SENSE MAGNETIC RESONANCE IMAGING RECONSTRUCTION USING NEURAL NETWORKS

Abstract

Disclosed herein is a method of training a neural network (214) to perform a SENSE magnetic resonance imaging reconstruction. The method comprises receiving (100) initial training data, wherein the initial training data comprises sets of initial training complex channel images each paired with a predetermined number of initial ground truth images. The method further comprises generating (102) additional training data by performing data augmentation on the initial training data such that the data augmentation comprises adding a distinct phase offset to each of the set of initial training complex channel images during generation of the sets of additional training complex channel images. The method further comprises inputting (104) the sets of additional training complex channel images into the neural network and receiving in response a predetermined number of output training images and performing deep learning using the output training images.

Claims

1. A method of training a neural network to perform a SENSE magnetic resonance imaging reconstruction, wherein the neural network is configured to output a predetermined number of reconstructed images in response to inputting multiple measured complex channel images acquired according to a magnetic resonance parallel imaging protocol, by separate coil elements or antennas on separate radio frequency channels wherein the method comprises: receiving initial training data, wherein the initial training data comprises sets of initial training complex channel images each paired with a predetermined number of initial ground truth images; generating additional training data by performing data augmentation on the initial training data, wherein the additional training data comprises sets of additional training complex channel images each paired with a predetermined number of additional ground truth images, wherein the data augmentation comprises adding a distinct phase offset to each of the set of initial training complex channel images during generation of the sets of additional training complex channel images; inputting the sets of additional training complex channel images into the neural network and receiving in response a predetermined number of output training images; calculating a training vector by inputting the predetermined number of output training images and the predetermined number of ground truth images into a loss function; and training the neural network by controlling a backpropagation algorithm with the training vector.

2. The method of claim 1, wherein the method further comprises removing a stitching artifact from the predetermined number of output training images before calculating the training vector.

3. The method of claim 1, wherein the neural network comprises convolutional layers, and wherein the convolutional layers are cyclical convolutional layers.

4. The method of claim 1, wherein the method further comprises cyclically padding boundaries of the additional training complex channel images before inputting them into the neural network.

5. The method of claim 1, wherein the magnetic resonance parallel imaging protocol is a multi-band SENSE magnetic resonance imaging protocol configured for acquiring a predetermined number of slices simultaneously, wherein each of the predetermined number of output training images corresponds to one of the predetermined number of slices, and each of the predetermined number of output training images is offset by a layer dependent translational shift, wherein the method further comprises shifting each of the each of the predetermined number of ground truth images by the layer dependent translational shift before calculating the training vector.

6. The method of claim 1, wherein the distinct phase offset to each of the set of initial training complex channel images is selected from any one of the following: a pseudorandom phase angle distribution, a random phase angle distribution, a chosen list of phase angles, and combinations thereof.

7. A medical system comprising: a memory storing machine executable instructions and a neural network, wherein the neural network is trained by the method of claim 1 to be configured for performing a magnetic resonance parallel imaging reconstruction by outputting a predetermined number of reconstructed images in response to inputting multiple measured complex channel images acquired according to a magnetic resonance parallel imaging protocol by separate coil elements or antennas on separate radio frequency channels; a processor configured for controlling the medical system, wherein execution of the machine executable instructions causes the processor to: receive the multiple measured complex channel images; and receive the predetermined number of reconstructed images by inputting multiple measured complex channel images into the neural network.

8. The medical system of claim 7, wherein the neural network is trained to perform a SENSE magnetic resonance imaging reconstruction, wherein the neural network is configured to output a predetermined number of reconstructed images in response to inputting multiple measured complex channel images acquired according to a magnetic resonance parallel imaging protocol, by separate coil elements or antennas on separate radio frequency channels wherein the method comprises: receiving initial training data, wherein the initial training data comprises sets of initial training complex channel images each paired with a predetermined number of initial ground truth images; generating additional training data by performing data augmentation on the initial training data, wherein the additional training data comprises sets of additional training complex channel images each paired with a predetermined number of additional ground truth images, wherein the data augmentation comprises adding a distinct phase offset to each of the set of initial training complex channel images during generation of the sets of additional training complex channel images; inputting the sets of additional training complex channel images into the neural network and receiving in response a predetermined number of output training images; calculating a training vector by inputting the predetermined number of output training images and the predetermined number of ground truth images into a loss function; and training the neural network by controlling a backpropagation algorithm with the training vector.

