Apparatus for reconstructing magnetic resonance images

Abstract

The present invention refers to an apparatus 130 for reconstructing MR images and / or parameter maps based on MR time-domain signals. A providing unit 133 provides time-domain signals acquired in time-domain MRI using a k-space sampling pattern and a magnetic resonance acquisition sequence. A providing unit 132 provides a subspace sampling operator that provides given k-space locations of the sampling pattern time subsamples of basis vectors of a compressed subspace. The compressed subspace can be used to compress the time-domain signals. A processing unit 133 processes the time-domain signals using the subspace sampling operator. A reconstruction unit 134 reconstructs MR images and / or parameter maps based on the processed time-domain signals. This allows for more accurate and less computationally resource-intensive reconstruction of MR images and / or parameter maps in the context of time-domain magnetic resonance imaging.

Description

[Technical Field]

[0001] The present invention relates to an apparatus, a method, and a computer program product for reconstructing a magnetic resonance image and / or a parameter map based on magnetic resonance time-domain signals acquired in time-domain magnetic resonance imaging. Furthermore, the present invention relates to a system for reconstructing a magnetic resonance image and / or a parameter map using the above-mentioned apparatus, method, and / or computer program product. Furthermore, the present invention relates to a sequence determination apparatus for determining an acquisition sequence for acquiring magnetic resonance time-domain signals in time-domain magnetic resonance imaging, and an acquisition sequence determined accordingly. [Background technology]

[0002] Time-domain magnetic resonance imaging not only provides qualitative analysis of the imaged object, but also quantitative analysis, potentially leading to the possibility of determining the actual tissue type imaged. However, time-domain magnetic resonance imaging generates a huge amount of data that must be analyzed, for example, using magnetic resonance fingerprinting. Therefore, while time-domain magnetic resonance imaging offers many advantages, it is computationally demanding. Furthermore, as heavy spatial subsampling is commonly used during acquisition, there is no time to spatially encode each time point of the measurement. This leads to increased reconstruction complexity. Therefore, compression algorithms have been developed that allow for the reconstruction of magnetic resonance images or parameter maps in a compressed subspace, thereby reducing the use of computational resources, particularly storage and computational resources. Furthermore, these compression algorithms allow for regularization of the reconstruction problem, so that even heavily undersampled measurements can be reconstructed. However, even when utilizing compressed subspaces, the calculations are still complex and computationally intensive, making them difficult to use in applications where results must be provided to physicians as quickly as possible, for example, in emergency situations. Furthermore, compression can introduce noise or make fingerprinting algorithms, particularly those often used to generate magnetic resonance images and / or parameter maps, less accurate. Furthermore, when compression is used, the accuracy and / or noise can be highly dependent on the magnetic resonance acquisition sequence used, and it is often difficult or nearly impossible to determine or predict an optimal, i.e., less noisy, acquisition sequence that will trigger the acquisition sequence for the compression algorithm prior to the actual acquisition.

[0003] It would therefore be advantageous if it were possible to enable a more accurate and at the same time less resource-intensive reconstruction of magnetic resonance images and / or parameter maps based on time-domain magnetic resonance imaging. Furthermore, it would be advantageous if magnetic resonance acquisition sequences could be determined in the context of utilizing compressive reconstruction algorithms that allow for a more accurate reconstruction of magnetic resonance images and / or parameter maps in this context. Summary of the Invention [Problem to be solved by the invention]

[0004] It is an object of the present invention to provide an apparatus, a method and a computer program product which enable a more accurate and less computationally resource intensive reconstruction of magnetic resonance images and / or parameter maps in the context of time-domain magnetic resonance imaging. Furthermore, it is a further object of the present invention to provide an apparatus, a method and a computer program product which enable in this context to provide magnetic resonance acquisition sequences which enable an even more accurate reconstruction of magnetic resonance images and / or parameter maps. [Means for solving the problem]

[0005] In a first aspect of the present invention, there is provided an apparatus for reconstructing magnetic resonance images and / or parameter maps based on magnetic resonance time domain signals acquired in a time domain magnetic resonance imaging formation, the apparatus comprising: a) an apparatus for providing time domain signals using a predetermined sampling pattern in k-space and a predetermined magnetic resonance acquisition sequence to provide time domain signals acquired in a time domain magnetic resonance imaging formation, b) an operator for providing a subspace sampling operator that provides given k-space locations of a sampling pattern time domain sub-sampling of basis vectors of a compressed subspace, the compressed subspace being usable to compress the time domain signals, c) a signal processing unit for processing the time domain signals using the subspace sampling operator, and d) a reconstruction unit for reconstructing magnetic resonance images and / or parameter maps based on the processed time domain signals.

[0006] Because the subspace sampling operator is provided to provide a sampling pattern of time sub-samples of basis vectors of a compressed subspace for given k-space locations that can be utilized to compress the time domain signal, and because the time domain signal is processed utilizing the subspace sampling operator, magnetic resonance images and / or parameter maps can be more directly, e.g., without iterative steps, and again more accurately, reconstructed based on the processed time domain signal utilizing the compression algorithm. Furthermore, because the subspace sampling operator is provided directly, i.e., can be calculated prior to acquisition of the time domain signal, it is possible to utilize the subspace sampling operator to optimize the magnetic resonance acquisition sequence, such that a magnetic resonance acquisition sequence can be determined based on the subspace sampling operator, which allows for even more accurate reconstruction of the magnetic resonance image and / or parameter map.

[0007] Generally, the device is configured to reconstruct a magnetic resonance image and / or a parameter map. The device can be implemented in any form of hardware and / or software provided by a general or dedicated computer system. In particular, the device can be implemented using distributed computing, e.g., as part of a computer network in which the device's functions are provided by different processors, servers, or computer systems. A magnetic resonance image can refer to any known magnetic resonance image commonly used in magnetic resonance imaging. For example, a magnetic resonance image can refer to a T1- or T2-weighted image, a gradient echo-based image, an inverse transform recovery-based image, a diffusion-weighted image, a perfusion-weighted image, etc. In this context, a parametric map can be the result of a quantitative analysis of a magnetic resonance signal and can refer to, for example, any type of tissue map, but can also refer to diffusion parameters, kinetic parameters, proton density, magnetization transfer saturation, longitudinal and effective transverse relaxation rates, etc. In the context of the present invention, a magnetic resonance time-domain signal is acquired in time-domain magnetic resonance imaging. Time-domain magnetic resonance imaging is characterized by the ability to resolve magnetization transients; in particular, signals are not necessarily measured in a steady state, as is typically the case with magnetic resonance signal measurements. An example of time-domain magnetic resonance imaging can be disclosed in the article "magnetic resonance fingerprinting", D. Ma et al., Nature, Vol. 495, 187-192 (2013).

