CN103027705B - Produce the method and system of the CT image data set of motion compensation - Google Patents

Abstract

The invention relates to a method for generating a motion-compensated CT image data record, in which a projection data record of a CT system (1) is acquired from a predetermined range of motion phases and projection angles, which allows a direct reconstruction of the CT image data record ; Determining the motion field iteratively by reconstructing the image with the first image resolution multiple times by means of a motion-compensated reconstruction method using a first analytical reconstruction algorithm and different motion fields each consisting of a large number of position-specific motion vectors The CT image data set and the motion field is determined using at least one predetermined mandatory condition; and the motion field is reconstructed with a second image resolution using a motion-compensated reconstruction method based on a second reconstruction algorithm and the determined motion field The final CT image dataset of . Furthermore, the invention relates to a computer system for image reconstruction and a CT system with such a computer system, in which the above-mentioned method is carried out during operation.

Description

Method and system for generating a motion-compensated CT image data set

technical field

The invention relates to a method for generating a motion-compensated CT image data record of a partially and periodically moving examination object, in particular a patient with a periodically moving organ or a periodically moving body region, using a sports field. method, the playing field consists of a large number of position-specific motion vectors. Furthermore, the invention relates to a computer system for image reconstruction and a CT system with such a computer system, in which the above-mentioned method is carried out during operation.

Background technique

It is generally known that due to cardiac motion during CT recordings, the recorded data are inconsistent and lead to image artifacts, which severely limit the clinical usability of the data. In order to avoid such image artifacts in modern CT cardiac imaging, phase-dependent representations of the heart are generated by recording or using cardiac phase-dependent data. Basically, retrospective and forward acquisition concepts exist for this purpose. In the case of a prospective acquisition concept, data are recorded only in a certain window around the resting phase of the heart and used for image reconstruction. A common goal of these schemes is to nearly freeze the heart motion and minimize data inconsistencies and thus optimize image quality.

However, due to a gantry rotation that is too slow relative to the heart motion or a heartbeat that is too fast relative to the gantry rotation, this strategy is not sufficient: a sufficiently good temporal resolution is achieved to calculate an artifact-free image. Various algorithms for improving the temporal resolution after the fact are known in the prior art. In H． T． Allmendinger, K. Stierstorfer, H. Bruder and T. Flohr's literature "Evaluation of a novel CT image reconstruction algorithm with enhanced temporal resolution", Proceedings of SPIE, p. 79611N, 2011 describes reducing the amount of data required by theoretical angular scanning below 180 degrees, where image quality has to be iteratively optimized due to incomplete data. In addition, in D. J． Borgert, V. Rasche and M. "Motion-Compensated and Gated Cone Beam Filtered Back-Projection for 3-DRotational X-Ray Angiography" by Grass, IEEE Transactions on Medical Imaging, Vol. 25, No. 7, pp. 898-906, Jul. 2006 discloses the data that can be taken into account for reconstruction during motion-compensated reconstruction given object motion. This process results in greatly improved image quality.

Finally, see also DE 10 2009 007 236 A1, which discloses a motion-compensated CT reconstruction method for at least partially moving objects. In this method, a moving examination object is scanned with a CT system and a cross-sectional image of the examination object is determined from the acquired detector data by means of an iterative algorithm, wherein motion information about the motion of the examination object during the data acquisition is taken into account in the iterative algorithm. This motion information is represented in the form of a motion field composed of a large number of position-specific vectors which describe the motion or displacement of the object at the respective position at the recording time. In order to determine the motion field, it is proposed here to compare two temporally separated CT recordings and to infer a location-specific motion from changes in the CT recordings.

But so far, the problem of correctly estimating motion in order to improve the image quality of the "best stage" image, ie the image obtained from the best still stage and thus the highest quality, has not been solved. Solutions to date only estimate motion through the registration of two 3D standard reconstructions of different cardiac phases. But so far it has not been possible to show an improvement in the quality of the "best stage" image, since this image inherently limits the temporal resolution of the registered data. On the contrary, the images of the poorer cardiac phases are greatly improved and thus, for example, other cardiac phases can be displayed with improved image quality.

Contents of the invention

The technical problem underlying the present invention is therefore to find a method and a CT system or computing system for image reconstruction which reduce residual image artifacts by an improved iterative determination of motion fields and subsequent motion compensation when reconstructing the image data , wherein flawed results should be avoided especially when iteratively determining the motion field.