9. The medical system of claim 7, wherein execution of the machine executable instructions further causes the processor to removing a stitching artifact from each of the each of the predetermined number of reconstructed images.

10. The medical system of claim 7, wherein execution of the machine executable instructions further causes the processor to cyclically padding boundaries of the multiple measured complex channel images before inputting them into the neural network.

11. The medical system of claim 7, wherein the magnetic resonance parallel imaging protocol is a multi-band SENSE magnetic resonance imaging protocol configured for acquiring a predetermined number of slices simultaneously, wherein each of the predetermined number of reconstructed images corresponds to one of the predetermined number of slices, and each of the predetermined number of output training images is offset by a layer dependent translational shift, wherein execution of the machine executable instructions further causes the processor to shift each of the each of the predetermined number reconstructed images by the layer dependent translational shift.

12. The medical system of claim 7, wherein the predetermined number is one.

13. The medical system of claim 7, wherein the medical system further comprises a magnetic resonance imaging system, wherein the magnetic resonance imaging system comprises a multi-channel RF system configured for acquiring antenna element dependent k-space data from an imaging zone of the magnetic resonance imaging system, wherein the memory further stores pulse sequence commands configured for acquiring the antenna element dependent k-space data according to the magnetic resonance parallel imaging protocol, wherein execution of the machine executable instructions further cause the processor to: acquire the antenna element dependent k-space data by controlling the magnetic resonance imaging system with the pulse sequence commands; and reconstruct the multiple measured complex channel images from the antenna element dependent k-space data.

14. The medical system of claim 13, wherein the pulse sequence commands are further configured to control the magnetic resonance imaging system to acquire coil sensitivity map k-space data according to the magnetic resonance parallel imaging protocol, wherein execution of the machine executable instructions further cause the processor to: acquire the coil sensitivity map k-space data by controlling the magnetic resonance imaging system with the pulse sequence commands; reconstruct a coil sensitivity map from the coil sensitivity map k-space data; reconstruct a predetermined number of algorithmically reconstructed images from the antenna element dependent k-space data and the coil sensitivity map; receive a quality indicator descriptive of the predetermined number of algorithmically reconstructed images, wherein the quality indicator indicates a successful reconstruction or a failed reconstruction; store the predetermined number of algorithmically reconstructed images as subject images in the memory if the quality indicator indicates a successful reconstruction; and proceed with inputting multiple measured complex channel images into the neural network if the quality indicator indicates a failed reconstruction; and store the predetermined number of reconstructed images as the subject images in the memory if the quality indicator indicates a failed reconstruction.

15. A computer program product comprising a neural network and machine executable instructions stored on a non-transitory computer readable medium for execution by a processor controlling a medical system, wherein the neural network is trained by the method of claim 1 to be configured for performing a SENSE magnetic resonance imaging reconstruction by outputting a predetermined number of reconstructed images in response to inputting multiple measured complex channel images acquired according to a magnetic resonance parallel imaging protocol by separate coil elements or antennas on separate radio frequency channels, wherein execution of the machine executable instructions causes the processor to: receive the multiple measured complex channel images; and receive the at least one reconstructed image by inputting multiple measured complex channel images into the neural network.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In the following preferred embodiments of the invention will be described, by way of example only, and with reference to the drawings in which:

[0058] FIG. 1 shows a flow chart which illustrates a method of training a neural network;

[0059] FIG. 2 illustrates an example of a medical system;

[0060] FIG. 3 shows a flow chart which illustrates a method of operating the medical system of FIG. 2;

[0061] FIG. 4 illustrates a further example of a medical system;

[0062] FIG. 5 shows a flow chart which illustrates a method operating the medical system of FIG. 4;

[0063] FIG. 6 illustrates a method of training a neural network for performing a SENSE reconstruction;

[0064] FIG. 7 compares synthesized and measured multi-band sense coil images;

[0065] FIG. 8 illustrates stitching artifact removal; and

[0066] FIG. 9 compares images reconstructed using algorithmic and neural network based multi-band SENSE reconstructions to fully sampled images.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0067] Like numbered elements in these figures are either equivalent elements or perform the same function. Elements which have been discussed previously will not necessarily be discussed in later figures if the function is equivalent.