[0008] The time-domain signal providing unit is configured to provide a time-domain signal. Generally, the time-domain signal providing unit can refer to a storage unit or can be communicatively coupled to a storage unit, where the time-domain signal is already stored on the storage unit, and the time-domain signal providing unit is configured to provide the signal stored on the storage unit. Furthermore, the time-domain signal providing unit may be, for example, a receiving unit for receiving the time-domain signal from an input unit or directly from a magnetic resonance imaging device via an interface and providing the received time-domain signal. The time-domain signal is acquired in time-domain magnetic resonance imaging using a predetermined sampling pattern in k-space and a predetermined magnetic resonance acquisition sequence. Various patterns in k-space are commonly used and known for acquiring the time-domain signal. Generally, the predetermined sampling pattern can refer to any pattern in k-space. However, preferably, the sampling pattern refers to a spiral or radial sampling pattern with interleaving. In this context, k-space is a spatial frequency domain to which magnetic resonance measurements can be directly mapped. The predetermined magnetic resonance acquisition sequence refers to a specific setting of a pulse sequence and pulsed magnetic field gradients used to acquire the time-domain signal. Preferably, a balanced gradient echo or impaired gradient echo acquisition sequence is utilized, however, a spin-echo sequence can also be used.

[0009] The operator providing unit is configured to provide the subspace sampling operator. The operator providing unit may be a storage unit or may be communicatively coupled to a storage unit in which the subspace sampling operator is already stored and then configured to provide it. Furthermore, the operator providing unit may be an input unit or may be communicatively coupled to an input unit, for example, for receiving the subspace sampling operator from a user, and then configured to provide the received subspace sampling operator. In general, the subspace sampling operator provides a given k-space position of a sampling pattern time subsamples of basis vectors of the compressed subspace. Thus, the subspace sampling operator depends on the predetermined sampling pattern used in k-space and the compressed subspace available for compressing the time-domain signal, which is generally also predetermined. In general, the compressed subspace refers to a subspace in which the time-domain signal can be compressed, for example, by mapping the time-domain signal to the compressed subspace, and the compressed subspace is defined by the respective basis vectors. The time subsampling of the basis vectors defines the respective time points of the time-domain signal-related subsampling of the basis vectors. The subspace sampling operator is preferably configured to provide a respective time subsampling of the basis vector to each k-space position of the sampling pattern. Furthermore, since in most cases different sampling patterns are utilized to acquire the time domain signal, the subspace sampling operator may comprise respective time subsamples of the basis vectors of the respective compressed subspaces for respective k-space locations of the different sampling patterns. In general, the subspace sampling operator may be predetermined prior to measurement of the time domain signal, in particular based on a selected, i.e., predetermined, sampling pattern and based on a selected, i.e., predetermined, compressed subspace.In a preferred embodiment, providing the subspace sampling operator includes generating the subspace sampling operator as a combination of a selection operator associated with a sampling pattern in k-space and a decompression operator including basis vectors of the compressed subspace that can be used to compress the signal into the compressed subspace. Generally, the selection operator is associated with the sampling pattern in k-space and, in particular, depends on the sampling pattern in k-space. For example, the selection operator provides a mapping between the sampling pattern in k-space and the measured time-domain signal, thus providing a mapping for each measurement at each time point of the measured time-domain signal to each point in k-space defined by the sampling pattern in k-space. Preferably, the selection operator further indicates that all values ​​in k-space that do not belong to the sampling pattern in k-space are set to zero. The decompression operator generally includes basis vectors of the compressed subspace onto which the signal can be mapped for compression. Preferably, the decompression operator is a linear matrix that provides an orthogonal time basis for the compressed subspace. In particular, the decompression operator, and thus the compressed subspace, is preferably determined using, for example, singular value decomposition of a matching dictionary used in a fingerprinting matching algorithm. However, other decompression operators based on other compressed subspaces and therefore other compression algorithms can also be used. For example, one could use a machine learning algorithm such as a latent space for an automatic decoder algorithm, or a compressed subspace determined using independent component analysis. The combination of the selection operator and the decompression operator is preferably a matrix multiplication in which the selection operator is applied to the decompression operator.

[0010] The signal processing unit is configured to process the time-domain signal using a subspace sampling operator. The construction unit is then configured to reconstruct a magnetic resonance image and / or a parameter map based on the processed time-domain signal. Generally, the processing of the time-domain signal depends on the algorithm used by the reconstruction unit to reconstruct the magnetic resonance image and / or the parameter map based on the processed time-domain signal. In particular, the subspace sampling operator is most often applied directly to the time-domain signal to determine the processed time-domain signal. Further processing may, for example, include further processing steps for preparing the time-domain signal before processing it. To reconstruct the magnetic resonance image and / or the parameter map based on the processed time-domain signal, respective known algorithms, in particular compression algorithms, may be used. In particular, fingerprinting algorithms may be used in which the processed time-domain signal is used to determine a matching signal, which is then compared in a matching process with, for example, a library of characteristic signals of the respective tissue sample to determine the magnetic resonance image and / or the parameter map. However, other reconstruction algorithms, such as machine learning algorithms based on the processed time-domain signal, iterative algorithms based on the processed time-domain signal, etc., may also be used to reconstruct the magnetic resonance image and / or the parameter map.

[0011] In a preferred embodiment, the processing of the time domain signal comprises This involves calculating TIFF2025537666000002.tif1136, where: TIFF2025537666000003.tif105 is the processed time-domain signal, y is the measured time-domain signal in k-space, w is the density compensation weighting, (SV) + is the pseudo-inverse of the subspace sampling operator, and E His a Hermitian of an encoding operator having a fast Fourier transform operator for converting signals in k-space to signals in image space and, optionally, a gridding operation for gridding the sampling pattern and a coil combination operator representing the coil characteristics of the acquisition magnetic resonance system. In particular, the processed time-domain signal is an image signal, i.e., refers to an image related to the measured time-domain signal, and is represented in a compressed domain defined by V. Furthermore, in this case, the processed time-domain signal can also be considered as a fingerprinting signal, since it can be used for fingerprinting matching with a dictionary. The encoding matrix E for non-Cartesian image reconstruction preferably refers to E=GFS, where G is the grid operator, F is the fast Fourier transform operator, and S is an operator representing the coil sensitivity. In some embodiments, a sampling density compensation w can be added to the Cartesian reconstruction, This results in a diagonal matrix in non-Cartesian k-space, resulting in TIFF2025537666000004.tif834. However, in iterative reconstruction methods, w can be omitted or integrated as part of E.

