Method for reconstructing an image data set from measurement data of an image recording device, image recording device, computer program and data carrier

Abstract

Method for reconstructing an image data set from magnetic resonance data (1) as first measurement data from an image recording device (10), wherein the first measurement data were recorded in a temporally and / or spatially subsampled manner and a compressed sensing algorithm is used to reconstruct the image data set, in which a boundary condition ensuring agreement with the measurement data and an objective function used in an iterative optimization and evaluating candidate data sets (3) for the image data set are used, wherein, in addition to the first measurement data, x-ray data (2) as second measurement data recorded with a second imaging modality different from the first imaging modality of the first measurement data, but with the same image recording device (10) and registered with the first measurement data are included in the reconstruction with the compressed sensing algorithm by modifying the boundary condition and / or objective function.

Description

The invention relates to a method for reconstructing an image data set from first measurement data of an image recording device, wherein the first measurement data have been recorded in a temporally and / or spatially undersampled manner and a compressed sensing algorithm is used for reconstructing the image data set, in which a boundary condition ensuring the correspondence with the measurement data and a target function used in an iterative optimization and evaluating candidate data sets for the image data set are used. In addition, the invention relates to an image recording device, a computer program and an electronically readable data carrier.Magnetic resonance imaging has meanwhile been established as a medical imaging modality. It brings with it a large number of significant advantages, but also various restrictions. One of these restrictions is that magnetic resonance imaging processes often take a longer time, with the possibilities of accelerated image acquisition being greatly limited. In particular, when achieving good temporal resolution, the temporal sampling rates of magnetic resonance imaging are often limited and require specific losses and / or very complex procedures.The temporal sampling rate of the magnetic resonance imaging is primarily dependent on the magnetic resonance sequence used, wherein in particular specific gradient echo magnetic resonance sequences (GRE) are used.First, in a general form with respect to target imaging modalities, the concept of compressed sensing has been proposed some time ago. This is a reconstruction technique that can be applied to time- and / or spatially subsampled measurement data of an imaging modality. Compressed sensing is based on the observation that not only natural images, i.e. photographs in particular, are accessible to compression with little or no visible loss of information, but this also applies to medical images. From this follows the question of whether, if the images to be recorded are compressible, most transform coefficients being negligible or unimportant, it is actually necessary to record all measurement data. The mathematical theory body of compressed sensing offers the possibility of reconstructing largely artifact-free image data sets from undersampled measurement data, even if the Nyquist condition is not fulfilled.In concrete terms, in compressed sensing, it is proposed, instead of directly reconstructing the image data set, to initially reconstruct a sparse version of the image data set, in which significantly fewer image elements contain significant image values. The mathematical statement of compressed sensing is now that that candidate dataset for the image dataset for which the l 1- norm becomes minimum from the candidate datasets for which, when applying a measurement operator depicting the measurement of the measurement data to the candidate dataset, the measurement data again result from which it is assumed that is correctly reconstructed. By means of a suitable optimization method, in this case specifically a minimization method, wherein customary algorithms can be used, it is therefore possible to find the candidate data set for which the target function, containing the l 1- norm of the sparsely populated version of the candidate data set, becomes minimal under the boundary condition that the measurement data are again obtained from the image data set under measurement conditions.To generate sparse versions of the candidate dataset, various transformations referred to in the literature as "saving operators", which are to be referred to herein as thinning operators, may be used. If, for example, a gradient operator is applied to a candidate dataset, only the edges visible in the candidate dataset remain as significant pixels, so that the resulting result is significantly less populated than the original candidate dataset. Other examples of thinning operators that are frequently used are wavelet transformations. The application of a thinning operator here corresponds substantially to a mapping of the image values of the candidate data set onto a sparse vector of coefficients which are assigned to the corresponding base functions of the thinning operator. The thinning operator may also be referred to as a thinning operator.In a paper by Michael Lustig et al., "Sparse