Method for generating series of magnetic resonance images with cross-frame iterative reconstruction

Abstract

The invention relates to a method for generating a series of n-dimensional magnetic resonance images from an MR merge series obtained by means of MRI measurements, in which the MR merge series comprises a plurality of merge frames (f1, f2, f3) with determined MR data, in which at least one merge frame is under-sampled, i.e. With missing MR data in addition to the determined MR data, in which at least one of the merge frames (f1, f2, f3) is under-sampled. The merged frames differ due to the values of x predefined parameters, where x = 1 or more, under which MR data is determined, the method comprising: a) calculating an n-dimensional temporary reconstruction kernel from temporary reference data of the reference frame; b) determining a temporary reconstruction frame by reconstructing MR data lacking in the MR merge series by means of a temporary reconstruction kernel; c) calculating an n + x-dimensional reconstruction kernel by calculation of MR data from the temporary reconstruction frames, where MR data of different temporary reconstruction frames are used for calculating the n + x-dimensional reconstruction kernel; d) determining other reconstructed frames by reconstructing data lacking in the merged frame by means of an n + x-dimensional reconstruction kernel; e) generating an n-dimensional magnetic resonance image from the reconstructed frame determined in step (d).

Description

Technical Field

[0001] The invention relates to a method for generating a series of magnetic resonance images from an MR merged series measured with the aid of an MRI, wherein the MR merged series comprises a plurality of merged frames with determined MR data, wherein at least one merged frame is undersampled, i.e. comprises missing MR data in addition to the determined MR data, wherein the merged frames differ due to the values ​​of x predetermined parameters (x=1 or greater) at which the MR data were determined. Background Art

[0002] This method is known from [US981].

[0003] Magnetic resonance imaging (MRI) is a widely used technique for non-invasively acquiring images of the interior of an object to be examined, wherein nuclear spins oriented in the direction of the main magnetic field (z direction) are excited by incident electromagnetic RF pulses (HF: high frequency). By temporally varying superposition of additional position-dependent magnetic fields for all three spatial directions, a position encoding is generated, which can be described as a trajectory through k-space (so-called k-space trajectory). MR signals are recorded during the traversal of the k-space trajectory. A data set consisting of NxM data voxels is obtained. An MR image is generated in position space by Fourier transformation.

[0004] In order to shorten the acquisition time during MRI recording, it is known to reduce the amount of image data to be recorded by incompletely sampling k-space during recording with multiple (real and / or virtual) detection coils (parallel imaging). Therefore, fewer than NxM encoding steps are performed and a reduced data set is obtained for each coil. In order to obtain a complete image from this reduced data set, the missing data must be reconstructed. For this purpose, reference data are used, from which a reconstruction kernel is determined, with the help of which the undersampled measurements can be completely reconstructed.

[0005] The reconstruction kernel is therefore used to reconstruct MR data (intensity values ​​and phase values ​​in k-space) from undersampled data sets, which are generated from MR measurements in which k-space is not fully sampled. In order to calculate (calibrate) the reconstruction kernel, the mathematical relationship (linear combination) of the reference points and the target points within the reference data is determined (linear interpolation). The reconstruction kernel therefore includes rules for how the MR data should be taken into account during reconstruction. The reconstruction kernel describes the influence of the recorded data voxels (determined MR data) on the data voxels to be reconstructed (missing MR data). The reconstruction kernel therefore includes the weights of the measured points when reconstructing the target points. The size of the reconstruction kernel gives how many measurement points of the reference data are used to calculate the reconstruction kernel.

[0006] [DE576] and [Herbst] disclose a method in which missing data of an MR segment data set are reconstructed twice: First, a provisionally reconstructed MR segment data set is calculated with the aid of a reconstruction kernel obtained from the reference data. By creating phase images from the provisionally reconstructed MR segment data set and adding these phase images to the reference image, a modified reference image containing phase information is obtained. From this, a second reconstruction kernel is again determined which, unlike the first reconstruction kernel, contains phase information. In this way, missing data of the MR segment data set can be reconstructed without phase artifacts.

[0007] In dynamic magnetic resonance tomography, moving objects are imaged by recording a series of images at a high frame rate and dividing the images into frames, wherein a frame contains data (time frame) associated with a specific time point within a motion cycle, such as the diastole during a heartbeat. Methods for generating different time frames are known from [US981], [DE040], [Zhao] and [Breuer].