The basis of the invention is an improved representation of the motion estimation by means of a motion-compensated reconstruction algorithm. Correspondingly, the result of motion-compensated reconstruction of the "best stage" image f _bp (x, s) directly depends on the parameters describing the motion For this purpose, the parameter s is estimated in such a way that the result satisfies certain image characteristics. Formally this can be done by taking the value function Implemented as an analysis metric minimization. If an analytical reconstruction algorithm such as the FDK algorithm (FDK = Feldkamp-Davis-Kress) is used for the reconstruction of the "best stage" image, then an efficient calculation specification can be given, which is calculated by the image characteristics of the reconstructed image (such as entropy, total variation and similar features) iteratively determine the parameters for motion compensated reconstruction. The motion field is thus determined from the CT data of the CT image data set for a single examination time point or examination phase of the motion cycle (without using CT image data for other time points or other examination phases of the motion cycle), A motion-compensated reconstruction can be carried out using this motion field.

Furthermore, in order to reduce the computational cost, the objective function can be calculated only through the partial images that contain motion. Formally, a motion map is calculated for this purpose, which indicates the probability that motion artifacts are present at this location in the image.

In the method according to the invention, for this purpose a motion field which is to be estimated as precisely as possible within the diagnostically relevant radiation time, that is to say describes the motion, is formed.

For this reason, propose following measures according to the present invention:

The value function can be defined using the measurement data p _in

$L\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)={\left|\right|p_{\mathrm{in}}\left(t\right)-A(\stackrel{\&Right\; Arrow;}{x},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})f(\stackrel{\&Right\; Arrow;}{x},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})\left|\right|}^2$ Formula 1)

Here, f refers to the image vector of gray values and A refers to the voxel-based projector that models the CT imaging system. vector Refers to the voxel vertices defined for time t in image space sports field. Reverse transformation.

In principle, the motion field can be calculated in an optimization method, ie the following optimization problem has to be solved.

${\min \arg }_{\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}L={\left|\right|p_{\mathrm{in}}-A(\stackrel{\&Right\; Arrow;}{\text{x}},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})f(\stackrel{\&Right\; Arrow;}{\text{x}},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})\left|\right|}^2$ Formula (2)

The following "updated" formula is obtained for the motion field using the gradient method:

${\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}_{k+1}={\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}_k+\mathrm{\γ}\&Center\; Dot;\frac{\∂L\left({\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}_k\right)}{\∂\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}$ Formula (3)

In this case, the step size γ can depend on the iteration step k.

Independent of optimization methods, the derivative of the value function usually has to be determined from the parameters of the playing field. According to the invention, the gradient fraction should be adjusted by means of the constraints to be applied This makes the solution to the computational motion field stable.

Several approaches are suggested for this:

1. Limit the motion field to the region B, where motion is detected with respect to the time point t under consideration. Set the gradient share in the remainder CB Motion maps are used to map areas of object motion. In this case, for example, the image signals can be compared with respect to two points in time t1, t2 adjacent to the point in time t. and Then as the distance between gray values for example one can use $\mathrm{MM}(\stackrel{\&Right\; Arrow;}{x},t){\mathrm{\Σ}}_{i=1}^N{(f({\stackrel{\&Right\; Arrow;}{x}}_i,\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}},t_1)-f({\stackrel{\&Right\; Arrow;}{x}}_i,\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}},t_2))}^2$ to compute motion graphs. The motion state can then be classified by means of the threshold value criterion in such a way that the scan region of the object under examination is divided into subregions with and without expected motion, the actual motion field being determined only in the moving subregion.

2. As the initial motion vector field, a physiological model of the typical motion of an organ (such as the heart or lungs) can be selected.

3. For iteratively determining the decay distribution of the motion field through about two different time points _t1 and _t2 and A loose registration of , to determine and use the initial motion field. With regard to the determination of the motion field on the basis of two temporally adjacent CT images, a large number of registration methods are known in the literature. See, for example, the document DE 10 2009 007 236 A1 already mentioned at the outset. Registration can eg be restricted to the coronary tree according to the segmentation step. Furthermore, a motion map can also be determined from the registration by only considering regions with strong deformations.

4. Since the motion is not independent of adjacent regions, the motion field can be smoothed with a 4D spatio-temporal filter kernel. For example, separate Gaussian filters or edge-preserving filters can be used for this purpose.

According to the parameters of the playing field, the derivative of the value function is determined as follows:

$\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

Formula (4)

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

Now the problem is that the directional derivative of projector A cannot be simply determined, because for example in the finite difference method at each vertex in the image volume the motion field has to be transformed into three spatial directions and each configuration has to be projected to in the data space.