MRI: the Application of Compressed Sensing for Rapid MR Imaging", Magnetic Resonance in Medicine 58:1182-1195 (2007), the application of compressed sensing to accelerated magnetic resonance imaging is described. Here, the implicit sparseness is utilized in magnetic resonance images, wherein the implicit sparseness means a transform sparseness, which means that the object on which the magnetic resonance imaging is based, which is to be imaged in the image dataset, has a sparse representation in a known and defined mathematical transformation domain. "sparsely populated" means that relatively little significant image elements with values that deviate from zero exist, wherein this can also be understood in a temporal dimension. However, the degree of possible subsampling in magnetic resonance is still limited, in particular if a certain spatial resolution is to be maintained, since a shortening of the acquisition time or the temporal sampling rate of the magnetic resonance imaging also continues to lead to a deterioration of the spatial resolution. Even using compressed sensing, the possibilities for accelerating magnetic resonance imaging are therefore limited.Compressed sensing has also already been proposed for other medical imaging modalities, for example for computed tomography, reference being made by way of example to an article by Guang-Hong Chen et al., "Prior image constrained compressed sensing (PICCS): A method to accurate reconstruction dynamic CT images from highly undersampled projection data sets", Medical Physics 35: 660-663 (2008). This is especially concerned with dynamic CT imaging, in which fringe artifacts occur if the Shannon / Nyquist requirements are not fulfilled. Accordingly, the compressed sensing approach is extended by generating a preliminary image as an additional boundary condition while not considering the change over time of the CT measurement data. Nevertheless, there are limitations in computed tomography as well as other medical imaging modalities to what extent undersampling is possible with the approval of compressed sensing.Compressed sensing has also already been proposed for the reconstruction of an image data set from measurement data of two imaging modalities, for example in the articles CUI, X. [et al.]: Total Variation Minimization-Based Multimodality Medical Image Reconstruction. Proc. of SPIE, Vol. 9212, 2014, pp 92121 D-1 to 92121 D-11 or XI, Y. [et al.]: Simultaneous CT-MRI Reconstruction for Constrained Learning Geometries Using Structural Coupling and Compressive Sensing. IEEE Transactions on Biomedical Engineering, Vol. 63, June 2016, pp. 1301-1309, published 18.5.2016.The object of the invention is therefore to specify an extension of the compressed sensing approach which allows a higher degree of temporal and / or spatial undersampling for measurement data of an imaging modality, in particular magnetic resonance imaging.This object is achieved according to the invention by a method according to claim 1, an image recording device according to claim 8, a computer program according to claim 9 and an electronically readable data carrier according to claim 10.Generally speaking, the present invention therefore proposes, in a method of the type mentioned at the beginning, that in addition to the first measurement data, second measurement data recorded with the first measurement data using a second imaging modality different from the first imaging modality of the first measurement data and registered with the first measurement data also enter into the reconstruction using the compressed sensing algorithm by modifying the boundary condition and / or target function.The invention therefore proposes to extend the already known method of compressed sensing to multimodal measurement data, so that it becomes possible to compensate specific restrictions of an imaging modality by image information from the other imaging modality. As a result, for example, a further acceleration of the acquisition can be achieved for the imaging modality of the first measurement data and / or, for example in the case of x-ray imaging as the first imaging modality, a radiation dose to which the patient is exposed can be further reduced. The method is to be provided for use in the medical field, that is to say the measurement data relate to a target area of a patient to be recorded.In a particularly advantageous embodiment of the present invention, it is provided that the second measurement data is also recorded with the image recording device with which the first measurement data is recorded. This means that a two-modality image recording device, which allows the acquisition of first measurement data of the first imaging modality and second measurement data of the second imaging modality, is used. This is linked to a marked improvement in the image quality of the image data set, since the acquisition of the image data sets that cross modality is distinguished primarily by a minimum temporal and spatial offset and a registration is already fundamentally given structurally.Expediently, the first measurement data is magnetic resonance data and the second measurement data is X-ray data, in particular computed tomography data, so that the first imaging modality is magnetic resonance, the second imaging modality is X-ray imaging. It is therefore possible with particular advantage to compensate for magnetic resonance-specific restrictions during rapid image