[0068] FIG. 1 shows a Fig. which illustrates a method of training a neural network to perform a SENSE magnetic resonance imaging reconstruction. First in step 100, initial training data is received. The initial training data comprises sets of initial training complex channel images each paired with a predetermined number of initial ground truth images. The initial training complex channel images are what are input into the neural network. The output of the neural network is then compared with the initial ground truth images to perform the deep learning of the neural network.

[0069] Next, in step 102, additional training data is generated by performing data augmentation on the initial training data. All of the traditional methods of data augmentation such as moving the location of images, rescaling them, inverting them and such may be performed. In this step however, the training complex channel images are additionally modified by adding a distinct phase offset to each of the set of initial training complex channel images. The images are represented in complex phase as both a real and imaginary component. This for example may be represented by two images of the same side; one has the real component and one has the imaginary component. It is also possible to represent each of these complex numbers as a magnitude and a phase. For each voxel the complex value of the voxel may be calculated in terms of phase and amplitude and then modified by adding a distinct phase offset to each channel.

[0070] After adding this phase offset then the new real and imaginary components for the two images which represent a single complex image may be calculated. This may be beneficial in the data augmentation because in real life magnetic resonance imaging systems there may be phase differences due to the wiring or the configuration of the coils and things like this. Adding the distinct phase offset then trains the neural network to function even when there are varying phase relationships.

[0071] The method then proceeds to step 104 where the sets of additional training complex channel images are input into the neural network and in response a predetermined number of output training images is received. Then in step 4 a training vector is calculated by comparing the predetermined number of output training images and the predetermined number of ground truth images into a loss function. Finally, in step 108, the neural network is trained by controlling a back-propagation algorithm with the training vector.

[0072] FIG. 2 illustrates an example of a medical system 200. The medical system 200 is shown as comprising a computer 202. The computer controls a processor 204 that is connected to a hardware interface 206, an optional user interface 208, and a memory 210. The hardware interface 206 may for example comprise such components or interfaces as a network interface. The hardware interface 206 may for example enable the processor 204 to communicate with other computer systems and/or to control other components of the medical system 200. The processor 204 is intended to represent one or more cores in one or more computing machines or devices. The user interface 208 may for example be used for the display of information and to provide a control for the medical system 200. The memory 210 may be any memory which is accessible to the processor.

[0073] The memory 210 is shown as containing machine-executable instructions 212. The machine-executable instructions 212 contain instructions which enable the processor 204 to control other components of the medical system 200 as well as to perform various data and image processing tasks. The memory 210 is further shown as containing a neural network. The neural network is configured for performing a SENSE magnetic resonance imaging reconstruction. This may be performed by inputting multiple measured complex channel images acquired according to a SENSE magnetic resonance imaging protocol. In response a predetermined number of reconstructed images is output. The memory 210 is shown as containing multiple measured complex channel images 216. The memory 210 is further shown as containing a predetermined number of reconstructed images 218 that were generated by inputting the multiple measured complex channel images 216 into the neural network 214.

[0074] FIG. 3 shows a flowchart which illustrates a method of operating the medical system 200 of FIG. 2. First in step 300 the multiple measured complex channel images 216 are received. Next in step 302 the predetermined number of reconstructed images 218 are received or generated by inputting the multiple measured complex channel images 216 into the neural network 214.

[0075] FIG. 4 shows a further view of a medical instrument 400. This medical instrument is similar to the one illustrated in FIG. 2 except it additionally comprises a magnetic resonance imaging system 402. The magnetic resonance imaging system 402 comprises a magnet 404. The magnet 404 is a superconducting cylindrical type magnet with a bore 406 through it. The use of different types of magnets is also possible; for instance it is also possible to use both a split cylindrical magnet and a so called open magnet. A split cylindrical magnet is similar to a standard cylindrical magnet, except that the cryostat has been split into two sections to allow access to the iso-plane of the magnet, such magnets may for instance be used in conjunction with charged particle beam therapy. An open magnet has two magnet sections, one above the other with a space in-between that is large enough to receive a subject: the arrangement of the two sections area similar to that of a Helmholtz coil. Open magnets are popular, because the subject is less confined. Inside the cryostat of the cylindrical magnet there is a collection of superconducting coils.

