Abstract:
A magnetic resonance imaging method includes acquisition of datasets of magnetic resonance data from an object. At least some of the datasets are undersampled in k-space. Each dataset relating to a motion state of the object. Images are reconstructed from each of the datasets by way of a compressed sensing reconstruction. Motion correction is applied to the reconstructed images relative to a selected motion state, so as to generate motion corrected images. A diagnostic image for the selected motion state is derived, e.g. by averaging from the motion corrected images.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention pertains to magnetic resonance imaging method in which magnetic resonance datasets are acquired from an object in motion. Further, the datasets are undersampled and reconstruction is performed by way of compressed sensing. 
       BACKGROUND OF THE INVENTION 
       [0002]    Such a magnetic resonance imaging method is known from the paper Compressed sensing in dynamic MRI′ by U. Gamper et al. in MRM 59(2008)365-373. 
         [0003]    The known magnetic resonance imaging method relates to cardiac MR imaging in which sparsely sampled datasets are acquired for each heart phase. Then on the basis of compressed sensing images are reconstructed for each heart phase. Each heart phase has the same number of sampling points and the sampling points (in the k-t space) should be closely separated. 
       SUMMARY OF THE INVENTION 
       [0004]    An object of the invention is to provide an magnetic resonance imaging method that improves the signal-to-noise ratio(SNR) of a diagnostic image that is based on undersampled magnetic resonance datasets. 
         [0005]    This object is achieved by a magnetic resonance imaging method according to the invention which includes
       acquisition of datasets of magnetic resonance data from an object   at least some of the datasets being undersampled in k-space   each dataset relating to a motion state of the object,   reconstruction of images from each of the datasets by way of a compressed sensing reconstruction,   application of a motion correction to the reconstructed images relative to a selected motion state, so as to generate motion corrected images and   derivation of a diagnostic image for the selected motion state from the motion corrected images.       
 
         [0012]    The problem of reconstruction of images from sparse or undersampled datasets that involve undersampling of k-space is solved by employing compressed sensing. Notably, the image quality of each of the reconstructed images may be different because the degree of undersampling and the details of incomplete k-space coverage may be different. These differences, and differences in SNR of these images are compensated by motion correction and by using the information of all motion corrected images in the diagnostic image. This leads to a diagnostic image that has a high SNR and low level of image artefacts. A simple and yet effective manner is to form the diagnostic image as the average of the motion corrected images. Thus, no data are rejected, efficiency is improved and SNR is maximised. 
         [0013]    These and other aspects of the invention will be further elaborated with reference to the embodiments defined in the dependent Claims. 
         [0014]    In one aspect of the invention, there is one dataset that has full k-space sampling and thus contains in essence all image information so that e.g. the image from the fully sampled dataset can be reconstructed by Fast Fourier Transformation (FFT). The image information from the FFT reconstructed image is then used as a priori information in the compressed sensing reconstruction of the images for the undersampled datasets. 
         [0015]    In another aspect of the invention, correlations between the images for different motion states are used as a priori information for the compressed sensing reconstruction. Notably, the correlations are derived from prior knowledge on the type of motion of the object. Notably, this implementation is well suited apply when periodic motion occurs. Good results are achieved when the motion is smooth, such as for example in respiratory motion of a patient to be examined. 
         [0016]    In a further aspect of the invention an affine 3D translation with linear transform motion correction method is applied. Such a motion correction very accurately corrects for respiratory motion. 
         [0017]    The invention also relates to a magnetic resonance examination system as defined in claim  8 . This magnetic resonance examination system achieves on the basis of magnetic resonance datasets, of which several are undersampled to produce a diagnostic image that has a high SNR and low level of image artefacts. The invention further relates to a computer programme as defined in claim  7 . The computer programme of the invention can be provided on a data carrier such as a CD-rom disk or a USB memory stick, or the computer programme of the invention can be downloaded from a data network such as the world-wide web. When installed in the computer included in a magnetic resonance imaging system the magnetic resonance imaging system is enabled to operate according to the invention and achieves on the basis of magnetic resonance datasets, of which several are undersampled to produce a diagnostic image that has a high SNR and low level of image artefacts. 
         [0018]    These and other aspects of the invention will be elucidated with reference to the embodiments described hereinafter and with reference to the accompanying drawing wherein 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]      FIG. 1 . shows a PAWS gating scheme. 
           [0020]      FIG. 2 . shows a scheme of a 3D magnetization prepared (T2-prep+fat suppressed) navigator (N) gated coronary angiography scan. 
           [0021]      FIG. 3  illustrates randomized k-t sampling. 
       