[0012] This calculation makes it possible to avoid a computationally resource-intensive repeated determination of the processed time domain signal, where the processed time domain signal refers to a sub-sampled image that can be used to determine a magnetic resonance image and / or a parameter map, for example by determining a fingerprint based on the processed time domain signal.

[0013] In a preferred embodiment, the processing of the time domain signal is based on a pseudo-inverse transform of the subspace sampling operator, and the pseudo-inverse transform of the subspace sampling operator is determined as the Moore-Penrose pseudo-inverse transform. In general, the Moore-Penrose pseudo-inverse transform is given by + =(A H A) ―1 A HThe least-squares algorithm can be used to solve equations of the general form Ax=b in terms of x by calculating (Ax=b), where A is a rectangular matrix. Preferably, A is selected so that the linear system of equations is overdetermined. In applying the Moore-Penrose pseudoinverse transform to the subspace sampling operator, A is set to the subspace sampling operator, e.g., SV. In a preferred embodiment, the step of reconstructing magnetic resonance images and / or parameter maps utilizes magnetic resonance fingerprinting, and the reconstruction of the magnetic resonance images and / or parameter maps is based on the processed time-domain signals used for dictionary matching. Examples of fingerprinting algorithms that can be used with the processed time-domain signals are disclosed, for example, in the publication "Magnetic resonance fingerprinting," D. Ma et al., Nature, Vol. 495, 187-192 (2013). Preferably, when using a fingerprinting algorithm and performing dictionary matching, the entries of the dictionary used in dictionary matching are compressed into a compressed subspace.

[0014] In a preferred embodiment, the apparatus further comprises an acquisition parameter verification unit configured to verify, based on the subspace sampling operator, the acquisition parameters of the acquisition sequence for acquiring the time-domain signal with respect to a matching error. Generally, the subspace sampling operator depends on the decompression operator and also on the sampling pattern, and thus can be predetermined based on the compression algorithm used. Therefore, the subspace sampling operator also enables prediction of the matching performance of each predetermined acquisition sequence. Therefore, the verification is preferably performed with respect to the matching error, for example, represented by an error score. In particular, a lower matching error indicates better image or parameter map quality. The matching error is an inherent aspect of the reconstruction that does not necessarily result in an exact solution of the magnetic resonance image or magnetic resonance parameter map. That is, the matching error represents the accuracy of the optimization solution or residual between the reconstruction solution, including the approximation, and the exact solution of the magnetic resonance image or magnetic resonance parameter map associated with the acquired time-domain signal, due to the compression into the compressed subspace and other aspects of solving the reconstruction optimization problem. When applied to magnetic resonance fingerprinting procedures that involve comparing a signal evolution with dictionary entries, the matching error may also represent the degree of accuracy of the match against the dictionary.

[0015] In a preferred embodiment, the acquisition parameter verification unit is further configured to determine an acquisition sequence based on the verification. For example, the apparatus may further comprise a potential acquisition sequence providing unit for providing respective acquisition parameters for a plurality of potential acquisition sequences. The acquisition parameter verification unit may then be adapted to verify each of the plurality of potential acquisition sequences, for example by calculating a respective matching error score based on the sub-sampling operator, and may then determine the potential acquisition sequence to be used as the acquisition sequence including the lowest matching error.

[0016] Preferably, the iterative algorithm may be utilized by an acquisition parameter validation unit having the steps of: a) providing a potential acquisition sequence; b) providing a target matching error; c) determining a matching error for the potential acquisition sequence based on a subspace sampling operator; d) validating the potential acquisition sequence by comparing the determined matching error with the target matching error; and d) based on the comparison, i) determining the potential acquisition sequence as an acquisition sequence, or ii) providing a new potential acquisition sequence, for example by modifying one or more acquisition parameters of the potential acquisition sequence.

[0017] Preferably, the matching error for a potential acquisition sequence is determined by the acquisition parameter verification unit using the following algorithm: In a first step, a dictionary and respective compression subspaces for compressing the dictionary are determined based on the potential acquisition sequence. Generally, any known method for determining a dictionary and respective compression subspaces for a given acquisition sequence can be used. Furthermore, a sampling pattern to be used when acquiring the time-domain signal is provided. For example, any of the sampling patterns described above can be used. An artificial time-domain signal can then be generated such that an exact match in the dictionary, i.e., ground truth parameters, for the artificial time-domain signal are known. For example, the generated dictionary can be used to generate an artificial processed signal based on the signal in the dictionary, and the artificial processed signal can be back-processed to generate a related artificial time-domain signal. In particular, a mixing operator can be used to mix the respective artificial time-domain signals to simulate k-space contributions to the processed signal. Furthermore, a predetermined sampling pattern can be used to generate the artificial time-domain signal based on the simulated mixing. A predetermined noise pattern can then be added to each artificial time-domain signal to receive a noisy artificial time-domain signal. In general, different predetermined noise patterns can be used, for example, in all determinations of matching errors. Furthermore, a sub-sampling operator can be generated based on the predetermined sampling pattern and the predetermined compressed subspace. Based on the sub-sampling operator, the noisy artificial time-domain signal can be processed so that the processed noisy artificial time-domain signal can be matched using a dictionary. Each matching result, e.g., values ​​of T1, T2, etc., can then be compared with the known matching from which the artificial time-domain signal was generated, i.e., with the ground truth parameters from which the time-domain signal was generated. Based on the comparison, an evaluation can be performed.For example, based on the comparison, a respective matching error can be determined, and the sequence can be verified based on the determined matching errors.

[0018] In a preferred embodiment, the acquisition parameters are verified based on the condition number of the subspace sampling operator. Generally, the condition number of the operator determines the noise amplification during the inversion of the operator. In practice, the smaller the condition number, the more robust the reconstruction with respect to noise amplification and the better the quality of the reconstructed image and / or parameter map. Furthermore, the subspace sampling operator, and thus the acquisition parameters of the acquisition sequence, are preferably determined to minimize the condition number of the subspace sampling operator. This minimization can be performed in any known optimization algorithm that uses the condition number as a minimization goal, and the acquisition parameters, e.g., the subsampling of the acquisition sequence, can be used as optimizable variables. However, the condition number can also be simply used to select, from multiple possible acquisition sequences, the sequence with the lowest condition number for acquiring each image.