acquisition by image information from X-ray imaging. The image recording device used is then expediently a combined magnetic resonance X-ray device, in particular a combined magnetic resonance computed tomography device, as has already been proposed in the prior art. In this way, a higher temporal sampling rate of the magnetic resonance images can be achieved, wherein nevertheless a sufficient spatial resolution is maintained. Overall, the method according to the invention thus makes it possible to eliminate basic restrictions in magnetic resonance imaging and to significantly extend the applicability in the medical environment. Image artifacts and image quality constraints are significantly reduced.It should also be noted here that an improvement with regard to magnetic resonance imaging, in particular a further acceleration of magnetic resonance imaging, is in principle conceivable even in combination with other imaging modalities, for example ultrasound imaging or the like, wherein the introduction of X-ray data into the compressed sensing reconstruction process has proven to be particularly advantageous, however.Within the scope of the present invention, known compressed sensing algorithms can be used in principle, so that it can be provided, for example, that the l 1- norm of a reconstructed candidate data set described by the application of a thinning operator sparsely occupied is used as at least part of the target function to be iteratively minimized in the compressed sensing algorithm, wherein the boundary condition comprises that the first measurement data are produced using a measurement operator depicting the measurement of the first measurement data on the candidate data set. The thinning operator is to be understood as the "saving operator" known from the publications.In general terms, for the more specific inclusion of the second measurement data in the reconstruction in the compressed sensing algorithm, it can be provided that virtual measurement data of the first imaging modality are ascertained from the second measurement data and / or virtual measurement data of the second imaging modality are ascertained from the current candidate dataset and / or a virtual comparison dataset of the first imaging modality associated with the current candidate dataset is ascertained from the second measurement data. The concept underlying these embodiments thus provides for the conversion of measurement data and / or images in the respective other imaging modality on the basis of known properties of the imaging modalities, for which purpose various possibilities have already been proposed in the prior art. For example, for the transformation of data between magnetic resonance imaging and x-ray imaging, it is known to use databases which map typical magnetic resonance values, for example proton density, relaxation times and the like, to attenuation values for x-ray radiation and vice versa, so that a conversion can take place. If measurement data, for example concrete projections, are to be derived, the corresponding measurement operators are to be used, which comprise a Fourier transformation into k-space for the magnetic resonance imaging and / or the system matrix comprising the recording geometry for the X-ray imaging. In this way, it is also possible, for example, to require in the boundary condition as a modification that the candidate data sets coincide with the second measurement data or to integrate intermediate data sets reconstructed from the second measurement data into the target function, for example by further thinning of the candidate data set in an additional term in which the difference between the intermediate data set and the candidate data set, or more precisely the l 1- standard thereof, is considered.Specific exemplary embodiments for a main application of the present invention, namely first measurement data of magnetic resonance imaging and second measurement data of X-ray imaging, are now presented below, which however can in principle also be transmitted to other modality combinations.Thus, a particularly advantageous embodiment in the case of X-ray data and magnetic resonance data provides that, in order to take into account the X-ray data in the boundary condition, a Radon transform is applied to a three-dimensional X-ray attenuation value set derived from the current candidate dataset of the iterative procedure and the virtual projections obtained in this way are compared with the X-ray data. The Radon transform is, of course, selected such that the recording geometries result which were also used for recording the X-ray data as second measurement data. This means, purely in principle, the already known compressed sensing reconstruction method is used, as is also described in the publications mentioned at the beginning, that is to say, at least the l 1- norm of the candidate data sets, to which the thinning operator has been explicitly or implicitly applied, is furthermore minimized in the target function, but the boundary condition is changed in each case, wherein it can be provided in particular that the boundary condition requires that the sum of the deviations of the magnetic resonance data from comparison data resulting from the use of a measurement operator, which maps the measurement of the first image data and comprises a Fourier transformation, on the candidate data set and the X-ray data from the virtual projections lies within a