[0076] Within the bore 406 of the cylindrical magnet 404 there is an imaging zone 408 where the magnetic field is strong and uniform enough to perform magnetic resonance imaging. A region of interest 409 is shown within the imaging zone 408. The magnetic resonance data that is acquired typically acquired for the region of interest. A subject 418 is shown as being supported by a subject support 420 such that at least a portion of the subject 418 is within the imaging zone 408 and the region of interest 409.

[0077] Within the bore 406 of the magnet there is also a set of magnetic field gradient coils 410 which is used for acquisition of preliminary magnetic resonance data to spatially encode magnetic spins within the imaging zone 408 of the magnet 404. The magnetic field gradient coils 410 connected to a magnetic field gradient coil power supply 412. The magnetic field gradient coils 410 are intended to be representative. Typically magnetic field gradient coils 410 contain three separate sets of coils for spatially encoding in three orthogonal spatial directions. A magnetic field gradient power supply supplies current to the magnetic field gradient coils. The current supplied to the magnetic field gradient coils 410 is controlled as a function of time and may be ramped or pulsed.

[0078] Adjacent to the imaging zone 408 is a radio-frequency coil 414 for manipulating the orientations of magnetic spins within the imaging zone 408 and for receiving radio transmissions from spins also within the imaging zone 408. The radio frequency coil 414 is shown as comprising multiple antenna elements 415. The multiple antenna elements 415 are used to each acquire k-space data during the SENSE magnetic resonance imaging protocol.

[0079] The radio-frequency coil 414 is connected to a radio frequency transceiver 416. The radio-frequency coil 414 and radio frequency transceiver 416 may be replaced by separate transmit and receive coils and a separate transmitter and receiver. It is understood that the radio-frequency coil 414 and the radio frequency transceiver 416 are representative. The radio-frequency coil 414 is intended to also represent a dedicated transmit antenna and a dedicated receive antenna. Likewise the transceiver 416 may also represent a separate transmitter and receivers. The radio-frequency coil 414 has multiple receive/transmit elements 415 and the radio frequency transceiver 416 may has multiple receive/transmit channels.

[0080] The transceiver 416 and the gradient controller 412 are shown as being connected to the hardware interface 106 of a computer system 102. The memory 210 is further shown as containing pulse sequence commands 430. The pulse sequence commands are configured for controlling the magnetic resonance imaging system to acquire k-space data according to a SENSE magnetic resonance imaging protocol. The pulse sequence commands 430 may also optionally be configured to acquire data for constructing a coil sensitivity map.

[0081] The memory 210 is further shown as containing antenna element dependent k-space data 432 that was acquired by controlling the magnetic resonance imaging system 402 with the pulse sequence commands 430. The memory 210 is also shown as optionally containing coil sensitivity map k-space data 434 that was also acquired by controlling the magnetic resonance imaging system 402 with the pulse sequence commands 430. The memory 210 is further shown as containing a coil sensitivity map 436 that was reconstructed from the coil sensitivity map k-space data 434.

[0082] The memory 210 is further shown as containing a SENSE reconstruction algorithm 438. To use this, the antenna element dependent k-space data 432 is first reconstructed into the multiple measured complex channel images 216. There is one channel that corresponds to each antenna element. Then the multiple measured complex channel images 216 and the coil sensitivity map 436 are used by the SENSE reconstruction algorithm 438 to construct a number of algorithmically reconstructed images 440 according to the SENSE magnetic resonance imaging protocol. The memory 210 is shown as optionally containing an image artifact detection module 442. For example, the algorithmically reconstructed images 440 can be input and folding artifacts and other artifacts for example might be detected using a neural network or other detection algorithm. Also, the algorithmically reconstructed images 440 could be displayed using a display of the user interface 208 to display them to a user. The user may then provide a quality indicator 444.

[0083] The image artifact detection module 442 may also be used to provide a quality indicator as an alternative. If the quality indicator 444 indicates that the algorithmically reconstructed images 440 have a sufficient quality they are then stored as a subject image 446. If not then the processor 204 may input the multiple measured complex channel images 216 into the neural network 214. The use of the optional SENSE coil sensitivity map 436 provides a system that may first try to correctly measure the coil sensitivity map and reconstruct the SENSE images and if this fails the neural network is then used as a second chance to try to reconstruct the SENSE images.