It is therefore proposed according to the invention to transform the cost function according to formula (1) into image space by considering the backprojected signal. This leads to the transformed value function:

$\hat{L}\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)={\left|\right|Q\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)(p_{\mathrm{in}}-A(\stackrel{\&Right\; Arrow;}{x},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})f(\stackrel{\&Right\; Arrow;}{x},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}))\left|\right|}^2$ Formula (5)

in is a motion compensated back projector.

pass $f(\stackrel{\&Right\; Arrow;}{x},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})=Q\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)\&CenterDot;p_{\mathrm{in}}$ Established:

$\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}<span\; class="notranslate">\; )</span>$

Formula (6)

$=2\&Center\; Dot;L\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)\&Center\; Dot;\frac{\&PartialD;}{\&PartialD;\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}(Q\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)(1-T\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right))\&CenterDot;p_{\mathrm{in}})$ in $T\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)=A(\stackrel{\&Right\; Arrow;}{x},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})Q\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right);$

The operator T as a combination of back-projection and forward-projection represents a low-pass filter, whereby 1-T represents a high-pass filter. The backprojector Q comprises convolution with a convolution kernel typical for computed tomography and the backprojection of the filtered signal into image space. Therefore, the item Only the filtering characteristics of the backprojection are changed. ignoring In the case of

$\frac{\&PartialD;}{\&PartialD;\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}\hat{L}\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)=2\&CenterDot;\hat{L}\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)\&Center\; Dot;\frac{\&PartialD;}{\&PartialD;\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}Q\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)\&Center\; Dot;p_{\mathrm{in}}=2\&Center\; Dot;\hat{L}\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)\&CenterDot;\frac{\&PartialD;}{\&PartialD;\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}\text{f}(\stackrel{\&Right\; Arrow;}{x},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})$ Formula (7)

calculate is simple because

$f(\stackrel{\&Right\; Arrow;}{x},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})=\underset{i}{\mathrm{\&Sigma;}}{\hat{p}}_{\mathrm{in}}(i,B(i,{\stackrel{\&Right\; Arrow;}{x}}^{\&prime;}))$ Formula (8)

can be described as a filtered measurement projection back projection. here, denote the backprojection coordinates of the CT geometric features in the i-th projection, and obtain:

$\frac{\&PartialD;}{{\&PartialD;\mathrm{the\; s}}_{i,\mathrm{the\; y}}}f(\stackrel{\&Right\; Arrow;}{x},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})=\frac{\&PartialD;}{{\&PartialD;u}^{\&prime;}}{\hat{p}}_{\mathrm{in}}(i,u^{\&prime;})\&Center\; Dot;\frac{\&PartialD;B(i,{\mathrm{the\; y}}^{\&prime;})}{{\&PartialD;\mathrm{the\; y}}^{\&prime;}}$ Formula (9)

The motion field can now be determined iteratively via equations (3) and (7). In this case, the sports field can be subjected to different forcing conditions, for example low-pass filtering. In addition, possible boundary conditions can also be specified for the sports field.

Corresponding to this basic idea, the inventor also suggests following method and device:

The core of the invention consists of a method for generating a motion-compensated CT image data record of a partially and periodically moving examination object, in particular a patient with a periodically moving organ or a periodically moving body region, using a sports field. , the motion field consists of a large number of position-specific motion vectors, the method has the following method steps:

- acquisition or transmission of a projection data set of a computed tomography system, containing predetermined motion phases and projection angle regions, said projection data set allowing direct reconstruction of the CT image data set,

- Determine the playing field iteratively by:

- multiple reconstructions of the CT image data set with the first image resolution by means of a motion-compensated reconstruction method using a first analytical reconstruction algorithm and different motion fields each consisting of a plurality of position-specific motion vectors,

- determine the playing field, preferably determine the optimal playing field, wherein the playing field is subject to at least one predetermined mandatory condition,

- reconstruction of the final CT image dataset with a second image resolution based on a second reconstruction algorithm and a motion field using a motion-compensated reconstruction method,

- storage of the final CT image data set or output of the final CT image data set on an image reconstruction system.