tolerance range. This ensures optimization with respect to the multimodal measurement data. As in the known compressed sensing reconstruction method, the Fourier transform of the reconstructed candidate data is matched to the actual magnetic resonance data, i.e. the k-space samples. In addition, however, a comparison with the X-ray data, specifically the projection data, should also take place. For this purpose, virtual X-ray measurement data are generated from the candidate data of the current candidate dataset, wherein corresponding procedures, as already explained, are known in the prior art and advantageously use a database which maps attenuation values and magnetic resonance values to one another. Corresponding virtual projections are calculated from these virtual attenuation values by a Radon transformation of the virtual attenuation values taking place, the projection direction of which corresponds to that of the actual X-ray data. A deviation of the current candidate dataset from the actual measurement data of both magnetic resonance imaging and X-ray imaging is thus calculated. This combined deviation is intended in particular not to exceed a specific threshold value which describes a tolerance range.It is particularly expedient here if the tolerance range is selected depending on the noise properties of the magnetic resonance data and the X-ray data. It is already known from the prior art that in the case of pure magnetic resonance imaging, the size of a threshold value describing the tolerance range is selected as a function of the noise level of the measurement data, that is to say of the magnetic resonance data. The exemplary embodiment of the present invention presented here is distinguished by a combined boundary condition, however, so that it is proposed to take into account both the noise level of the magnetic resonance data and the noise level of the X-ray data for the corresponding determination of an adequate threshold value, wherein in a development, the noise behavior of the simulation of the virtual projections can additionally also be taken into account, and therefore in particular the transformation with the aid of a database, the Radon transformation and possibly other measures used.An alternatively or additionally usable embodiment provides that, for the use of the X-ray data in the target function, either a comparison data set for the candidate data set is determined by reconstruction of a three-dimensional intermediate data set from the X-ray data and mapping of the attenuation values of the intermediate data set to magnetic resonance values or virtual projections by applying a Radon transform to a three-dimensional X-ray attenuation value set derived from the current candidate data set of the iterative procedure. The comparison data set or the virtual projections can then be used to modify the target function in order to take account of the X-ray data.Specifically, it can be provided here that the objective function is determined as the weighted sum of the l 1- norm a difference either of the candidate dataset and the comparison dataset or of the virtual projections and the X-ray data, to which difference a first thinning operator has been applied, and the l 1- norm of the candidate dataset to which a second thinning operator has been applied. The l 1- norm of the sparse candidate data set is therefore also minimized, but an additional term to be minimized is added, which in a first embodiment variant is formed as the difference between the candidate data set and the comparison data set. For this purpose, x-ray data are generated using an x-ray system of the combined image recording device, according to which, in order to ensure adequate matching within the optimization algorithm, virtual magnetic resonance image data in the form of the comparison data record are generated from these x-ray data, wherein corresponding procedures, as already discussed, are fundamentally known in the prior art and can use, for example, a database linking x-ray attenuation values and magnetic resonance values. For this embodiment variant, it is of course necessary that the X-ray data can be reconstructed to form a three-dimensional intermediate data set (with X-ray attenuation values). This is not necessary in the second embodiment variant, since the X-ray data can be applied directly there on the projection plane. For this purpose, virtual projections, as already described with respect to the modification of the boundary condition, in particular using the database and the Radon transform, are derived from the candidate data set, the at least one projection direction or generally speaking recording geometry of which corresponds to that of the actually measured X-ray data.In both variant embodiments, the deviation of the current candidate data set from the actual second measurement data of the X-ray imaging is thus taken into account. Thus, within the compressed sensing algorithm, an adequate matching of the first and the second measurement data is used in order to ensure an adaptation of the iterative reconstruction using the thinning operator.A weighting coefficient describing the weighting in the sum can depend on the ultimately desired result, i.e. the what the image data set is intended to show predominantly. If the time resolution is particularly important, the comparison term can be weighted with the X-ray data to a lesser extent than in cases in which the spatial