[0084] FIG. 5 illustrates a method of operating the medical system 400 of FIG. 4. First in step 500 the antenna element dependent k-space data 432 is acquired by controlling the magnetic resonance imaging system 402 with the pulse sequence commands 430. Next in step 502 the multiple measured complex channel images 216 are reconstructed from the antenna element-dependent k-space data 432. Then in step 504 the coil sensitivity map k-space data 434 is acquired by controlling the magnetic resonance imaging system with the pulse sequence commands 430. The coil sensitivity map k-space data 434 can be acquired before the antenna element k-space data 432. Then in step 506, the coil sensitivity map 436 is reconstructed from the coil sensitivity map k-space data 434 according to a SENSE magnetic resonance imaging protocol. The coil sensitivity map 436 may be reconstructed before the multiple measured complex channel images 216 are reconstructed.

[0085] Then in step 508 the predetermined number of algorithmically reconstructed images 440 are reconstructed using the coil sensitivity map 436 and the multiple measured complex channel images 216 as input to the SENSE reconstruction algorithm 438. Next in step 510 a quality indicator is received that is descriptive of the predetermined number of algorithmically reconstructed images 440. As was mentioned above, this may be done automatically or may be signals that are received via the user interface. Step 511 is a decision box and the question is: is the reconstruction successful. If the answer is yes then the method proceeds to step 514 and the predetermined number of algorithmically reconstructed images are stored in the memory 210 as subject images 446. If the answer is no then the method proceeds to steps 300 and 302 of FIG. 3. After step 302, step 512 is performed. In step 512 the predetermined number of reconstructed images 218 are stored in the memory as the subject image or images 446.

[0086] Parallel Imaging methods like SENSE employ receive coil arrays to trade SNR against scan time by under sampling. However, SENSE requires an additional coil sensitivity scan (reference scan) to unfold the under sampled images, which takes some extra scan time. Moreover, motion-corruption of the ref scan will potentially propagate into the SENSE reconstruction of the subsequent diagnostic scan impairing image quality.

[0087] Examples may provide for a neural network for reconstruction of the under-sampled data without the need of a SENSE reference scan, thus improving the motion robustness and the workflow significantly.

[0088] SENSE is a parallel imaging technique, which allows the reconstruction of under sampled MRI data by employing the complementary spatial information provided by a receive coil array. Thus, an additional calibration scan, the so-called SENSE reference scan, is required to determine the spatial sensitivities of the individual receive coil elements of the employed array to unfold the backfolded under sampled images. Multiband (MB)-SENSE is a parallel imaging technique, which applies the sensitivity encoding idea not in the phase encoding direction, but in the slice, direction using SENSE to disentangle the simultaneously acquired slices.

[0089] The U-NET is a type of convolutional neural network (CNN) topology, which was proposed for biomedical image segmentation tasks. The network consists of a contracting path and an expansive path, which leads to the u-shaped architecture. The contracting path is a typical convolutional network that consists of repeated application of convolutions, each followed by a rectified linear unit (ReLU) and a max pooling operation. During the contraction, the spatial information is reduced while feature information is increased. The expansive pathway combines the feature and spatial information through a sequence of up-convolutions and concatenations with high-resolution features from the contracting path.

[0090] Neural networks have been shown to improve parallel image reconstruction, however focusing on non-uniform under sampling patterns with auto calibration lines or enhancing compressed sensing strategies. A multilayer perceptron architecture has been used to remove aliasing artefacts from uniformly under sampled images, however, for reduction factors up to 2 only.

[0091] As outlined above, standard SENSE requires a reference scan, which needs extra scan time for acquisition and may increase motion sensitivity. Moreover, the imperfect orthogonality of the coil sensitivities and thus coil data will result in noise enhancement in the reconstructed images, especially at higher SENSE factors.

[0092] MRI data is complex-valued data. This is due to the complex transmit and receive coil sensitivities showing a spatial phase variation. Moreover, effects like off-resonance, imperfect shims, eddy currents, etc., cause spatial phase variations in the reconstructed images. The spatial phase variations of the data originating from the individual receive coil elements provide essential information required for the unfolding of under-sampled images by the SENSE algorithm, and it is clear that also a neural network used for image unfolding will benefit from this information. However, the global phase offsets of the individual receive coil elements are a matter of MRI system calibration and are arbitrary. Also, B0 and B0-shim related phase variations are arbitrary and difficult to predict. Therefore, the neural networks have to utilize the spatial phase variation of the receive coils, without getting confused by phase variations originating from other sources, which is a difficult task.