Since the registration of the sports fields is the subject of the invention, it can also be applied to methods in which two or three image data sets are determined. In the method according to the invention (contrary to the prior art) on the one hand the sports field is not determined by comparing two or more image data records, but the motion vector of the sports field is determined only from the data of a single image data record, which A unique image data set consists of a plurality of tomographic 2D cross-sectional images or a single 3D image acquired at the same time interval and distributed about the z-axis of the acquired CT system by finding motion vectors which are ultimately obtained by A motion-compensated reconstruction (that is, a reconstruction in which the calculation of the tomographic representation is performed using a motion field and for compensating the position-specific motion described there) results in a reconstructed image in which In the reconstructed image, one or more image features representing a measure of the motion blur of the image are optimized such that a minimum motion blur can be assumed. In order to determine the playing field, at least one mandatory condition is applied to the playing field here, which is derived from the foreknowledge, that is to say from the information obtained before the execution of the iteration.

As at least one mandatory condition for the motion field, for example, a spatial boundary of the motion field to be determined can be used, wherein the spatial boundary is smaller than the spatial perimeter of the final CT image data set and lies within the final CT image data set, and wherein in addition Outside the boundaries the motion vector takes on the value zero in the playing field. Gradient fractions outside the bounds are thus set to zero when using the gradient descent method.

Alternatively, a predetermined physiological motion model for the motion in the scanning region or a subregion located there may also be used as at least one mandatory condition for the motion field. This completely precludes incorrect calculations leading to other motion patterns.

Furthermore, an initial motion field can also be used in the iterative determination as at least one mandatory condition for the motion field, which is determined on the basis of two temporally separated CT image data records of the examination object that are not strictly registered.

Furthermore, a motion field filter can also be used as at least one mandatory condition for the motion field, wherein for the filtering, for example, a separate Gaussian filter, in particular an edge-preserving filter, or a spatiotemporal smoothing filter kernel can be used.

In order to produce the sharpest possible image from the start, it is advantageous if the projection angle range from which the detector data originates is 180° plus the fan angle of the beam used for scanning. This corresponds to the minimum value of the projection angle range at which tomographic recordings can be performed in conventional reconstruction techniques.

Furthermore, it is proposed to use the following methods as analytical reconstruction methods: FDK reconstruction method (FDK=Feldmann-Davis-Kress), Clack-Defrise reconstruction method, reconstruction method based on Hilbert transform, reconstruction method based on Fourier transform, The Radon method.

For example, one or more of the following image features can be used as an optimization criterion for determining the sports field: entropy, total variation/total fluctuation, compressibility.

Furthermore, it is advantageous for carrying out the method according to the invention that, as usual in cardiac reconstruction, detector data are collected from a plurality of motion cycles for generating the projection data sets used. In this case, for example, the detector data are collected from a (possibly relatively narrow) predetermined phase range in each case over several heartbeats until the desired projection angle range is scanned, so that due to the detector data used for the reconstruction the full range is already present. A small motion blur is possible, but this is further reduced by the method according to the invention.

Furthermore, it is advantageous if the motion field is not determined using the entire area of the tomographic representation, but only with respect to a partial area of the object. In this way, on the one hand, the required computing power can be reduced, and on the other hand, it can be limited to the actually relevant region, so that externally located artifacts do not interfere.

Based on the previously described method for determining a motion field, a method for generating a motion-compensated CT image data record of a partly and periodically moving object, in particular a patient with a beating heart, is now also proposed, which method has The method steps are as follows:

- acquisition or transmission of a projection data set of a computed tomography system, containing predetermined motion phases and projection angle regions, said projection data set allowing direct reconstruction of the CT image data set,

- determine the playing field according to the invention,

- reconstruction of the final CT image dataset with a second image resolution based on a second reconstruction algorithm and a motion field using a motion-compensated reconstruction method,

- storage of the final CT image data set or output of the final CT image data set on an image reconstruction system.

A motion-compensated reconstruction calculation is thus carried out on the basis of the motion field determined according to the invention and a tomographic representation is calculated in which at least as far as possible motion artifacts are eliminated. Overall, a further improved tomographic image is obtained starting from the "best phase" detector data, without using further detector data for this purpose than is already required for reconstructing the image.

Although in principle it is possible to base the calculation of the motion field on the same positional resolution as the calculation of the final image, it is advantageous that the first image (for calculation of the motion field) has a higher resolution than the second image (of the final CT representation) Lower resolution.

It is also advantageous if the second reconstruction algorithm differs from the first reconstruction algorithm. It is thus possible, for example, to use relatively simple analytical algorithms within the scope of the determined motion field, which allow as fast a reconstruction as possible, and for the final reconstruction of the CT representation to use more complex algorithms which produce the best images.