resolution, which is more readily encoded in the X-ray data, is also relevant. If, in one example, a four-dimensional image data record of a ventricle is to be obtained, both the time resolution and the spatial resolution are important, so that a coordination must take place, which can be given, for example, by a weighting of the term that brings about the coordination with the X-ray data of approximately 30-50%.A further degree of freedom for optimizing the image data set is given with different selection of the thinning operators, that is to say the first and the second thinning operators can be selected differently for optimizing the quality of the image data set, in particular for compensating for the disadvantages of the imaging modalities. For example, if an accelerated acquisition of the magnetic resonance data is to take place, the spatial resolution is rather small there, while in X-ray imaging, for example computed tomography, the spatial resolution is rather good. Accordingly, the thinning operators, in particular with regard to their spatial and temporal components, can be derived in such a way that these particular properties, and therefore the temporal and spatial resolution of the individual imaging modalities, are taken into account in the terms that contain the measurement data of these modalities.In this regard, it should also be noted in general that for the general realization of the compressed sensing algorithm, known configurations are basically used with respect to the reconstruction of magnetic resonance datasets, such as are already known for the adaptation of candidate datasets in optimization steps and the like. Wavelet transformations are preferably used as thinning operators.In addition to the method, the invention also relates to an image recording device, having a control device designed to carry out the method according to the invention. The image recording device is preferably designed as a combined magnetic resonance X-ray device, thus allowing both magnetic resonance imaging and X-ray imaging in coordinate systems registered with one another. The control device has a compressed sensing unit which is designed to carry out a compressed sensing algorithm in the extension described here, and therefore also takes into account the second image data, in particular the X-ray data, accordingly. All the embodiments relating to the method according to the invention can be transferred analogously to the image recording device according to the invention, so that the already mentioned advantages can also be obtained therewith.The invention further relates to a computer program which can be loaded directly into the memory of a computing device, in particular a control device of an image recording device, and has program means for carrying out the steps of the method according to the invention when the computer program is executed in the computing device, in particular the control device of the image recording device. The computer program according to the invention can be stored on an electronically readable data carrier according to the invention, which therefore comprises electronically readable control information stored thereon, which comprises at least the mentioned computer program and are configured such that, when the data carrier is used in a computing device, in particular the control device of the image recording device, they carry out a method described herein. The data carrier can expediently be designed as a non-transient data carrier, in particular a CD-ROM.Further advantages and details of the present invention are evident from the exemplary embodiments described below and on the basis of the drawing. The following are shown: FIG. 1 is a diagram for explaining a first exemplary embodiment of the method according to the invention, FIG. 2 is a diagram for explaining a second exemplary embodiment of the method according to the invention, and FIG. 3 shows an image recording device according to the invention.The method according to the invention is explained in more detail in the present case for the case in which the first measurement data is magnetic resonance data and the second measurement data is X-ray data, wherein all measurement data have been recorded with the same image recording device. In this case, a further acceleration of the magnetic resonance imaging is to be achieved by further subsampling, wherein losses arising in the magnetic resonance imaging are to be compensated for by the X-ray imaging which is carried out in particular substantially simultaneously and the resulting X-ray data, which are additionally included in the compressed sensing algorithm expanded according to the present invention.The diagram of FIG. 1 illustrates essential relationships and processes in a first exemplary embodiment of the method according to the invention, in which the X-ray data are taken into account in a boundary condition of the compressed sensing algorithm.The starting point here is the magnetic resonance data 1 and the X-ray data 2, wherein candidate datasets 3 from the former alone, i.e. the magnetic resonance data 1, are used in the context of the iterative reconstruction, which is indicated by the arrow 4, for minimizing the target function. The optimization method for ascertaining the image dataset x can therefore be formulated as where z MR denotes the candidate dataset, i.e. magnetic resonance images in the spatial domain, and ψ denotes the thinning operator used, for example a wavelet transformation.However, modified compared to a common compressed sensing algorithm is the boundary condition into which the X-ray data 2 also enter, as can be seen in formula (2) and FIG. 1. In formula (2), y MR denotes the first measurement data, i.e. the magnetic resonance data 1, as k-space samples. Y x-ray denotes the second measurement data, i.e. the X-ray data 2, in the projection space. F denotes a Fourier transformation, R a Radon transformation and ε represents a specific threshold value which defines a tolerance range in which the current candidate data set z MR must correspond to the measurement data.As can be seen from the diagram of FIG. 1, in order to be able to evaluate the boundary condition, a transformation 5 is first applied to the candidate data set 3 in order to obtain a virtual X-ray attenuation value set, which is denoted by z MRvirtualx-ray in the formula. For this purpose, a database can be used, for example, in which attenuation values are assigned to magnetic resonance values, as has already been proposed in the prior art. The X-ray attenuation value set is then subjected to a Radon transform 6 with respect to the projection directions in which X-ray data 2 are present. In this way, virtual projections are produced which can be compared with the X-ray data 2 by subtraction 7 in the boundary condition. Analogously, by applying a Fourier transformation 8 as a measurement operator to the candidate data set 3, it is possible to ascertain comparison data which can likewise be compared with the magnetic resonance data 1 by subtraction 9. The threshold value ε, which defines the tolerance range in which deviations in the two comparisons may be present, is selected depending on the noise level of the magnetic resonance data 1, the X-ray data 2 and the transformations 5, 6.FIG. 2 illustrates a modified second exemplary embodiment of the method according to the invention, in which the X-ray data 2 are directly incorporated into the iterative reconstruction, which is in turn symbolized by an arrow 4, by the target function being changed. In this second exemplary embodiment, only the magnetic resonance data are used in the boundary condition, wherein there are, however, two different variants of how the X-ray data 2 can enter into the target function. In the first variant, the optimization to be performed can be described by where z x-rayvirtual MR is a comparison data set derived from the X-ray data, α represents a weighting parameter, and ψ 1 and ψ 2 are thinning operators. The comparison data set has been determined by reconstruction of a three-dimensional intermediate data set from the X-ray data 2 and mapping the attenuation values of the intermediate data set to magnetic resonance values, wherein the database already mentioned can also be used here. An alternative embodiment variant of the second exemplary embodiment, which permits direct use of the X-ray data 2, can be written as where z MRvirtualx-ray again represents an X-ray attenuation value set which was derived from the candidate data set 3 as described above. Of course, the projection directions of the Radon transform also correspond here to the projection directions of the actual X-ray data 2. in other words, virtual projections are also determined again in this second embodiment variant, which, however, are directly incorporated into the target function in that, as can be seen from formula (4), a weighted sum of two terms is formed analogously to formula (3). The weighting factor α is to be selected in accordance with the desired result, so that, for example, given a particular importance of the time resolution α, it is possible to select a rather small value, but then, if the spatial resolution becomes more important, α can also be selected to be correspondingly larger, so that a larger proportion of the good spatial resolution of the X-ray data 2 acts in the iterative reconstruction.Also, the thinning operators ψ 1 and ψ 2 may be chosen differently to accommodate constraints on the modalities, as detailed in the general description. Thus, the corresponding advantages of the imaging modalities, here especially the time resolutions and the spatial resolutions, are emphasized by focusing on the thinning.FIG. 3 finally shows, in an abstract, functional representation, an image recording device 10 according to the invention, which is designed as a combined magnetic resonance X-ray device 11. Accordingly, the image recording device 10 comprises as subsystems an X-ray system 12, in particular a computed tomography system, and a magnetic resonance system 13, which enable the X-ray imaging or magnetic resonance imaging and the coordinate systems of which are registered with one another. For example, it can be provided that the main magnet unit of the magnetic resonance system 13 is perforated centrally in order to create space for a computed tomography gantry of the X-ray system 12.The operation of the image recording device 10 is controlled by a control device 14, which is also designed to carry out the method according to the invention.Although the invention has been illustrated and described in more detail by the preferred exemplary embodiment, the invention is not restricted by the disclosed examples and other variations can be derived therefrom by the person skilled in the art without departing from the scope of protection of the invention.