[0008] [US981] and [DE040] disclose a reconstruction method in which different time frames are used for generating the reconstruction kernel. In this case, data from adjacent frames are used (kt-GRAPPA). Thus, the influence of adjacent time information is used in this method in order to improve the quality of the reconstruction. A disadvantage of these methods is that reference data are required for each frame, which reference data are usually recorded as part of each measurement in a series of measurements. This method prolongs the necessary measurement time.

[0009] [Zhao] discloses a reconstruction method in which, in order to keep the required amount of reference data small, a smaller reconstruction kernel is first calibrated. A reconstruction (with artifacts) is performed with this smaller reconstruction kernel. Then, a larger reconstruction kernel (i-GRAPPA) is calibrated from this reconstruction, which can be used for a low-artifact reconstruction. However, only data within the corresponding time frame is considered here.

[0010] Another possibility for generating a reconstruction kernel is the integration (averaging) of parts of a measurement series with different encodings. This method is known from [Breuer] (t-GRAPPA). The reconstruction kernel generated in this way includes information / data from different time frames, but no information about how the data from different time frames are related to one another. In this method, no reference data within the time frame is required. However, due to the averaging, the time resolution for calibration is reduced, while the requirements on the length of the measurement series, the phase consistency of the data and the encoding are increased. Summary of the invention

[0011] The object of the present invention is to provide a method in which information from adjacent frames is used for calibrating the reconstruction kernel and the measurement time is simultaneously shortened.

[0012] According to the invention, this object is achieved by a method according to claim 1 .

[0013] The method according to the invention comprises the following method steps:

[0014] a) calculating an n-dimensional temporary reconstruction kernel from the temporary reference data of the reference frame;

[0015] b) determining a provisional reconstruction frame by reconstructing the missing MR data in the MR merge series by means of the provisional reconstruction kernel;

[0016] c) calculating an n+x-dimensional reconstruction kernel from the MR data of the temporary reconstruction frame, wherein MR data of different temporary reconstruction frames are used to calculate the n+x-dimensional reconstruction kernel;

[0017] d) determining other reconstructed frames by reconstructing the missing data in the merged frame with the aid of an n+x dimensional reconstruction kernel;

[0018] e) generating an n-dimensional magnetic resonance image from the reconstructed frame determined in step (d).

[0019] In a binning frame (Binning-Frame) or simply a binning frame (BinFrame), only MR data are included, for which a predetermined parameter has a predetermined value (e.g. a determined diffusion gradient) or is located in the same predetermined parameter interval (e.g. a determined time interval). For example, the average value of the parameter interval can be used as a representative value of the parameter in the parameter interval.

[0020] An MR merge series is obtained by a large number of scans, by which k-space data (MR data) are detected at k points defined in k-space. An MR merge series includes a plurality of merged frames and can be shown as a kt sampling pattern of data detected in kt space.

[0021] During the scan, MR data (k-space data voxels) are determined using certain values ​​of predefined parameters (e.g. using certain diffusion gradients or at certain points in time during a cycle). The k-space data of each scan are formed, for example, in a Cartesian grid in two dimensions of k-space (ky and kx), where ky is the phase encoding direction and kx is the frequency encoding direction or another phase encoding direction. For three dimensions, the phase encoding direction kz is added. The entirety of the scans for the predefined parameters forms a merged frame.

[0022] The reconstructed frame includes the MR data of the corresponding merged frame and the reconstructed data of the data missing in the corresponding merged frame.

[0023] According to the invention, a temporary n-dimensional reconstruction kernel is first calculated, with the aid of which a temporary reconstruction frame is determined. The data of the temporary reconstruction frame are then used as reference data for determining an n+x-dimensional reconstruction kernel. The dimensionality of the reconstruction kernel is determined in particular by the following factors: the dimension to be reconstructed, the number of coils used for the measurement (parallel imaging), and the number of parameters that are decisive for the division of the data into merged frames. The number of coils is not relevant for the inventive concept and is therefore not considered in the following. The dimensionality of the n+x-dimensional reconstruction kernel is greater than the n-dimensional temporary reconstruction kernel by the number x of parameters, the values ​​of which are decisive for the differentiation of the merged frames.

[0024] The MR image is determined from the other reconstructed frames, for example (in the case of reconstruction in k-space) by Fourier transformation.

[0025] The MR merge series used as the basis for the method according to the invention are obtained with the aid of MRI measurements.

[0026] While the value of a parameter (diffusion gradient) is varied discretely, for example in diffusion-weighted imaging (and thus the MR data can already be assigned to the corresponding merged frames by applying the diffusion gradient), the MR data must be divided into discrete "bins" in the case of a continuous change of the parameter (for example, at time points within a cycle in cardiac measurements). Therefore, the MR data is divided into different "bins" according to the parameter value and forms "merged frames". Therefore, the value of the predefined parameter plays a decisive role in the division of the MR data into different merged frames. In other words, the merged frames are distinguished by the value of the predefined parameter.

[0027] Each merged frame (f1, f2, f3) can include MR data from different detection coils (parallel imaging). In this case, the detection coils can exist both real and virtual, wherein the virtual coils can be generated from a combination of multiple real coils or from individual real coils taking into account the symmetric properties of k-space, as described in [DE579]. The merged frames are usually undersampled, which means that MR data are not measured for the entire k-space, so that MR data are missing in the merged frame. Preferably, a merged frame includes MR data from all coils used, as long as the predefined parameters for the MR data are in the same parameter interval.

[0028] Preferably, an echo planar imaging (EPI) measurement sequence is used for the MRI measurement. In this case, the MR data are preferably recorded by means of a single-shot measurement. This variant is particularly advantageous because no implicit reference data can be measured during EPI recording.

[0029] In a special variant of the method according to the invention, the at least one predetermined parameter is the direction and / or the amplitude of the diffusion gradient used in the MRI measurement.

[0030] In this case, MR merged series are measured by means of diffusion-weighted magnetic resonance tomography (DW-MRI). In this variant, merged frames (diffusion frames) contain MR data that have been measured by applying certain diffusion gradients.

[0031] The MR merge series (here a diffusion sequence) in this variant comprises a plurality of diffusion frames.

[0032] In another variant, the at least one predetermined parameter comprises a time coordinate within a cycle. A specific time coordinate within a cycle is a time point at a specific time interval from the start of the cycle.

[0033] In this variant, the merged frames are referred to as time frames. Periodically recurring events are recorded (e.g. movement patterns, in particular heartbeats, breathing). In this variant, the time frame contains the MR data recorded at specific periodic time points / periodic time intervals. Thus, in the case of periodic events, the MR data do not have to be recorded directly one after the other within a time frame, but rather at specific periodic time points / time intervals (e.g. with respect to the diastole of the heart).

[0034] The MR merge series (here a time series) in this variant comprises a plurality of time frames.

[0035] In another variant, the at least one predetermined parameter comprises an echo time or an inversion time used in the MRI measurement.

[0036] Here, the merged frame is also referred to as a time frame. In this variant, the time frame contains the MR data recorded in a certain time interval (within the echo time). This variant is used in particular when non-periodic events are to be recorded.

[0037] In another variant, the MR merge series can also be measured by using a flow-sensitive MR sequence. The flow-direction-dependent encoding gradients are then used as parameters for the imaging.

[0038] The encoding of the MR data in the MR merged frame can be periodic, wherein preferably the GRAPPA (Generalized autocalibrating partially parallel acquisitions) or CAIPIRINHA (Controlled Aliasing in Parallel Imaging Results in Higher Acceleration) reconstruction methods are applied. Alternatively, it is also possible that the encoding of the MR data in the MR merged frame is irregular in at least one dimension, wherein preferably the SPIRiT reconstruction method is applied.

[0039] Preferably, only merged frames whose values ​​for predefined parameters lie within a predefined interval (adjacent merged frames) are used to reconstruct missing data of the merged frame. This ensures that the merged frame used for reconstruction contains information about the other reconstructed frames to be reconstructed.

[0040] “Adjacent merged frames” do not have to be recorded successively in time, but only need to be similar in their parameter values.

[0041] Adjacent diffusion frames are understood to be diffusion frames whose MR data were recorded with similar diffusion gradients, i.e. with diffusion gradients that do not change or do not change significantly the information to be inferred from the MR image. Directly adjacent diffusion frames are diffusion frames containing MR data that were determined with the next or previously used value of the diffusion gradient or the echo time.