It should also be pointed out that it is not necessarily necessary to use only a single reconstruction algorithm within the scope of the determination of the playing field. It is also possible first of all to roughly determine the playing field by means of a very simple "coarse" reconstruction and then to carry out a "fine tuning" of the playing field using a more complicated reconstruction method.

The first reconstruction algorithm must be an analytical reconstruction algorithm, whereas the second reconstruction algorithm can be an analytical, iterative or non-analytic reconstruction algorithm, where the application of known post-hoc image improvement is also within the scope of the invention.

Furthermore, detector data can be collected from one or more motion cycles for generating the projection data sets used, in particular in the case of cardiac CT examinations.

In addition to the method according to the invention, the inventor proposes a computing system for image reconstruction having a memory for storing a computer program and a processor for executing the stored computer program, wherein in the memory At least one computer program is provided, which executes the method steps of the method according to the invention when the computing system is running.

A CT system having the computing system described above is also within the scope of the present invention.

Description of drawings

The invention and preferred exemplary embodiments are explained in greater detail below with the aid of the drawing, in which only the features necessary for understanding the invention are shown. The following reference numbers are used: 1: CT system/C-arm system; 2: first X-ray tube; 3: first detector; 4: second X-ray tube; 5: second detector 6: housing 7: rotating arm; 8: examination couch; 9: system axis; 10: computing system; 11: contrast agent applicator; 12: EKG wire; P: patient; Prg ₁ -Prg _n : computer program. In the attached picture:

Figure 1 shows a CT system for performing the method according to the invention;

Figure 2 shows a C-arm system for carrying out the method according to the invention;

FIG. 3 shows a tomographic CT sectional image with superimposed motion fields reconstructed without motion compensation;

Fig. 4 shows the CT sectional image of the tomography of the heart obtained by dual-source CT examination;

Fig. 5 shows the tomographic CT cross-sectional image of the heart obtained by single-source CT examination;

FIG. 6 shows a reconstruction of a tomographic CT sectional image of the heart obtained from a single-source CT examination using the motion-compensated reconstruction according to the invention.

detailed description

FIG. 1 shows an example of a CT system 1 with a computing system 10 with which the method according to the invention can be carried out. The CT system 1 has a first tube/detector system with an x-ray tube 2 and an oppositely arranged detector 3 . Optionally, the CT system 1 has a second X-ray tube 4 and a detector 5 arranged opposite. The two tube/detector systems are located on a gantry, which is arranged in a gantry housing 6 and rotates about a system axis 9 during scanning. The patient P is located on a movable examination couch 8 which is moved either continuously or sequentially along the z-axis or the system axis 9 through the scanning field located in the gantry housing 6, wherein the x-ray Attenuation of X-ray radiation emitted by the tube.

During the measurement, a bolus of contrast agent can be injected into the patient P by means of the contrast agent applicator 11 , so that blood vessels can be better identified or a perfusion measurement can be performed. In cardiac recordings, cardiac activity can additionally be measured by means of EKG lead 12 and EKG-gated scans can be carried out.

The CT system is controlled and the method according to the invention is executed by means of a computing unit 10 in which are located computer programs Prg ₁ -Prg _n which can also carry out the method according to the invention described above. In addition, image data can also be output by the computing unit 10 .

Alternatively, the method according to the invention can also be carried out in conjunction with detector data from a CT system of the type C-arm system 1 (shown in FIG. 2 ). The C-arm system 1 shown here likewise has an x-ray tube 2 and a detector 3 arranged opposite and designed in a planar manner. Both systems are rotated around the patient P in any position by means of the swivel arm 7 . In this case, the patient P is situated on a patient table 8 which additionally has a contrast agent application system 11 in order to inject a contrast agent, if necessary, for visualization of blood vessels. Furthermore, an EKG scan (not shown in detail) can also be carried out in this C-arm system for determining the cardiac cycle and the cycle phases embedded therein.

Likewise, the system is controlled by a computing unit 10 having in its memory a computer program Prg ₁ -Prg _n which, among other things, can also carry out the method according to the invention for determining the playing field and with which the playing field can be An optimal motion-compensated reconstruction of the tomographic image data is carried out.

FIG. 3 shows a tomographic CT sectional image reconstructed without motion compensation with a superimposed representation of a motion field consisting of a large number of motion vectors or motion vectors. These vectors or vector bundles at each vertex describe a measure of the probability of movement in the indicated direction for each vertex based on previously found motion blur bundles in the reconstructed image.