[0019] In a further aspect of the present invention, there is provided a sequence validation apparatus for validating acquisition sequences for acquiring magnetic resonance time domain signals in time domain magnetic resonance imaging, the apparatus comprising: a) an acquisition sequence for providing potential acquisition sequences including respective acquisition parameters and predetermined sampling patterns; b) an operator for providing subspace sampling operators for providing given k-space locations of predetermined sampling pattern time subsamples of basis vectors of a compressed subspace, wherein the compressed subspace can be used to compress the acquired time domain signals using the potential acquisition sequences; and c) an acquisition parameter validation unit for validating acquisition parameters of the potential acquisition sequences for acquiring the time domain signals with respect to a matching error based on the subspace sampling operators. Preferably, the apparatus further comprises an acquisition parameter generation unit for generating the acquisition sequences based on the validation of the acquisition parameters of the potential acquisition sequences.

[0020] In general, the same definitions and embodiments as described above with respect to the first aspect of the invention are applicable to this aspect of the invention, and in particular the embodiments described with respect to verifying and determining acquisition parameters for an acquisition sequence for acquiring a time domain signal based on a subspace sampling operator may also be embodiments of this aspect of the invention.

[0021] In a further aspect of the present invention, there is provided a system for reconstructing magnetic resonance images and / or parameter maps based on magnetic resonance time domain signals acquired in time domain magnetic resonance imaging, the system comprising: a) a magnetic resonance imaging system configured to acquire time domain signals in time domain magnetic resonance imaging using a predetermined sampling pattern in k-space and a predetermined magnetic resonance acquisition sequence; and b) an apparatus as described above and / or a sequence determination apparatus as described above.

[0022] In a further aspect of the present invention, a computer-implemented method for reconstructing magnetic resonance images and / or parameter maps based on magnetic resonance time-domain signals acquired in time-domain magnetic resonance imaging is presented, the method comprising the steps of: a) providing time-domain signals acquired in time-domain magnetic resonance imaging using a predetermined sampling pattern in k-space and a predetermined magnetic resonance acquisition sequence; b) providing a subspace sampling operator that provides given k-space locations for sampling pattern time-domain sub-sampling of basis vectors of a compressed subspace, wherein the compressed subspace can be used to compress the time-domain signals; c) processing the time-domain signals using the subspace sampling operator; and d) reconstructing magnetic resonance images and / or parameter maps based on the processed time-domain signals.

[0023] In a further aspect of the present invention, a computer-implemented sequence validation method for validating acquisition sequences for acquiring magnetic resonance time domain signals in time domain magnetic resonance imaging is presented, the method comprising the steps of: a) providing potential acquisition sequences including respective acquisition parameters and predetermined sampling patterns; b) providing subspace sampling operators that provide given k-space locations of time subsamples of the predetermined sampling pattern of basis vectors of a compressed subspace, wherein the compressed subspace can be used to compress the time domain signals acquired using the potential acquisition sequences; and c) validating the acquisition parameters of the potential acquisition sequences for acquiring the time domain signals with respect to a matching error based on the subspace sampling operators.

[0024] In a further aspect of the present invention, an acquisition sequence for acquiring magnetic resonance time domain signals in time domain magnetic resonance imaging is presented, determined using a sequence determination device as described above and / or a sequence determination method as described above.

[0025] In a further aspect of the present invention, a computer program product for reconstructing magnetic resonance images and / or parameter maps based on magnetic resonance time domain signals acquired in time domain magnetic resonance imaging is provided, the computer program product causing an apparatus as described above to perform the method as described above.

[0026] In a further aspect of the present invention, a computer program product for determining an acquisition sequence for acquiring magnetic resonance time domain signals in time domain magnetic resonance imaging is provided, the computer program product causing the above-mentioned sequence determination device to perform the above-mentioned sequence determination method. It is to be understood that such an apparatus, such a method, such a system and such a computer program product may have similar and / or identical preferred embodiments, in particular as defined in the dependent claims.

[0027] It is to be understood that a preferred embodiment of the invention can also be any combination of the dependent claims or the above embodiments with the respective independent claim.

[0028] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter. [Brief explanation of the drawings]

[0029] [Figure 1] 1 shows a schematic and exemplary system for reconstructing magnetic resonance images and / or parameter maps. [Figure 2] 1 shows, schematically and exemplarily, a flow chart of a method for reconstructing magnetic resonance images and / or parameter maps. [Figure 3] 10A-10C show schematic and exemplary parameter maps illustrating improved reconstruction when utilizing the above systems and / or methods. [Figure 4] 10 shows, schematically and exemplarily, a visualization of the effect of a selection operator on a decompression operator. DETAILED DESCRIPTION OF THE INVENTION

[0030] 1 shows a schematic and exemplary system for reconstructing magnetic resonance images and / or parameter maps based on magnetic resonance time-domain signals acquired in time-domain magnetic resonance imaging. The system comprises a magnetic resonance imaging system having a magnetic resonance imaging controller 120 and an apparatus 130 for reconstructing magnetic resonance images and / or parameter maps based on magnetic resonance time-domain signals acquired by the magnetic resonance imaging system. Optionally, the system 100 may comprise a sequence determination apparatus 110 for determining an acquisition sequence for acquiring magnetic resonance time-domain signals in time-domain magnetic resonance imaging performed by the magnetic resonance imaging system.

[0031] If a sequence determination device is present, it can be utilized to determine an optimized acquisition sequence that can be utilized by the magnetic resonance imaging control unit 120 to acquire time-domain signals utilizing the magnetic resonance imaging unit 121. The sequence determination device 110 comprises an operator providing unit 111 and an acquisition parameter determination unit 112. The operator providing unit 110 is configured to provide a subspace sampling operator. For example, the operator providing unit 111 can provide the subspace sampling operator by accessing a storage unit in which the subspace sampling operator is already stored or by receiving the subspace sampling operator, for example, via an input unit. However, the operator providing unit 111 can also be configured to generate the subspace sampling operator and provide the generated subspace sampling operator. For example, the operator providing unit 111 can be configured to calculate the subspace sampling operator based on a user input indicating a respective sampling pattern of the magnetic resonance acquisition and based on information regarding the utilized compression, e.g., information indicating a decompression operator. Such accessed, received, or generated subspace sampling operator can then be provided for further processing, for example, to the acquisition parameter determination unit 112. In general, the subspace sampling operator provides a given k-space location of a predetermined sampling pattern that is used to acquire time-domain signal time subsamples of basis vectors of the compressed subspace. Thus, the subsampling operator can be predetermined based on a given, i.e., predetermined, sampling pattern to be used during acquisition of the time-domain signal and based on a compressed subspace to be used when reconstructing a magnetic resonance image based on the time-domain signal. The compressed subspace can generally be used to compress the time-domain signal and can be determined, for example, using known compression algorithms, in particular, using single value decomposition.Thus, the subspace sampling operator subsequently utilized in the reconstruction of the magnetic resonance images and / or parameter maps may be predetermined and provided, and then also utilized to optimize the acquisition sequence for acquiring the time domain signals performed by the acquisition parameter determination unit 112. In particular, utilizing a predetermined subspace sampling operator for determining the acquisition sequence makes it possible to optimally adapt the acquisition sequence to the subsequently performed reconstruction and to optimize the interaction between the acquisition sequence utilized for acquiring the time domain signals and the reconstruction algorithm utilizing the subspace sampling operator. Further details and examples regarding how the acquisition parameter determination unit 112 can determine acquisition parameters based on the subspace sampling operator are provided further below.