[0093] Examples may provide for an appropriately configured multi-dimensional neural network (e.g. a U-net) to do SENSE reconstructions without any knowledge of coil sensitivities of coil correlation kernels.

Such an invention can find many applications in 2D multi-slice and potentially also in 3D (or even higher dimensional) MR imaging reconstructing images in case of no or incomplete or corrupted coil sensitivity information.

[0094] The application of a U-NET neural network to perform a SENSE reconstruction is discussed below. The Cartesian under sampled data in image space (i.e. the back-folded images) are used as input for a neural network. The N complex receive channels result in 2N real input channels (real and imaginary part can be handled as separate channels) for the U-net. The output images have the same size as the input images, where the number of output channels corresponds to the under-sampling factor R usually also dubbed in SENSE as acceleration factor. Thus, the aliasing structures in the backfolded source images are separated into different output channels (FIG. 6 below), those are appropriately shifted to reflect the conditions during the actual measurement. This structure makes use of the fact that the backfolding pattern, including the shifting CAIPIRINHA, is known in advance, and hence, the neural network needs solely performing unfolding of local features without considering long distances. For the output images, modulus images are considered (e.g. sum of squares or sum of magnitudes). For the network, a standard U-Net (see below) is proposed, that learns the relation between the input (N folded complex images) to the output (R unfolded output images).

[0095] FIG. 6 illustrates a way of generating training data for training the neural network 214. First fully sampled complex multi-coil data 600 is acquired. This is data for individual channels 602. Complete images are reconstructed and these are used to generate images with a simulated CAIPIRINHA shift or other translational shift. These images may be used to calculate additional ground truth images 606 or label images. This is done by calculating a sum of magnitudes. By combining images and performing under sampling training images 608 may be generated. These training images have the random phase component added to them and they are therefore the additional training complex channel images 608.

[0096] FIG. 6 illustrates a MB-SENSE reconstruction using a U-NET neural network. For training of the U-Net, label images and training images can be derived from fully sampled images. First, the fully-sampled images are shifted in phase-encoding direction according to the CAIPIRINHA shift selected for the under sampled acquisition to reduce the g factor (e.g. ⅓ field-of-view for MB-factor=3). The fully sampled label images are generated by superposition of the images from the different receive channels using e.g. sum-of-magnitude or root-sum-of-squares. The under sampled training images are generated by superposition of the slices belonging to one MB acquisition. During training, random phases are applied to each receive channel (φ.sub.ch) and to each slice (φ.sub.sl) to improve robustness against potential phase variations. The yellow boxes in the label and training images on the right illustrate that the features remain at their positions in the image.

[0097] Fully sampled images are used for synthetization of training data (cf. FIG. 1 for details). Both training and label images can be synthesized from the fully sampled images training images by appropriate superposition in image space.

[0098] Phase variations from B0 shims, eddy currents, etc. are a big problem for U-Net (and other neural networks) based reconstruction of under sampled images, because the actual phase affects the interference pattern (add or subtract) of the aliased images (FIG. 2). This can effectively be addressed using data augmentation. During synthetization of the MB images used for training, random phase shifts φ.sub.sl are applied to each sub-slice. This can be done statically (in advance) or on-the-fly during training. As a side effect, this augmentation addresses also the Wong phase used for peak B1+ reduction during transmission, which does not have to be accounted for separately. It is conceivable to add instead of the constant also a linear phase variation across the images during training.

[0099] In addition, to address arbitrary phase offsets of the receive channels, random phase offsets φ.sub.ch are added to the receive channel. This makes the neural network robust against channel dependent phase changes after e.g. a recalibration or installation of the system. The mathematical formula is given in the following,

[00001]$\begin{array}{cc}{m}_{\mathrm{synth},\mathrm{ch}}=e^{-i{\phi }_{\mathrm{ch}}}\stackrel{\mathrm{mb}-\mathrm{factor}}{\underset{\mathrm{sl}=0}{.Math.}}{m}_{\mathrm{sl},\mathrm{ch}}.Math.e^{-i{\phi }_{\mathrm{sl}}}& \left[1\right]\end{array}$

[0100] where m.sub.sl,ch where denotes the shifted source data image for MB slice sl and receive channel ch, and m.sub.synth,ch is the resulting augmented synthesized training image for receive channel ch. Ideally, the phase augmentation is repeated for each training epoch to increase the variability of the data, and hence the robustness of learning.