The section is also marked in the image with a dotted rectangle, which is shown magnified in the lower right corner of the image. The individual motion vectors can be recognized particularly well in the enlarged image, which are particularly pronounced in their direction in the peripheral region of the imaged heart. The motion field is determined using a value function transformed to image space and its derivative:

$\frac{\&PartialD;}{\&PartialD;\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}\hat{L}\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)=2\&CenterDot;\hat{L}\left(\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}\right)\&Center\; Dot;\frac{\&PartialD;}{\&PartialD;\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}}}f(\stackrel{\&Right\; Arrow;}{x},\stackrel{\&Right\; Arrow;}{\mathrm{the\; s}})$ Formula (10)

As a mandatory condition, for example, it can be required here that the divergence of the sports field is not allowed to disappear in the section marked by the dashed line.

As already described earlier, the result of motion-compensated reconstruction of an image f _bp (x, s) directly depends on the parameters describing the motion According to the invention, these parameters s corresponding to the motion vectors are determined by optimizing the image characteristics of the image reconstructed with motion compensation using these parameters. This can be done, for example, on the basis of a large number of image datasets reconstructed with different motion fields by applying the cost function Implemented as an analytical metric minimization, where the playing field is varied until the value function is optimal.

In order to be able to provide an efficient calculation specification for iteratively determining the parameters s for the motion-compensated reconstruction via one or more image features (eg gradient descent), an analytical reconstruction algorithm should be used for the reconstruction. In addition, in order to reduce the computational complexity of the playing field, it is also possible to calculate the playing field only from partial images which contain the expected relevant movements.

A motion model can be used for determining the playing field. This sports model M: The actual position x′=M(i,x,s) is calculated at the original position x based on the parameter s for the capture time of the i-th projection. An example for a motion model is a dense sports field. For each position y in the jth projected image there exists a displacement vector The formula is:

M(i, x, s)=x+s _{i, x} = x'. Formula (11)

However, other sparse motion fields (for example consisting of B-splines) or other linear basis functions, as well as nonlinear basis functions, such as NURBS (=Non-Uniform Rational B-Spline, non-uniform rational B-Spline, can also be used within the scope of the present invention B-spline curve).

As a specific example of a motion-compensated reconstruction algorithm, reference may be made to the known motion-compensated FDK reconstruction algorithm, which has been cited above published in the literature of et al. This FDK algorithm is one of the algorithms routinely used in clinical CT. It can be mathematically passed the following back projection formula f: to describe:

$f(x,\mathrm{the\; s})=\underset{i}{\mathrm{\&Sigma;}}Q(i,x^{\&prime;})p(i,A(i,x^{\&prime;}))$ Formula (12)

$f(x,\mathrm{the\; s})=\underset{i}{\mathrm{\&Sigma;}}Q\left(\text{i,}{x}^{\&prime;}\right)p(i,u^{\&prime;})$ Formula (13)

functionp: Allows access to the projection value p(i,u) of the convolution of the ith projection image at detector position u. Function A: The 3D image position x is mapped to the 2D detector position u=A(i,x) in the i-th projection image. Here, the exact formulation depends on the system geometry used. Function Q: is the weighting function used to correct for data redundancy. The exact formula again depends on the system geometry and shooting mode.

A key component of this scheme is defining a suitable value function. It has been shown in the literature, for example, that the compactness or compressibility of an image represents a suitable measure for acquisition image artifacts. Examples for this are entropy, general measures of compressibility eg based on cosine transforms or wavelet transforms, or the TV (Total Variation) norm.

As a specific embodiment, the entropy is given here, and the value function is calculated as follows by using it:

Formula (14)

where P: The probability of occurrence of an image value in Hounsfeld-Einheit, ie a CT value h∈HU, in the reconstructed image f(x,s) is given. In this case, the target value can be calculated with respect to the entire image or also only in a subregion Ω of the image determined by means of a motion map (see below). For example, the Pine window density estimation method can be used Determine the probability function analytically, which is given by:

$P(h,\mathrm{the\; s})=\frac{1}{\left|\mathrm{\&Omega;}\right|}\underset{x\&Element;\mathrm{\&Omega;}}{\mathrm{\&Sigma;}}K(f(x,\mathrm{the\; s})-h).$ Formula (15)

The Pai window density estimation method is based on the kernel function K, such as the Gaussian kernel (Gauβkern), for which:

$K\left(x\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}}\exp (-\frac{1}{{2\mathrm{\&sigma;}}^2}{x}^2).$ Formula (16)

In this case, the standard deviation σ>0 determines the smoothness of the density function P.