[0032] If the sequence determiner 110 is part of the system 100, the so-determined acquisition sequence for acquiring time-domain signals may then be provided to the magnetic resonance imaging control unit 120. However, if the sequence determiner 110 is omitted in the system 100, any other known suitable acquisition sequence may be utilized by the magnetic resonance imaging control unit 120. The magnetic resonance imaging control unit 120 then controls the magnetic resonance unit 121 to acquire time-domain signals from a patient 122 lying on a patient table 123. The so-acquired time-domain signals may then be provided to an apparatus 130 for reconstructing magnetic resonance images and / or parameter maps from the time-domain signals.

[0033] The apparatus 130 comprises a time-domain signal providing unit 131, an operator providing unit 132, a signal processing unit 133, and a reconstruction unit 134. Furthermore, the apparatus 130 may also comprise a display unit 135, for example for displaying reconstructed magnetic resonance images and / or parameter maps, and / or an input unit 136 allowing a user to interact with the apparatus 130, for example by providing a mouse, a keyboard, etc. The time-domain signal providing unit 131 may in this example be realized, for example, as an interface unit for interfacing with the magnetic resonance imaging control unit 120, for receiving time-domain signals from the magnetic resonance imaging control unit 120 and providing them for further processing, for example to the signal processing unit 133. However, in other embodiments the time-domain signal providing unit 131 may also be configured, for example, to receive time-domain signals already stored on a storage unit or a network and to access the storage unit or a network for providing the accessed time-domain signals, respectively. Furthermore, in other embodiments the time domain signal providing unit can be considered to include the magnetic resonance imaging control unit 120 and optionally the magnetic resonance imaging unit 121, and in such embodiments the time domain signal providing unit is configured to directly acquire the time domain signals and provide the acquired time domain signals. Generally, the time domain signals are acquired using a predetermined sampling pattern in k-space and a predetermined magnetic resonance acquisition sequence, in particular a magnetic resonance acquisition sequence determined by the magnetic resonance acquisition sequence determination unit 110.

[0034] The operator providing unit 132 may be similar to the operator providing unit 110 of the magnetic resonance acquisition sequence determining device 110. In particular, the operator providing unit provides a subspace sampling operator as already described above. If the magnetic resonance acquisition sequence determining device 110 is present in the system 100, the operator providing unit 132 is particularly configured to provide the same subspace sampling operator used to determine the acquisition sequence of the time domain signals. Otherwise, it can provide a respective subspace sampling operator based on the respective sampling pattern and the respective compression algorithm used.

[0035] The signal processing unit 133 is then configured to process the time domain signals using a subspace sampling operator, and the reconstruction unit 134 is configured to reconstruct magnetic resonance images and / or parameter maps based on the processed time domain signals. Further details and preferred examples of the processing of the time domain signals and the reconstruction of magnetic resonance images and / or parameter maps are described below.

[0036] FIG. 2 schematically and exemplarily shows a flowchart of a method 200 for reconstructing magnetic resonance images and / or parameter maps. The method 200 includes a step 220 for reconstructing magnetic resonance images and / or parameter maps, and optionally includes a step 210 for initially determining an acquisition sequence for acquiring magnetic resonance time-domain signals in time-domain magnetic resonance imaging, based on which the magnetic resonance images and / or parameter maps are constructed. If step 210 is present in the method 200, in a first step 211, a subspace sampling operator is provided, for example, according to the principles described above with reference to FIG. 1. In step 212, acquisition parameters of an acquisition sequence for acquiring time-domain signals can be determined based on the subspace sampling operator. These steps can be performed, for example, according to the principles described with reference to the sequence determination device 110. The respectively determined acquisition parameters can then be provided to a magnetic resonance imaging system for acquiring the respective time-domain signals; these steps are not shown in FIG. 2. Step 220 then includes, in a first step 221, providing time-domain signals acquired in time-domain magnetic resonance imaging using a predetermined sampling pattern in k-space, for example the magnetic resonance acquisition sequence determined above. In step 222, a subspace sampling operator is provided, which, if present in step 210, is the same subspace sampling operator used to determine the magnetic resonance acquisition sequence. In step 223, the time-domain signals are processed using the subspace sampling operator, and in step 224, magnetic resonance images and / or parameter maps are reconstructed based on the processed time-domain signals. In general, step 220 can be performed, for example, by the apparatus 130 described with reference to FIG. 1 .

[0037] Details and preferred embodiments are described below. In a preferred example, magnetic resonance images and / or parameter maps are reconstructed using magnetic resonance fingerprinting. In general, the performance of dictionary matching in magnetic resonance fingerprinting is difficult to comprehensively analyze due to the complex interaction between object-dependent spatial subsampling artifacts and the coding power of the sequence. When using compressed matching, the computational execution time can be significantly reduced, but the selection of the dimension of the compressed subspace remains ad hoc in most cases. When moving toward shorter acquisition sequences to reduce acquisition time, a performance degradation is observed. This degraded performance can often only be compensated for by advanced reconstruction methods, which lead to significant computational overhead and unclear convergence characteristics.

