, in addition to the data interface 6, re-binning unit 7 and the Figure 1In addition to the modules shown, movement module 30, positioning module 31, imaging module 32 and transfer module 33, the reconstruction unit 8 also has further modules with which the system 9 is designed for a method as described in Figure 3 shown. These additional modules are:

[0129] A ray simulation module 34 designed to calculate a ray through the image voxels VB starting from an image point.

[0130] A motion simulation module 35 designed to determine the motion data of a motion state M corresponding to the column image position p in the comparison intermediate image ZV from the motion profile BP and to shift the positions of beam and image voxels VB relative to one another according to the motion data of the motion profile BP to the motion state M.

[0131] A simulation acquisition module 36 designed to accumulate values ​​of the image voxels VB along the ray with the relative displacement of ray and image voxels VB and to acquire the accumulated values ​​for the position p, q in the comparison intermediate image.

[0132] Figure 6 shows an image of moving voxels V. The solid cube shows 27 voxels V, of which the voxel V in the top right corner is imaged in its original voxel position x. This image was the projection image B during the recording and is the result of an iterative process (see Figure 3 ) the comparison intermediate image ZV. As can be seen, a ray (solid arrow) traverses several voxels on its way to the image, so that the image value on the image does not necessarily have to match the image value of the voxel (and usually does not, hence the complex backprojection).

[0133] The representation could also show an intermediate image Z with inverted arrows.

[0134] During a recording, the cube moves along the dot-dash arrow to a different position, indicated by a dashed cube. After the movement (depending on the motion state MI, M), the voxel is located at a reference voxel position x M or a changed voxel position x' and is imaged at a completely different location in the image (dashed arrow).

[0135] The movement shown here is a very simple one, with the voxels still remaining in their original configuration. In reality, this movement is usually more complex, and each voxel can move individually. However, a normal examination always shows a closed configuration in which neighboring voxels move very similarly. For example, a beating heart moves, but its walls (fortunately) always form a closed body.

[0136] Figure 7shows a re-binning of a projection image B (top), which was recorded with a conical beam profile on a helical trajectory (see sketch on the right), to an intermediate image Z (bottom). Due to the calculations performed during re-binning, the motion state M of the intermediate image Z changes with the columns (direction p), but not with the rows (direction q). The center of the intermediate image Z contains the same motion state M as the projection image B before re-binning. When moving to the right in the image, the previous motion states M are present, while when moving to the left in the image, the subsequent motion states M are present. The exact position of each motion state M in the intermediate image Z must be calculated individually, as it depends on several parameters.

[0137] Looking at the sketch at the bottom right, it becomes obvious that the intermediate image Z in this example does not have a completely parallel geometry, but only a semi-parallel one. Only when viewed in the p-direction are the rays completely parallel. This is not the case along the q-direction. However, this does not pose a problem for the invention, since the q-coordinate is only needed to select the image values ​​and can be easily determined.

[0138] Figure 8 shows a selection of a motion state M and outlines the determination of a movement of the voxel position x'.

[0139] The most accurate motion compensation method would be to use the exact motion for each motion state (i.e., at each column image position p) of each intermediate image Z for the backprojection step. However, this leads to memory problems with the current implementation of the reconstruction algorithms. A compromise can be applied that achieves good results with less memory.

[0140] For this purpose, during the backprojection of the intermediate images Z, motion data from the motion profile BP are preselected for a number of the intermediate images Z, in particular for each intermediate image Z from the motion profile BP for the initial motion state MI and for at least one earlier and at least one later motion state M. Here, in addition to the initial motion state MI with the number 20, these are the motion states M 27 and 13.

[0141] Thus, for each intermediate image Z, three motion states M1 and M are used: one in the center, one on the left, and one on the right. The intermediate motions are interpolated, for example, using linear interpolation from the preselected motion data at positions 13, 20, and 27. However, it must be noted that the left and right motion states M do not necessarily have to be furthest to the left or right, as these areas of the intermediate image Z may not be reached depending on parameters such as the field of view. The best position can be calculated individually, taking these parameters into account.

[0142] The motion state M (at p above the curly bracket) can now be calculated, and the changed voxel position x' of voxel V can be calculated based on preselected motion data for motion states 27 and 13 based on interpolated motion data. The proximity to neighboring motion states M can be incorporated in the form of a weighting.

[0143] Figure 9 shows a comparison of the results of the method according to the invention. The images show a simulated scan of a clock phantom reconstructed using the WFBP algorithm.

[0144] On the left (0) is an image of the stationary object to be imaged as a reference, or rather, its reconstruction result, as it should ideally appear after reconstruction. To the right (>0) is an image of a moving object (during translation) or its reconstruction result with uncompensated motion. Serious artifacts caused by the motion can be seen. This image is intended to be improved by the invention.

[0145] The third image (SdT) shows a reconstruction according to the state-of-the-art (motion compensation method according to Schäfer et al.) combined with the WFBP algorithm. Although the artifacts were significantly reduced, some artifacts remain, which arise from the fact that incorrect image information was assigned to the voxels during reconstruction.

[0146] The right image (E) shows a reconstruction according to the inventive method, where the method was applied only once (and no additional iteration steps). Virtually no motion artifacts can be seen. It should be noted that although the right and left images appear identical at first glance, slight differences become apparent upon closer inspection (e.g., subtraction). In the case shown here, the object's movement was 100% known. More complex movements could also cause slight artifacts in the inventive method, but these can be reduced with iterations of the method.

[0147] Finally, it should be noted once again that the methods described in detail above, as well as the computed tomography system 1 shown, are merely exemplary embodiments that can be modified in a variety of ways by those skilled in the art without departing from the scope of the invention. Furthermore, the use of the indefinite articles "a" or "an" does not exclude the possibility that the respective features may be present in multiple instances. Likewise, the terms "unit" and "module" do not exclude the possibility that the respective components consist of several interacting subcomponents, which may also be spatially distributed. The term "a number" is to be understood as "at least one."