With the aid of a motion map, the determination of the motion field according to the invention can be limited to only those important subregions of the image which actually exhibit motion artifacts. This is specifically achieved by restricting computation to a subset of all possible image positions for the entire image. The matching of this image position is directly reflected in the calculation formula. The use of such a motion map can reduce the calculation time, increase the sensitivity of the image metrics and thus achieve an improved image quality. Here, the motion map describes a subset Ω of the image volume to be reconstructed.

Take the following two scenarios for determining motion maps as examples:

- Compute two adjacent phase-dependent reconstructions. The set Ω is all pixels whose absolute difference exceeds a threshold.

- Compute two adjacent phase-dependent reconstructions. Perform 3D/3D registration. The set Ω is all those pixels whose motion vector exceeds the threshold.

According to the invention, the motion estimation is carried out by means of an optimization algorithm, ie the motion field is determined from a large number of position-specific motion vectors or movement vectors. find parameters here This parameter minimizes to find the value function That is to say:

Formula (17)

For the definition of this optimization problem, arbitrary image criteria or image features can be used, such as the entropy of the reconstructed image, the total variation, or the compressibility of the image data, where the minimization or maximization of one or more image features shows Out of the best determined playing fields. Analytical derivatives of all provided components (ie reconstruction and analysis functions) can be calculated for fast and robust calculations. An optimization problem thus expressed is solved by using an optimization method, such as gradient descent, Newton's method, stochastic optimization, evolutionary optimization, or exhaustive methods.

In order to optimize a specific solution, it is also possible within the scope of the invention to adjust the term Complementary optimization problems. This can optimize specific features of the playing field. The sum of the lengths of the motion vectors is mentioned here as an example. In this case, each movement results in an increased adjustment value, but in this case the image analysis measure becomes smaller. The solution that best optimizes the image metrics and adjustment terms is now found according to the weights of the two terms. Thus, mathematically, for example, the parameters can be described as follows by means of additional terms:

Formula (18)

Thus, the proposed method achieves for the first time improved "best-stage" reconstruction through motion estimation and motion compensation. Furthermore, the proposed method is used to improve other motion phases or cardiac phases, or for noise reduction or better dose application. The high sensitivity and fast calculation of the proposed method are given by the motion map, since all components can be calculated quickly and thus can be used in the clinical field.

The reduction of motion blur for the "best stage" images is shown in FIGS. 4 to 6 from the CT cross-sectional images of the cardiac examination. Figure 4 shows a photograph of a "best stage" cross-sectional image of the heart derived from a conventional reconstruction based on a dual-source CT scan. Figure 5 shows the same section, but reconstructed from data using a single-source CT scan. FIG. 6 shows again the same section, likewise reconstructed from the data of a single-source CT scan, but using the method according to the invention. All detector data originate from the cardiac phase of 74% of the cycle. As can be seen, motion blur is minimal in the dual-source shot (Fig. 4), while in the conventionally reconstructed single-source shot (Fig. 5) the temporal resolution is insufficient to show the coronal at the arrow without artifacts artery. However, by using the method according to the invention on the same detector data set as used in FIG. 5 , motion artifacts can be significantly reduced, so that an almost artifact-free representation according to FIG. 6 is also obtained from single-source data. .

In conclusion, the present invention proposes to iteratively and use the images transformed into the CT image data set by finding the extremum of at least one image feature in the motion-compensated reconstructed tomographic data set by using the projection data of a single CT image data set The motion field is determined using a spatial value function, wherein for the iterative determination of the motion field one or more mandatory conditions for the motion field are used, and the final CT is generated by motion-compensated reconstruction from the thus determined motion field and the projection data sets already used icon.

Although the invention has been illustrated and described in detail by means of preferred examples, the invention is not limited to the disclosed examples and other solutions can be deduced therefrom by a skilled person without departing from the scope of protection of the invention.