[0038] The use of subspace sampling operators as described above allows for the interaction of the magnetic resonance acquisition sequence, acquisition schedule, e.g., the number of interleaves, acquisition order, etc., to be clearly understood, particularly the optimal dimensions of the subspace and noise amplification for compressed dictionary matching. At the same time, the use of subspace sampling operators allows for the best possible estimate of coefficients for a selected compression basis to be achieved in closed form. It also allows for the automatic selection of the optimal dimension of the compressed subspace given a target noise performance. In particular, noise performance depends on the condition number of the subspace sampling operator. Therefore, since the subspace sampling operator depends on the compression space, e.g., via the decompression operator that determines the compressed subspace, the compressed subspace, and therefore its dimension, can also be optimized with respect to yielding a low compression number for the subspace sampling operator. Any known direct or indirect optimization algorithm can be utilized for this optimization. In general, the present invention is based on the insight that decompression operators in the form of subspace sampling operators can be explicitly inverted under reasonable assumptions. This avoids the need for iterative methods during magnetic resonance fingerprinting reconstruction for more difficult sequences, e.g., shorter sequences.

[0039] As a starting point, most reconstruction algorithms solve the least squares problem TIFF2025537666000005.tif929 should be resolved.

[0040] where: TIFF2025537666000006.tif105 is the processed time-domain signal, i.e., in this embodiment, the compressed fingerprinting signal, y is the time-domain signal, SV is the subspace sampling operator generated by the decompression operator V and the selection operator S for each location in k-space, and E is an encoding operator having a fast Fourier transform operator for converting the signal in k-space to a signal in image space and, optionally, a gridding operation for gridding the sampling pattern and a coil combination operator representing the coil characteristics of the acquisition magnetic resonance system. In general, the solution is constrained to lie in a compressed subspace that spans the basis vectors provided by the decompression operator V. The decompression operator V may be, for example, UΣV HThe subspace sampling operator S can be obtained via single-value decomposition from the complete dictionary D used in the fingerprinting reconstruction algorithm according to =D. An example of the effect of the selection operator S on the decompression operator V to form the subspace sampling operator is shown schematically and exemplarily in FIG. 4. The upper part of the diagram shows an example representation of the temporal basis vectors of the compressed subspace represented by the decompression operator V. The lower part of the diagram shows the representation of the selection operator for different measurements of interleaving, i.e., different sampling patterns. The arrows indicate the selection of the temporal basis vectors, i.e., subsampling, as an effect of the selection operator acting on the decompression operator. As shown schematically in FIG. 4, the subspace sampling operator provides a given k-space location for the sampling pattern temporal subsamples of the temporal basis vectors of the compressed subspace. However, it should be noted that FIG. 4 merely provides an exemplary and graphical visualization of the mathematical effects of the two operators and does not accurately represent the mathematical result, i.e., the subspace sampling operator.

[0041] A widely used method for accelerating convergence in iterative methods is to use a preconditioner that approximately inverts the system matrix, in which the eigenvalues ​​are clustered as close to 1 as possible. Specifically, the property A matrix with TIFF2025537666000007.tif618 is introduced, which is yields TIFF2025537666000008.tif973. The subspace sampling operator is This has the advantage that it can be exactly inverted so that a new problem is obtained that leads to linear equations that can be easily computed in TIFF2025537666000009.tif955.

[0042] gridding with sampling density compensation w, It can be solved directly using TIFF2025537666000010.tif933.

[0043] Sampling density compensation can be omitted if an iterative approach to solving the above problem is used. In general, in this case, if the encoding operator optionally includes non-uniform FFT and coil sensitivity, this formulation is similar to using a conjugate gradient scheme to solve the detection problem. As a result, the above formulation can also be applied with additional spatial undersampling. For example, encoding a smaller field of view in a spiral acquisition results in fewer measured interleaves and therefore a higher sampling rate over time, resulting in better conditioning.

[0044] Given the above straightforward method for calculating the conditions of use, we also provide a simple method for evaluating the performance of a magnetic resonance acquisition sequence based solely on the temporal sampling rate, which can be used to optimize the acquisition sequence. This is in stark contrast to previous methods presented in the literature that rely on simulating the complete data acquisition and reconstruction process, which involves assumptions about the imaged object and significant computational overhead. This is orthogonal to the Cramer-Rao-Lower-Bound based sequence optimization method, which is primarily concerned with the "encoding ability" of the sequence, without considering the acquisition. In particular, as shown below, optimization of the acquisition sequence can be based on the condition number of the SV. In general, the pseudoinverse transform can be computed as a Moore-Penrose pseudoinverse transform, which can be expressed as follows, depending on the shape of V: TIFF2025537666000011.tif1152 or I have one of them, TIFF2025537666000012.tif1354.

[0045] (SV) +The singular values ​​of determine the condition number of the problem and therefore directly determine the noise propagation characteristics. As the singular values ​​approach 0, this means that the problem worsens and requires the use of a magnetic resonance acquisition sequence, acquisition scheme, e.g., more cost-effective interleaving, or reducing the subspace dimension. Furthermore, since the condition number directly indicates the noise propagation during the inverse calculation, and the lower the condition number, the better the inversion accuracy, optimization algorithms can be used to optimize acquisition parameters with respect to leading to a low condition number; i.e., minimizing the condition number can be used to determine the optimal acquisition sequence.

[0046] Based on the above, magnetic resonance images and / or parameter maps can be reconstructed using, for example, magnetic resonance fingerprinting. Generally, in magnetic resonance fingerprinting, dictionary matching is performed. This dictionary matching typically involves matching dictionary entries TIFF2025537666000013.tif84 and the specifically normalized and processed time domain signal By maximizing the dot product in coefficient space between TIFF2025537666000014.tif105 This is achieved as TIFF2025537666000015.tif12130.

[0047] The "hat" means that the signal is compressed into a low-dimensional compressed subspace spanned by the basis vectors provided by the decompression operator V, which can be obtained as already mentioned above by a single-value decomposition of the complete dictionary D. In general, the uncompressed fingerprinting signal x is compressed into a low-dimensional compressed subspace spanned by the basis vectors provided by the decompression operator E H The spiral acquisition consists of gridding, FFT, and coil combination. Hcombines the time points on the magnetic resonance time domain signal with the acquired k-space positions, essentially filling the undersampled k-space with zero filling. w performs density compensation for non-Cartesian trajectories. This is Introducing compression, this results in TIFF2025537666000016.tif828. It will be corrected to something like TIFF2025537666000017.tif957.

[0048] V H operates in the time domain, while E H operates in the spatial domain and hence the subspace sampling operator V H S H This latter step works because , or equivalently SV can be introduced. Note that this operator is defined per k-space position per interleave in the case of a spiral acquisition.

[0049] The operation of S on V is to subsample in time the basis vectors of the compressed subspace. These remaining subsampled representative time signals are no longer guaranteed to be orthogonal. In this case, the Hermitian conjugate is not a useful approximation of the inverse matrix. Rather, the above equation is a recursive recursion of the already determined equation above. It can be approximated with TIFF2025537666000018.tif933.