Claims

Method for reconstructing an image data set from magnetic resonance data (1) as first measurement data of an image recording device (10), wherein the first measurement data have been recorded in a temporally and / or spatially undersampled manner and a compressed sensing algorithm is used for reconstructing the image data set, wherein a boundary condition ensuring correspondence with the measurement data and a target function used in an iterative optimization and evaluating candidate data sets (3) for the image data set are used, wherein x-ray data (2) as second measurement data recorded with a second imaging modality different from the first imaging modality of the first measurement data but the same image recording device (10) and registered with the first measurement data are also included in the reconstruction with the compressed sensing algorithm by a modification of the boundary condition and / or target function, characterized in that, wherein virtual measurement data of the first imaging modality are determined from the second measurement data for inclusion in the reconstruction and / or virtual measurement data of the second imaging modality are determined from the current candidate dataset (3) and / or a virtual comparison dataset of the first imaging modality associated with the current candidate dataset (3) is determined from the second measurement data, and wherein a database linking X-ray attenuation values and magnetic resonance values is used for determining virtual magnetic resonance data from X-ray data and / or for determining virtual X-ray data from magnetic resonance data.Method according to Claim 1, characterized in that the l 1- norm of a candidate data record (3) reconstructed sparsely occupied by the application of a thinning operator is used as at least part of the target function to be iteratively minimized in the compressed sensing algorithm, wherein the boundary condition comprises the first measurement data being produced using a measurement operator mapping the measurement of the first measurement data on the candidate data record (3).Method according to one of the preceding claims, characterized in that, in order to take into account the X-ray data (2) in the boundary condition, a Radon transform (6) is applied to a three-dimensional X-ray attenuation value set derived from the current candidate data set (3) of the iterative procedure, and the virtual projections obtained in this way are compared with the X-ray data (2).Method according to Claim 3, characterized in that, in the boundary condition in which the sum of the deviations of the magnetic resonance data (1) from comparison data resulting from the measurement of the first image data and the X-ray data (2) from the virtual projections using a measurement operator which maps the measurement of the first image data and comprises a Fourier transformation (8) is within a tolerance range, the tolerance range is selected as a function of the noise properties of the magnetic resonance data (1) and of the X-ray data (2).Method according to one of the preceding claims, characterized in that, for the use of the X-ray data (2) in the target function, either a comparison data record for the candidate data record (3) is determined by reconstruction of a three-dimensional intermediate data record from the X-ray data (2) and mapping of the attenuation values of the intermediate data record to magnetic resonance values or virtual projections by applying a Radon transform (6) to a three-dimensional X-ray attenuation value record derived from the current candidate data record (3) of the iterative procedure.Method according to claim 5, characterized in that the objective function is determined as a weighted sum of the l 1- norm of a difference of either the candidate data set (3) and the comparison data set or the virtual projections and the X-ray data (2) to which a first thinning operator has been applied and the l 1- norm of the candidate data set (3) to which a second thinning operator has been applied.Image recording device (10), having a control device (14) designed to carry out a method according to one of the preceding claims.A computer program which performs the steps of a method according to any one of claims 1 to 6 when executed on a computing device.Electronically readable data carrier on which a computer program according to claim 8 is stored.

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