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       [0022]      FIG. 1 . shows a PAWS gating scheme in which (a) the respiration navigator signal (green) that measures the right hemi-diaphragm displacement over time is used to decide which bin will be filled in time. Using an appropriate sampling scheme at the end of the scan (b) k-space is filled in a variable density random fashion. Using an appropriate k-space sampling scheme, in the bins containing the incomplete data sets an incoherent data distribution is realised, with the central k-space part sampled completely. This allows reconstruction of all the data in all bins via compressed sensing (CS) [8]. The individual images can be motion-corrected and averaged to improve SNR. Additionally also the correlation among the individual images (bins), which reflect slightly different motion states, can be used to improve CS reconstruction. In this approach a certain motion model (affine: 3D translation+linear transform [rotation, stretching] described by 12 parameters [9] or more sophisticated ones) can be incorporated into the CS reconstruction. The objective in choosing k-space sampling scheme is to achieve quasi-random quasi-isotropic k-space coverage in all bins with incomplete k-space coverage. 
         [0023]    One potential sampling pattern can be achieved by means of Golden ratio profile ordering. Golden ratio has been previously used in radial sampling [10,11] to achieve quasi-isotropic k-space coverage over the total duration of the scan as well as for an arbitrary time window extracted from a scan for dynamic imaging. However, Golden ratio can also be used to determine the profile ordering in Cartesian sampling by choosing the point on the Cartesian grid lying closest to the coordinates determined by the Golden ratio. 
         [0024]      FIG. 3  illustrates randomized k-t sampling. Full sampling of the k-space centre is performed in the beginning followed by incoherent k-t sampling. Random sampling, Golden ratio, Poisson disk sampling or Halton sampling are possible choices for the sampling pattern in k-t space. 
         [0025]    Alternatively, initial estimation of the period duration of respiratory motion can be used to determine the k-space sampling to achieve the desired k-space coverage. This can be achieved by performing the sampling in several time frames with randomized undersampling in k-space and along the temporal direction ( FIG. 3 ). 
         [0026]    Several possible choices for the randomized k-t trajectory include random sampling, Poisson disk sampling, Halton sequence and Golden ratio. Initial sampling of a fully sampled k-space centre followed by centre-out acquisition of the randomized trajectory in each frame might be appropriate. 
         [0027]    At the end of the acquisition, one of the bins is fully sampled and all the others are undersampled. The reconstruction is performed for instance by solving for each bin the optimization problem: 
         [0000]      Min Σ i  ∥F ui x i −y i ∥ 2 +∥Ψx i ∥ 1  
 
         [0028]    Where F ui  is the undersampled Fourier transform operator for bin i, x i  is the image y i  is the measurement vector and is the sparsifying transform (e.g. wavelets or finite differences). Another possibility is to use the fully sampled image in the 11 term 
         [0000]      MinΣ i ∥F ui x i y i ∥ 2 +∥Ψ(x i −x c )∥ 1  
 
         [0000]    to achieve higher sparsity. 
         [0029]    The images reconstructed in this way can be used to estimate the transformation matrices A, (translation, rotation) for each bin relative to the fully sampled bin. These matrices can be used in a second step to further improve the image quality by adding the self consistency term 
         [0000]      MinΣ i ∥F ui x i −y i ∥ 2 +∥Ψ(x i −x c )∥ 1 +∥A i x i −x c ∥ 2  
 