[0050] Therefore, the fingerprinting signal can be easily calculated using subspace sampling operators without iterations and then used in dictionary matching.

[0051] Figure 3 shows T2 matching results demonstrating the effectiveness of the proposed method. In particular, the T2 map (a) on the left is obtained using standard dictionary matching without the use of a subspace sampling operator. The T2 map (b) in the center is reconstructed using dictionary matching after the reconstruction of the fingerprinting signal using the time-domain signal processed with the subspace sampling operator according to the above equation. The T2 map (c) on the right is reconstructed using an iterative approach without the subspace sampling operator, specifically using five conjugate gradient iterations to determine the fingerprinting signal. The noise in the background in panel (b) is due to different thresholds. Images (b) and (c) are nearly identical, indicating high quality and low noise.

[0052] In a preferred embodiment, a subspace sampling operator is further used for validation and, optionally, for determining the acquisition sequence, as described below. In particular, the acquisition sequence is preferably validated and determined with respect to expected matching performance, e.g., with respect to expected matching error. Matching performance, particularly the matching error, is given by the accuracy and precision with which matching can be performed, and thus parameters such as T1, T2, etc. can be determined. In general, the matching error for magnetic resonance fingerprinting may depend on the encoding power of the acquisition sequence, i.e., the sequence's potential for measuring the respective parameters, the sampling pattern, particularly spatial undersampling of the sampling pattern, as well as the inherent signal-to-noise ratio of the measurement and reconstruction algorithm employed. In the case of a fully sampled sampling pattern, the sequence's encoding power, and therefore the sequence's suitability for a particular matching, can be easily determined, e.g., using the Cramer-Rao Bound. However, previous attempts to include the effects of spatial undersampling have been limited to very specific applications or have been computationally very resource-intensive. The present invention makes it possible to overcome these drawbacks by utilizing the above-mentioned undersampling operator for fast and computationally cheap calculation of the respective fingerprinting signal via the processed time domain signal, in particular with this approach the influence of undersampling on the sampling pattern can be included in the sequence verification and decision in a simple, trajectory-independent and object-independent way.

[0053] A detailed example of a preferred algorithm for verifying and then determining the acquisition sequence is described below. This algorithm can be executed by a respective dedicated or general-purpose computing system, in particular by a respective sequence verification device configured to execute the method using a respective calculation unit. First, respective possible acquisition sequences are provided. For example, one or more of such possible sequences can be already stored in a respective storage device or can be received from a user via an input unit. Based on the possible acquisition sequences, a dictionary D and a compressed time subspace V can be calculated. Furthermore, a sampling pattern, in particular a subsampling pattern, for example, a spiral acquisition with 10 interleaves, can be selected via input from a user or can be predetermined. Next, an artificial time-domain signal is determined, whose matching parameters, such as T1, T2, etc., are already known as ground truth parameters. For example, a random selection of a fingerprinting signal s can be generated from a previously generated dictionary using predetermined matching parameters. Preferably, the fingerprinting signal is a non-normalized signal, thus providing correct relative amplitudes. A random unitary matrix M can then be used to mix the fingerprinting signals so that their appearance is spatially distributed, simulating the signal mixture typically found in k-space. However, the random unitary matrix M can be completely different from the encoding found in k-space. This has the advantage of allowing for the selection of a matrix that is computationally easy to handle. Optionally, of course, a respective encoding matrix representing the encoding in k-space can also be used. Thus, the matrix can refer to a fast Fourier transform that results in the simulated k-space, but this would impose an unnecessary specific structural interpretation on the operation of the algorithm. Next, the respective mixed signals m = Ms can be calculated. Complex Gaussian noise can then be added to the mixed signals to simulate the noise expected in the measured time-domain signal.To generate the artificial time-domain signal, a sampling pattern, particularly subsampling, is added, e.g., selected for each interleaf I at each measured time point. Noise can also be added after the subsampling is applied. Furthermore, a subspace sampling operator can be determined based on the decompression operator and the respective sample pattern. An artificial fingerprinting signal can then be determined based on the determined artificial time-domain signal and the subspace sampling operator. For example, a first coefficient c can be calculated by applying a pseudo-inverse subsampling operator to the artificial time-domain signal, followed by a Hermite-of-mixing operator M. Based on the artificial fingerprinting signal, compressive matching for matching parameters can be performed to obtain estimates of, for example, T1, T2, etc. Based on a comparison between known and estimated matching parameters, an error, i.e., a matching error, can be evaluated. Based on this matching error, optimization can be performed. For example, error minimization based on the acquisition sequence can be performed. Alternatively, a target matching error can be provided, and the matching error can be compared to this target to find a sequence that meets this target. In general, the optimization landscape can often be expected to be very complex, with many local minima. However, in most cases, finding an absolute minimum is not necessary; minimization can be considered successful even if a local minimum is found. Generally, genetic algorithms or gradient descent algorithms can be utilized for optimization algorithms such as simulated annealing. Preferably, if an absolute minimum is found, multiple types of optimization algorithms with variable starting points are applied. However, in most cases, it is expected that many minima will have similar performance, and finding a global minimum is not important. Furthermore, it can be advantageous to use low-dimensional parameterization, for example, via spline interpolation, to reduce the number of optimization parameters, i.e., the acquisition sequence.In general, hyperparameters for optimization that can be utilized to prime the optimization can include the size of the subspace, i.e., the number of example tissue parameter combinations to evaluate the number of coefficients, and the range of T1 / T2 to optimize the relative weighting of the T1 / T2 errors.

[0054] Although the above examples refer primarily to reconstruction methods that utilize matching, the subspace sampling operator can also be used in any other reconstruction method that utilizes subspace, i.e., compression, and the effects of specific sampling patterns, e.g., T2 shuffling.

[0055] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.

[0056] In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality.

[0057] A single unit or device may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

[0058] The procedures performed by one or several units or devices, such as processing of the detection signals to measure medical parameters, authentication, control of the medical monitoring system, etc., may be performed by any other number of units or devices. These procedures, in particular the control of the medical monitoring system according to the management methods performed by the medical monitoring system controller, may be implemented as program code means of a computer program and / or as dedicated hardware.

[0059] The computer program may be stored / distributed on a suitable medium, such as an optical storage medium or a solid-state medium, supplied together with or as part of other hardware, but may also be distributed in other forms, such as over the Internet or other wired or wireless telecommunications systems.

[0060] Any reference signs in the claims should not be construed as limiting the scope.