[0042] Adjacent time frames are understood to be time frames whose MR data were recorded at similar periodic time points. Parameter values ​​are considered to be similar if the changes in the MR images and / or in the k-space data caused by different parameter values ​​are within a predefined acceptance range (i.e., if the changes in the MR images caused by different parameter values ​​do not significantly affect the information to be extracted from the MR images and are therefore considered acceptable by the user).

[0043] Preferably, the MR merge series is sorted with respect to the parameters (if it is not already sorted) so that the MR data are included in the correct order when calibrating the n+x dimensional reconstruction kernel.

[0044] Not all merged frames of an MR merge series have similar values ​​for the predefined parameters. Nevertheless (typically), the reconstruction kernel is calculated from all merged frames of the MR merge series. However, to reconstruct data voxels (missing data), only MR data from the own and from adjacent merged frames are used. The number of (i.e. adjacent) merged frames used during reconstruction is defined by the size of the reconstruction kernel: the greater the difference in parameters of the merged frames, the smaller the size of the reconstruction kernel is selected in the "parameter dimension". This means, therefore, that only a small number of merged frames are taken into account during reconstruction. The size of the n+x-dimensional reconstruction kernel or the number of "adjacent" merged frames is preferably in the range of 2-10. The selection of the kernel size is described in detail in [DE040].

[0045] Preferably, the n-dimensional temporary reconstruction kernel is a t-GRAPPA kernel, i.e. a kernel determined by summing / averaging the MR data of different time frames. In this case, no reference measurement is required, since the MR data used to create the temporary reconstruction kernel are data from a merged MR series. This allows for a fully sampled reference measurement to be dispensed with.

[0046] Alternatively, a temporary reconstruction kernel can also be calculated from a fully sampled reference measurement.

[0047] Preferably, the MR merge series has merge frames with different encodings, in particular different phase encodings.

[0048] In a special variant of the method according to the invention, the encoding of the MR data of the combined sequence is periodic and preferably the GRAPPA (GeneRalized Autocalibrating Partial Parallel Acquisition) or, in particular, the CAIPIRINHA (Controlled Aliasing in Parallel Imaging Results in Higher Acceleration) reconstruction method is used, thereby achieving a fast reconstruction.

[0049] Alternatively, the encoding of the MR data is irregular and the SPIRiT (Iterative Self-consistent Parallel Imaging Reconstruction from Arbitrary k-Space) reconstruction method is preferably used. This method can also reconstruct data that (in contrast to the MR data determined during the scan) are not located on a Cartesian grid in k-space.

[0050] In order to further improve the quality of the reconstruction, steps c) and d) can be repeated, wherein the calculation of the n+x-dimensional reconstruction kernel in step c) is performed from the MR data of further reconstruction frames that have been previously determined.

[0051] Preferably, the reconstruction in step (d) is performed in k-space.The MR data are then frequency data.

[0052] Alternatively, a partial reconstruction or a complete reconstruction can also be carried out in position space.

[0053] Other advantages of the present invention are derived from the description and the drawings. According to the present invention, the features described above and to be described in detail below can be applied individually or in any combination. The embodiments shown and described should not be understood as an exhaustive enumeration, but rather as an exemplary feature for describing the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 The method according to the invention is shown schematically.

[0055] Figure 2 A reference frame when calibrating a temporary reconstruction kernel, an undersampled merged frame when reconstructing, and a temporary reconstructed frame when calibrating an n+x-dimensional reconstruction kernel are shown, wherein the undersampled merged frame is identically encoded.

[0056] Figure 3 A reference frame when calibrating a temporary reconstruction kernel, an undersampled merged frame when reconstructing, and a temporary reconstructed frame when calibrating an n+x-dimensional reconstruction kernel are shown, wherein the merged frame is encoded differently. DETAILED DESCRIPTION

[0057] Figure 1 The method according to the invention is schematically shown, with which a series of MR images I1, I2, I3 is generated from a merged series with undersampled merged frames f1, f2, f3. For simplicity, only three merged frames f1, f2, f3 are shown in the figure.

[0058] First, in the context of calibration, the n-dimensional temporary reconstruction kernel vK is calculated from the reference frame fR (see also Figure 2 and Figure 3 ).