[0101] FIG. 7 illustrates synthesized data 700 and measured MB data 702. It can be seen that these result in different interference patterns where the arrow is located. This difference may be caused by phase variations caused by the B0 shim eddy currents or other factors. This illustrates the importance of performing the data augmentation with a phase variation.

[0102] For the image data layout described above the output images of the U-Net may be shifted to correct for the CAIPIRINHA shift, which may result in stitching artifacts resulting from the imperfect convolution performed by the U-Net at the image borders (FIG. 8 below). These artifacts can be avoided by cyclic padding of the input data and training the network on the padded data. The reconstructed images are then cropped to the original size and shifted back. An alternative approach would be to implement a cyclic convolution for the U-Net.

[0103] FIG. 8 illustrates a stitching artifact removal. The images in the top row labeled 800 show two images with a stitching artifact indicated by the arrows. This for example may be caused by cyclic shifting of U-net reconstructed images. One way of avoiding this is to perform cyclical padding of the training data. The image in the middle 802 shows an additional padding region 803 that has been added to the image 802. This may be added to the training data. The images 804 show the results of a reconstruction by a neural network that used training data similar to the image in 802. In this example the arrows do not show the stitching artifact.

Example I

[0104] Experiments were performed on ten healthy volunteers using a 3T MRI scanner. A standard brain survey scan (3 orientations: SAG, TRA, COR, 3 slices, about 30 s scan time) was acquired for nine different head postures (moving head both from left to right and from neck to chest). In addition, corresponding MB acquisitions were performed (3 orientations: SAG, TRA, COR, MB-factor=3, shift factor=3, about 10 s scan time). The fully sampled standard survey images of nine volunteers were used to train a U-Net for MB reconstruction as described above (cf. FIG. 8) using the Keras API of Tensorflow. The U-Net consisted of 4 down-sampling steps (each preceded by two convolution steps) and corresponding up-sampling steps and convolutions. Stochastic gradient descent using least-squares was used as optimizer. On-the-fly data augmentation as described above was performed to account for phase variations.

[0105] The trained U-Net was used to reconstruct the MB images of the remaining volunteer, which was not used for training of the network. While MB-SENSE leads to severe artifacts when the head posture changes between ref scan and MB-scan, the MB-U-Net reconstructions is more robust and results in image quality comparable to the fully-sampled scan (FIG. 4).

[0106] FIG. 9 illustrates the effectiveness of using a neural network to perform a reconstruction for an MB SENSE reconstruction. The images in column 900 have been reconstructed using a conventional algorithm for performing the MB SENSE reconstruction. The image shows a number of static motion artifacts that were called by a fixed change of the head position between the reference scan used to get the coil sensitivity map and the scan for the images. There are a number of ghosting artifacts which are pointed out by the arrows. In the middle column 902 are images that are reconstructed using the neural network. It can be seen that there are no ghosting images. In the third column 904 are images that were reconstructed using full sampling of k-space. It can be seen that the images in column 902 compare very favorably to the fully sampled images 904. The reconstruction of the neural network was able to avoid the artifacts that are visible in the images in column 900.

Example 2

[0107] Data Pre- and Post-Processing

[0108] For some neural network architectures, such as the proposed U-NET architecture it may be beneficial to use some special data pre- and post-processing in both k-space and image domain, which is outlined in more detail in the following.

[0109] The employed U-NET disentangles the aliased (i.e. superimposed) MB images via different output channels, but does not correct for the CAIPIRINHA shift, which has to be done retrospectively as post-processing step by cyclic shifts of the output images by a certain fraction of the FOV (field-of-view) in PE direction (phase encoding, for the examples shown here: left-right). For instance, in the example shown above, two of the three images have to be shifted by one third of the FOV to the left or right, respectively, to have the anatomy in the image center again. If the pixel size of the image is not a multiple of three in PE direction, some kind of interpolation it may be beneficial to perform the resulting sub-pixel shift. This can be avoided by appropriate pre-processing of the acquired k-space data by zero-padding in the k-space domain before images are reconstructed by Fourier transformation. For the example shown above, one would add empty lines to aim for a multiple of three k-space lines in total (e.g. 258 instead of 256). Then, the CAIPIRINHA shift is a pure integer pixel shift of the final image, which is easy to perform.