[0061] The present invention relates to an apparatus for reconstructing MR images and / or parameter maps based on MR time-domain signals. A providing unit provides time-domain signals acquired in time-domain MRI using a sampling pattern in k-space and a magnetic resonance acquisition sequence. The providing unit provides subspace sampling operators that provide given k-space locations of the sampling pattern time subsamples of basis vectors of a compressed subspace. The compressed subspace can be used to compress the time-domain signals. A processing unit processes the time-domain signals using the subspace sampling operators. A reconstruction unit reconstructs MR images and / or parameter maps based on the processed time-domain signals. This enables more accurate and less computationally resource-intensive reconstruction of MR images and / or parameter maps in the context of time-domain magnetic resonance imaging.

Claims

1. 1. An apparatus for reconstructing a magnetic resonance image and / or a parameter map based on magnetic resonance time domain signals acquired in time domain magnetic resonance imaging, said apparatus comprising: a time domain signal providing unit for providing a time domain signal acquired in time domain magnetic resonance imaging using a predetermined magnetic resonance acquisition sequence and a predetermined sampling pattern in k-space; an operator providing unit for providing a subspace sampling operator that provides, for a given k-space location of the sampling pattern, a time subsample of a basis vector of a compressed subspace, the compressed subspace being usable for compressing the time domain signal; a signal processing unit for processing the time domain signal using the subspace sampling operator; a reconstruction unit for reconstructing the magnetic resonance image and / or parameter map based on the processed time domain signals, the reconstruction comprising an explicit inverse or pseudo-inverse of the subspace sampling operator; An apparatus having:

2. 2. The apparatus of claim 1, wherein providing the subspace sampling operator comprises generating the subspace sampling operator as a combination of a selection operator associated with the sampling pattern in k-space and a decompression operator comprising basis vectors of a compressed subspace that can be used to compress a signal into the compressed subspace.

3. The step of processing the time domain signal comprises: Calculating is the processed time domain signal, y is the measured time domain signal in non-Cartesian k-space, w has density compensation weighting, (SV) + is the pseudo-inverse of the subspace sampling operator, and E H 3. The apparatus according to claim 1, wherein the sigma is a Hermite of an encoding operator comprising a Fast Fourier Transform operator for transforming signals in k-space into signals in image space, and optionally a gridding operation for gridding the sampling pattern, and a coil combination operator representing coil characteristics of an acquisition magnetic resonance system.

4. 4. The apparatus according to claim 1, wherein the step of processing the time domain signal is based on a pseudoinverse of the subspace sampling operator, the pseudoinverse of the subspace sampling operator being determined as a Moore-Penrose pseudoinverse.

5. 5. The apparatus of claim 1 , wherein the step of reconstructing the magnetic resonance image and / or parameter map utilizes magnetic resonance fingerprinting, and the reconstruction of the magnetic resonance image and / or parameter map is based on the processed time domain signals utilized for dictionary matching.

6. 6. The apparatus according to claim 1, further comprising an acquisition parameter validation unit configured to validate acquisition parameters for an acquisition sequence for acquiring the time domain signal with respect to a matching error based on the subspace sampling operator.

7. The apparatus of claim 6 , wherein the acquisition parameters are validated based on a condition number of the subspace sampling operator.

8. 1. A sequence verification apparatus for verifying an acquisition sequence for acquiring magnetic resonance time domain signals in time domain magnetic resonance imaging, the apparatus comprising: an acquisition sequence providing unit for providing possible acquisition sequences having respective acquisition parameters and a predetermined sampling pattern; an operator providing unit for providing a subspace sampling operator that provides, for a given k-space location of the predetermined sampling pattern, time sub-samples of basis vectors of a compressed subspace that can be used to compress time domain signals acquired using the possible acquisition sequences; an acquisition parameter validation unit for validating acquisition parameters of the potential acquisition sequences for acquiring the time domain signals with respect to a matching error associated with the reconstruction of a magnetic resonance image or a magnetic resonance parameter map from the compressed magnetic resonance time domain signals based on the conditioning of the subspace sampling operator; A sequence verification device comprising:

9. The sequence verification apparatus of claim 8 , further comprising an acquisition parameter generation unit for generating an acquisition sequence based on verification of acquisition parameters of the potential acquisition sequence.

10. 1. A system for reconstructing magnetic resonance images and / or parameter maps based on magnetic resonance time domain signals acquired in time domain magnetic resonance imaging, the system comprising: a magnetic resonance imaging system configured to acquire time domain signals in time domain magnetic resonance imaging using a predetermined sampling pattern in k-space and a predetermined magnetic resonance acquisition sequence; A device according to any one of claims 1 to 7 and / or a sequence verification device according to any one of claims 8 to 9. A system having:

11. 1. A computer-implemented method for reconstructing magnetic resonance images and / or parameter maps based on magnetic resonance time domain signals acquired in time domain magnetic resonance imaging, the method comprising: providing time domain signals acquired in time domain magnetic resonance imaging using a predetermined sampling pattern in k-space and a predetermined magnetic resonance acquisition sequence; processing the time domain signal utilizing the subspace sampling operator; reconstructing the magnetic resonance image and / or parameter map based on the processed time domain signals, the reconstruction comprising an explicit inverse or pseudo-inverse of the subspace sampling operator; A method comprising:

12. 1. A computer-implemented sequence verification method for verifying an acquisition sequence for acquiring magnetic resonance time domain signals in time domain magnetic resonance imaging, the method comprising: providing a sequence of possible acquisitions having respective acquisition parameters and a predetermined sampling pattern; providing a subspace sampling operator that provides, for a given k-space location of the predetermined sampling pattern, a time subsample of a basis vector of a compressed subspace that can be used to compress time domain signals acquired using the possible acquisition sequences; verifying acquisition parameters of the potential acquisition sequences to acquire the time domain signal for matching errors based on conditioning of the subspace sampling operator; A method comprising:

13. An acquisition sequence for acquiring magnetic resonance time domain signals in time domain magnetic resonance imaging verified using the sequence verification device according to claim 8.

14. 12. A computer program product for reconstructing magnetic resonance images and / or parameter maps based on magnetic resonance time domain signals acquired in time domain magnetic resonance imaging, said computer program product causing an apparatus according to any one of claims 1 to 7 to perform the method according to claim 11.

15. 13. A computer program product for determining an acquisition sequence for acquiring magnetic resonance time domain signals in time domain magnetic resonance imaging, the computer program product causing an apparatus according to claim 8 to perform the method according to claim 12.

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