Claims

1. Method for motion compensation in CT reconstruction comprising the steps: - providing projection images (B) of a CT scan, - creating intermediate images (Z), wherein the intermediate images (Z) are created from a rebinning of gaps in the projection images (B), - calculating slice images (S) by means of a back projection of the intermediate images (Z) on predetermined voxels (V) of the slice images (S), wherein for each intermediate image (Z) and for each voxel (V) based on a predetermined motion profile (BP) of the voxels (V) during the recording of the projection images (B), the following steps are carried out: a) selecting an initial state of motion (MI) based on the intermediate image (Z), b) calculating a reference voxel position (xM) of the voxel (V) from its original voxel position (x) and from the motion profile (BP) relating to the initial state of motion (MI), c) calculating a gap image position (p), at which the voxel (V) at the reference voxel position (xM) has been mapped in the intermediate image (Z), d) determining an amended state of motion (M) of the voxel (V) based on the calculated gap image position (p), e) calculating an amended voxel position (x') of the voxel (V) from its original voxel position (x) and the motion profile (BP) relating to the amended state of motion (M), f) calculating an amended image position (p', q') at which the voxel (V) has been mapped at the amended voxel position (x') in the intermediate image (Z), g) using an image value of the intermediate image (Z) at the amended image position (p', q') for the back projection.

2. Method according to claim 1, wherein the initial state of motion (MI) corresponds to a gap image position (p), which lies substantially in the centre of the intermediate image (Z) and one such initial state of motion (MI) is preferably selected for each intermediate image (Z).

3. Method according to claim 2, wherein that gap in the intermediate image (Z), which lay precisely in the centre of the image in one of the projection images (P), corresponds as the centre.

4. Method according to one of the preceding claims, wherein with the back projection of the intermediate images (Z) for a number of intermediate images (Z), in particular for each intermediate image (Z) for the initial state of motion (MI) and at least for an earlier and at least one later state of motion (M), motion data is preselected from the motion profile (BP), the motion data relating to the amended state of motion (M) is interpolated from this motion data and the amended voxel position (x') of the voxel (V) is calculated on the basis of this interpolated motion data relating to the amended state of motion (M), preferably wherein the interpolation is based on those states of motion (M) which lie closest to the amended state of motion (M), preferably wherein the distance between the image positions of the states of motion (M) are incorporated in the form of a weighting.

5. Method according to one of the preceding claims, wherein the following steps are run through at least once before using the image value for the back projection between the steps e) and f): - calculating an amended gap image position (p') at which the voxel (V) has been mapped at the amended voxel position (x') in the intermediate image (Z), - determining an amended state of motion (M) of the voxel (V) based on the amended gap image position (p'), - calculating an amended voxel position (x') of the voxel (V) from its original voxel position (x) and the motion profile (BP) relating to the amended state of motion (M).

6. Method according to one of the preceding claims, wherein when the intermediate images (Z) are created, a rebinning of the gaps of the projection images (B) is carried out to such an extent that those gaps in the projection images (B), which have been recorded with in each case parallel x-rays in a plane orthogonal to the gaps, are used for an intermediate image (Z).

7. Method according to one of the preceding claims, wherein the intermediate images (Z) are filtered for an improved reconstruction result, in particular by means of a folding and / or a Fourier transform, wherein with a preferred folding, a filtered intermediate image (Z) is calculated by means of a predefined kernel, in particular a ramp filter, such as e.g. a Shepp-Logan kernel, and / or an intermediate image (Z) is preferably subject to a Fourier transform and multiplied by an adjusted filter in the Fourier space.

8. Method according to one of the preceding claims, wherein after calculating the slice images (S) from the intermediate images (Z), the following steps are carried out: i) reconstruction of comparison intermediate images (ZV) from the slice images based on the motion profile (BP), ii) comparison of the comparison intermediate images (ZV) with the intermediate images (Z), iii) creation of revised slice images (S) based on the comparison, iv) iterative repetition of the steps i) to iii) with the slice images (S) created last.

9. Method according to claim 8, wherein with the reconstruction of the comparison intermediate images (ZV) for each pixel of each comparison intermediate image (ZV), the pixels of the comparison intermediate images (ZV) are determined according to the following steps: - calculating a beam through the image voxel (VB) starting from a pixel of the comparison intermediate image (ZV), - determining the motion data for a state of motion (M) corresponding to the gap image position (p) in the comparison intermediate image (ZV) from the motion profile (BP), - shifting the positions of beam and image voxels (VB) relative to one another corresponding to the motion data of the motion profile (BP) relating to the state of motion (M), in particular wherein the beam is moved according to the motion data, - accumulating values of the image voxel (VB) along the beam with the relative shift in beam and image voxels (VB), - taking over the accumulated values for the position (p, q) in the comparison intermediate image (ZV).

10. System (9) for motion compensation in CT reconstruction, comprising means for carrying out a method according to one of the preceding claims.

11. Control facility (10) for controlling a computed tomography system (1) comprising a system according to claim 10 and / or designed to carry out a method according to one of claims 1 to 9.

12. Computed tomography system comprising a control facility (10) according to claim 11.

13. Computer program product with a computer program, which can be loaded directly into a storage facility of a control facility (10) of a computed tomography system (1), having program segments in order to carry out all steps of the method according to one of claims 1 to 9 when the computer program is executed in the control facility (10) of the computed tomography system (1).

14. Computer-readable medium, on which program segments which can be read in and executed by a computer unit are stored, in order to execute all steps of the method according to one of claims 1 to 9 when the program segments are executed by the computer unit.