[0110] Another pre- and post-processing step relates to the stitching artifact removal. The stitching artifact is due to the fact that the employed U-NET implementation does not perform a cyclic convolution of the data, although the input images are cyclic in PE direction (see e.g. FIG. 7, means that the image could be repeated after the last line on the right with the first line on the left). Hence, the first and last lines of the output images are corrupted and cause a dark stitching artifact after shifting the image to the center. This could be ideally addressed by performing cyclic convolutions in the neural network. However, this is not supported by the chosen Neural Network platform (Tensorflow). Therefore, additional pre- and post-processing steps were performed as workaround. The input images were cyclically continued by a few lines on the left and the right before feeding it into the network. This was done by copying small stripes of data from left to right and vice versa (FIG. 8). The artifact is then in a redundant area of the image and can be removed by cropping the output images to the original size before performing the shift to the center again.

[0111] While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments.

[0112] 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. 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. A single processor or other unit 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 measured cannot be used to advantage. A 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 via the Internet or other wired or wireless telecommunication systems. Any reference signs in the claims should not be construed as limiting the scope.

LIST OF REFERENCE NUMERALS

[0113] 100 receiving initial training data [0114] 102 generating additional training data by performing data augmentation on the initial training data where the data augmentation comprises adding a distinct phase offset to each of the set of initial training complex channel images during generation of the sets of additional training complex channel images [0115] 104 inputting the sets of additional training complex channel images into the neural network and receiving in response a predetermined number of output training images [0116] 106 calculating a training vector by inputting the predetermined number of output training images and the predetermined number of ground truth images into a loss function [0117] 108 training the neural network by controlling a backpropagation algorithm with the training vector [0118] 200 medical system [0119] 202 computer [0120] 204 processor [0121] 206 hardware interface [0122] 208 user interface [0123] 210 memory [0124] 212 machine executable instructions [0125] 214 neural network [0126] 216 multiple measured complex channel images [0127] 218 predetermined number of reconstructed images [0128] 300 receive the multiple measured complex channel images [0129] 302 receive the predetermined number of reconstructed images by inputting multiple measured complex channel images into the neural network [0130] 400 medical system [0131] 402 magnetic resonance imaging system [0132] 400 medical instrument [0133] 402 magnetic resonance imaging system [0134] 404 magnet [0135] 406 bore of magnet [0136] 408 imaging zone [0137] 409 region of interest [0138] 410 magnetic field gradient coils [0139] 412 magnetic field gradient coil power supply [0140] 414 radio-frequency coil [0141] 415 antenna element [0142] 416 transceiver [0143] 418 subject [0144] 420 subject support [0145] 430 pulse sequence commands [0146] 432 antenna element dependent k-space data [0147] 434 optional coil sensitivity map k-space data [0148] 436 coil sensitivity map [0149] 438 SENSE reconstruction algorithm [0150] 440 algorithmically reconstructed images [0151] 442 image artifact detection module [0152] 444 quality indicator [0153] 446 subject image [0154] 500 acquire the antenna element dependent k-space data by controlling the magnetic resonance imaging system with the pulse sequence commands [0155] 502 reconstruct the multiple measured complex channel images from the antenna element dependent k-space data [0156] 504 acquire the coil sensitive map k-space data by controlling the magnetic resonance imaging system with the pulse sequence commands [0157] 506 reconstruct a coil sensitivity map from the coil sensitivity map k-space data [0158] 508 reconstruct a predetermined number of algorithmically reconstructed images from the antenna element dependent k-space data and the coil sensitivity map [0159] 510 receive a quality indicator descriptive of the predetermined number of algorithmically reconstructed images, wherein the quality indicator indicates a successful reconstruction or a failed reconstruction [0160] 512 store the predetermined number of reconstructed images as the subject images in the memory if the quality indicator indicates a failed reconstruction [0161] 514 store the predetermined number of algorithmically reconstructed images as subject images in the memory if the quality indicator indicates a successful reconstruction [0162] 600 fully sampled complex multi-coil data [0163] 602 channel [0164] 604 artificial Caipirinha shift [0165] 606 additional ground truth images [0166] 608 additional training complex channel images [0167] 700 synthesized data [0168] 702 measured MB data [0169] 800 images with stitching artifacts [0170] 802 example of cyclic padding of input images [0171] 803 padding region [0172] 804 result of using cyclic padding [0173] 900 images reconstructed using MB SENSE algorithm [0174] 902 reconstruction using neural network [0175] 904 fully sampled images