         [0030]    The approach can be combined with parallel imaging and can additionally be undersampled in the CS sense. No data are rejected, efficiency is improved and SNR is maximised. 
       EXAMPLE NO (I) 
       [0031]      FIG. 2 . shows a scheme of a 3D magnetization prepared (T2-prep +fat suppressed) navigator (N) gated coronary angiography scan. A standard whole heart Cartesian CMR protocol is used [1]. It includes navigator gating, EKG triggering, magnetization preparation and TFE signal detection. A T 2  preparation sequence is employed to improve the contrast between blood and myocardium, and fat signal pre-saturation is used to suppress the epi-cardial fat that is embedding the coronary vessels (see  FIG. 2 ). A PAWS like gating scheme is used as shown in  FIG. 1 . The bin width is set to an acceptable value of 5 mm to freeze respiratory motion. As an option the most probable motion state is estimated just before the scan by acquiring some navigator value statistics. This motion state can optionally be used as a reference for prospective tracking. During the acquisition the navigator signal is evaluated and it is deceived prospectively to which bin the data measured next will belong. Alternatively, motion can be estimated on the basis of the CS-reconstructed undersampled data sets, where the CS reconstruction has been shown to provide sufficient image quality for an imaged-based motion detection, making additional navigators superfluous. 
         [0032]    A special k-space sampling scheme is defined, with some emphasis to fill the central part of k-space for each bin first. In the outer part of k-space random or Poisson disk sampling is performed. The temporal order of this sampling order is influenced by the ideas of golden section sampling to ensure that at the time of scan termination for each bin that might be filled differently (number of profiles wise) a incoherent sample distribution can be realized allowing for CS reconstruction. The scan is terminated if one bin is completely filled. CS based image reconstruction is performed either for each bin individually followed by appropriate registration and image combination or by a more accurate joint CS approach incorporating a potential model in the reconstruction process. 
       EXAMPLE NO (II) 
       [0033]    A standard whole heart Cartesian CMR protocol is used [1], but in this protocol the sampling during the R-R interval was increased by using two or three individual sampling segments each belonging to a separate CMRA data set. An acquisition like this was proposed by Stehning et al.[12] for a radial (stack-of-stars) approach, but here a Cartesian sampling with variable density random sampling is proposed. In this approach for each 3D data the same number of total profiles are acquired, but less than necessary to fulfil the Nyquist sampling criteria, but the distribution in k-space differs for the three data sets. After acquisition of a pre-defined number of profiles sampling is terminated and CS image reconstruction is performed. The motion induced relationship among all these three individual data sets is used in the CS reconstruction. This example is also useful in other anatomies, where motion cannot easily be assed prospectively, such as involuntary head motion in brain scans. 
       EXAMPLE NO (III) 
       [0034]    A combination of the sampling approach described in example(I) and (II). 
         [0035]    This approach is applicable to cardiac MRI especially in coronary MR angiography (CMRA), but is applicable in other anatomies as well. Examples include 3D abdominal free breathing applications, or high resolution brain imaging, where patient groups are subject to involuntary head motion. 
         [0036]    REFERENCES 
         [0037]    [1] Kim et al. NEJM 2001; 27;345:1863. 
         [0038]    [2] Weber et al. MRM 2003;50:1223. 
         [0039]    [3] Nehrke et al. JMRI 2006;23:752. 
         [0040]    [4] Sachs T S, et al., MRM 1994; 32,639-45. 
         [0041]    [5] McConnell M V, et al. MRM. 1997; 37: 148-52. 
         [0042]    [6] Jhooti P, et al. MRM. 2000; 43:470-80. 
         [0043]    [7] Bhat, et al. ISMRM 2010; #669 
         [0044]    [8] Lustig M, et al. MRM 2007;58:1182-95. 
         [0045]    [9] Manke et al. MRM 2003;50:122-131. 
         [0046]    [10] Winkelmann S et al, IEEE Trans Med Imag 26:68-76 
         [0047]    [11] Chan Ret al ISMRM Workshop Non Cart Imaging 2007 
         [0048]    [12] Stehning C, et al. MRM 2005;53:719-23.