Claims (21)

1. A method for generating a motion-compensated CT image data set of a partially and periodically moving examination object using a motion field, the motion field being composed of a large number of position-specific motion vectors, the method having the following Method steps: 1.1. Acquisition or transmission of a projection data set of a computed tomography system (1) comprising predetermined motion phases and projection angle regions, said projection data set allowing direct reconstruction of a CT image data set, 1.2. Determine the playing field iteratively by: 1.2.1. Multiple reconstruction of a CT image data set with a first image resolution by a motion-compensated reconstruction method using a first analytical reconstruction algorithm and different motion fields each consisting of a plurality of position-specific motion vectors ,and 1.2.2. Determining the playing field, wherein said playing field is subject to at least one predetermined mandatory condition, wherein the mandatory condition originates from foreknowledge, ie from information obtained before the execution of the iteration, 1.3. Reconstructing the final CT image dataset with a second image resolution based on a second reconstruction algorithm and a motion field in the case of a motion-compensated reconstruction method used, 1.4. Storing the final CT image data set or outputting the final CT image data set on an image reconstruction system. 2. The method according to the preceding claim 1, characterized in that, 2.1. The spatial boundary of the sports field to be determined is used as at least one mandatory condition for the sports field, wherein 2.2. said spatial boundary is smaller than the spatial perimeter of the final CT image data set, and 2.3. The spatial boundary is located inside the final CT image data set, 2.4. where the motion vector takes the value zero in the playing field outside the boundary. 3. The method as claimed in claim 1, characterized in that a predetermined physiological movement model is used as at least one mandatory condition for the sports field. 4. The method according to claim 1, characterized in that an initial motion field is used as at least one mandatory condition for the motion field in the iterative determination, based on loosely registering two temporally separated The CT image data set is used to determine the initial motion field. 5. The method as claimed in claim 1, characterized in that a filter of the sports field is used as at least one mandatory condition for the sports field. 6. The method according to the preceding claim 5, characterized in that a separate Gaussian filter is used for the filtering. 7. The method as claimed in claim 5, characterized in that an edge-preserving filter is used for the filtering. 8. The method according to the preceding claim 5, characterized in that a spatio-temporal smoothing filter kernel is used for filtering. 9 . The method as claimed in claim 1 , characterized in that the projection angle range is 180° plus the fan angle of the beams used. 10 . 10. The method according to any one of the preceding claims 1 to 8, wherein the analytical reconstruction method is one of the following methods: - FDK reconstruction method (FDK=Feldmann-Davis-Kress), - Clack-Defrise rebuild method, - a reconstruction method based on the Hilbert transform, - reconstruction method based on Fourier transform, -Radon method. 11. The method according to any one of the preceding claims 1 to 8, characterized in that at least one of the following image features is used as the image feature to be optimized: -entropy, - total variation/total volatility, - Compressibility. 12 . The method as claimed in claim 1 , characterized in that detector data are collected from a plurality of motion cycles for generating the projection data set used. 13 . 13. The method according to any one of the preceding claims 1 to 8, characterized in that the first image resolution is lower than the second image resolution. 14. The method according to any one of the preceding claims 1 to 8, characterized in that the second reconstruction algorithm is different from the first analytical reconstruction algorithm. 15. The method according to the preceding claim 14, characterized in that the second reconstruction algorithm is an analytical reconstruction algorithm. 16. The method of claim 14, wherein the second reconstruction algorithm is an iterative reconstruction algorithm. 17. The method according to the preceding claim 14, characterized in that the second reconstruction algorithm is a non-analytic reconstruction algorithm. 18. The method according to any one of the preceding claims 1 to 8, characterized in that the periodically moving organ is the patient's heart. 19. The method according to any one of the preceding claims 1 to 8, characterized in that the periodically moving organ is the patient's lungs. 20. A device for generating a motion-compensated CT image dataset of a partly and periodically moving examination object using a motion field, the motion field consisting of a plurality of position-specific motion vectors, said device having: 20.1. for the acquisition or transmission of a projection data set of a computed tomography system (1), comprising predetermined motion phases and projection angle regions, said projection data set allowing direct reconstruction of components of a CT image data set, 20.2. Means for iteratively determining a playing field by: 20.2.1. Multiple reconstruction of a CT image data set with a first image resolution by a motion-compensated reconstruction method using a first analytical reconstruction algorithm and different motion fields each consisting of a plurality of position-specific motion vectors ,and 20.2.2. Determining the playing field, wherein said playing field is subject to at least one predetermined constraint, wherein the forcing condition is derived from foreknowledge, that is to say from information obtained before performing an iteration, 20.3. A means for reconstructing a final CT image dataset with a second image resolution based on a second reconstruction algorithm and a motion field in the case of a motion-compensated reconstruction method used, 20.4. Means for storing said final CT image data set or outputting said final CT image data set on an image reconstruction system. 21. A CT system (1) having a device according to claim 20 above.