[0059] With the aid of an n-dimensional temporary reconstruction kernel vK, a reconstruction of the individual undersampled merged frames f1, f2, f3 is performed. The result of this reconstruction is a temporarily reconstructed reconstruction series with temporary reconstruction frames f1', f2', f3'. According to the invention, the undersampled merged series (in k-space) of MR measurements are individually reconstructed (temporary reconstruction) using parallel imaging.

[0060] The temporary reconstructed frames f1', f2', f3' are now used to calculate a higher-dimensional (n+x-dimensional) reconstruction kernel K, which contains the associations across the merged frames (BinFrame-übergreifende) between target points (points / data voxels, which correspond to the missing data / data voxels in the merged frames f1, f2, f3) and reference points (points / data voxels, which correspond to the MR data / data voxels determined in the merged frames f1, f2, f3). ). Figure 2 and 3 . The temporary reconstruction series is thus a reference data set that allows the determination of reconstruction rules with the inclusion of adjacent measurements (merged frames) of the merged series. How much higher the dimensionality of the reconstruction kernel K is than the dimensionality of the temporary reconstruction kernel vK depends on the number x of parameters used to distinguish the merged frames.

[0061] A further reconstruction of the undersampled merged frame f1, f2, f3 is performed with the aid of an n+x-dimensional reconstruction kernel K. The result of this reconstruction is a further reconstruction series with further reconstructed frames f1", f2", f3", from which MR images I1, I2, I3 can then be generated with the aid of a Fourier transform. In order to improve the result, the n+x-dimensional reconstruction kernel can be recalculated from the further reconstructed frames f1", f2", f3" and the merged frame f1, f2, f3 (in Figure 1 This can be repeated as many times as desired before the MR images I1, I2, I3 are generated.

[0062] Figure 2 and Figure 3 Different merged frames in k-space are shown, wherein determined MR data are shown as solid lines and missing data are shown as dashed lines. Furthermore, reference points S and target points T are shown, which are used here by way of example for calculating the reconstruction kernel.

[0063] exist Figure 2 and Figure 3 The calibration of the temporary reconstruction kernel vK from the reference frame fR is schematically shown in area (a) of FIG. The reference frame fR is fully sampled (fully sampled), but may be smaller than the merged frame. The temporary reconstruction kernel vK calculated from the reference frame fR contains a mathematical association between the reference point S and the target point T of the reference frame fR.

[0064] exist Figure 2 and Figure 3 The temporary reconstruction with the aid of the temporary reconstruction kernel vK is schematically shown in area (b) of . Figure 2 and Figure 3It is shown that, using the mathematical association between the reference point S and the target point T of the temporary reconstruction kernel vK, each undersampled merged frame f1, f2, f3 is reconstructed individually, resulting in Figure 1 The temporary reconstructed frames f1', f2', f3' are shown in region (c) of FIG. Here, all missing data (target points T) of all merged frames f1, f2, f3 have been determined with the aid of the temporary reconstruction kernel vK.

[0065] Now, an n+x-dimensional reconstruction kernel K is calculated from the temporary reconstructed frames f1', f2', f3', which comprises a mathematical association across frames between a target point T (exemplarily shown as the target point T of the temporary reconstructed frame f2') and reference points S from different temporary reconstructed frames f1', f2', f3'. Figure 2 and Figure 3 Here, a linear combination is determined, which establishes an association between the reference points S of the different merged frames f1', f2', f3' and the target point T. Therefore, for each target point T there is a linear combination, which contains the reference points of different frames.

[0066] exist Figure 2 In the variant shown, all merged frames f1, f2, f3 are identically coded (illustrated by the same sequence of solid and dashed lines). In this variant, the reference frame fR is preferably generated by fully sampled predictors (reference measurements).

[0067] Alternatively, the reference frame fR can also be generated by summing the MR data of different adjacent merged frames f1, f2, f3 of an undersampled merged series. This presupposes that the merged frames are coded differently, as in Figure 3 As shown in Figure 3 In the example shown, only merged frames f1 and f3 are encoded identically, while merged frame f2 has another encoding. Specifically, in the example shown, the encoding is selected so that data missing in merged frame f1 (dashed line) is present in merged frame f2 (solid line) and vice versa, so that by adding merged frames f1 and f2, a fully sampled reference frame can be obtained.

[0068] In the context of the invention described here, the reference frame is always fully sampled (full sampling). Despite the same dimensions, the size of the reference frame may be smaller than the size of the magnetic resonance image or the merged frame. Thus, the reference frame can, for example, only correspond to the central area of ​​the magnetic resonance image or the merged frame.

[0069] Reference numerals list

[0070] f1, f2, f3 merged frames

[0071] f1', f2', f3' Temporary reconstruction frames

[0072] f1”, f2”, f3” other reconstructed frames

[0073] fR Reference frame

[0074] K Reconstruction kernel

[0075] vK Temporary rebuild core

[0076] I1, I2, I3 MR images

[0077] S Reference point

[0078] T Target point

[0079] References

[0080] [Zhao]T.Zhao,X.Hu

[0081] Iterative GRAPPA(iGRAPPA) for Improved Parallel Imaging Reconstruction

[0082] Magnetic Resonance in Medicine 59:903-907(2008)

[0083] [Herbst] M.Herbst

[0084] Autocalibrating segmented diffusion-weighted acquisitions

[0085] Magn Reson Med.2021;00:1-14

[0086] [Breuer] F.Breuer et al.

[0087] Dynamic Autocalibrated Parallel Imaging Using Temporal GRAPPA(TGRAPPA)

[0088] Magnetic Resonance in Medicine 53:981-985(2005)

[0089] [US981]US2006050981A1

[0090] [DE040]DE102007015040B3

[0091] [DE576]DE102020202576B4。

Claims

1. A method for generating a series of n-dimensional magnetic resonance images from a combined MR series measured by means of MRI, wherein: An MR merge series comprises a plurality of merged frames (f1, f2, f3) with determined MR data, wherein at least one merged frame is undersampled, i.e. has missing MR data in addition to the determined MR data, wherein the merged frames differ due to the values ​​of x predefined parameters, wherein x=1 or greater, at which the MR data were determined, the method comprising: a) calculating an n-dimensional temporary reconstruction kernel from the temporary reference data of the reference frame; b) determining a provisional reconstruction frame by reconstructing the missing MR data in the MR merge series by means of the provisional reconstruction kernel; c) calculating an n+x-dimensional reconstruction kernel from the MR data of the temporary reconstruction frame, wherein MR data of different temporary reconstruction frames are used to calculate the n+x-dimensional reconstruction kernel; d) determining other reconstructed frames by reconstructing the missing data in the merged frame with the aid of an n+x dimensional reconstruction kernel; e) generating an n-dimensional magnetic resonance image from the reconstructed frame determined in step (d).

2. The method according to claim 1, characterized in that In the MRI measurements, an echo planar imaging measurement sequence is used.

3. The method according to claim 1 or 2, characterized in that: The at least one predetermined parameter is the direction and / or the amplitude of the diffusion gradient used in the MRI measurement.

4. The method according to claim 1 or 2, characterized in that: The at least one predetermined parameter comprises a time coordinate within a period.

5. The method according to claim 1 or 2, characterized in that: The at least one predetermined parameter is the echo time used during the MRI measurement.

6. The method according to any one of the preceding claims, characterized in that The encoding of the MR data in the MR merged frames is periodic, wherein preferably the GRAPPA or CAIPIRINHA reconstruction method is used, or the encoding of the MR data in the MR merged frames is irregular in at least one dimension, wherein preferably the SPIRiT reconstruction method is used.

7. The method according to any one of the preceding claims, characterized in that For the reconstruction of the missing MR data, only merged frames are used whose values ​​for the predefined parameters lie within a predefined interval.

8. The method according to any one of the preceding claims, characterized in that The MR merge series has merged frames with different encodings.

9. The method according to claim 8, characterized in that The n-dimensional temporary reconstruction kernel is the t-GRAPPA kernel.

10. The method according to claim 8 or 9, characterized in that: The encoding of the MR data of the merged series is periodic, wherein the CAIPIRINHA reconstruction method is preferably used, or the encoding of the MR data of the merged series is irregular in at least one dimension, wherein the SPIRiT reconstruction method is preferably used.

11. The method according to any one of the preceding claims, characterized in that Steps c) and d) are repeated, wherein the calculation of the n+x-dimensional reconstruction kernel in step c) is performed based on the MR data of other reconstruction frames that have been previously determined.

12. The method according to any one of claims 1 to 11, characterized in that The reconstruction in step (d) is performed in k-space.

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