Neural network guided motion correction in magnetic resonance imaging

Abstract

Described herein is a medical system (100, 300) comprising a memory (110) storing machine executable instructions (120) and a motion estimation neural network (122, 700, 800, 900, 1000) configured to output trajectory data (130) in response to receiving a test motion trajectory (128) as input. Execution of the machine executable instructions causes the computing system (104) to: receive (200) measured k-space data (124) describing an object (318); performing (202) motion estimation of the object between discrete acquisitions of the sequence by solving an optimization problem to determine a calculated motion trajectory of the object in a predefined coordinate system, where the trajectory data is used to modify the optimization problem; and reconstructing (204) a final motion-corrected magnetic resonance image (136) from the measured k-space data and the calculated motion trajectory in the predefined coordinate system.

Description

Technical Field

[0001] The present invention relates to magnetic resonance imaging and, in particular, to motion-corrected magnetic resonance imaging. Background Art

[0002] As part of the process for producing images inside a patient's body, a magnetic resonance imaging (MRI) scanner uses a large static magnetic field to align the nuclear spins of atoms. This large static magnetic field is called the B0 field or main magnetic field. MRI can be used to measure various quantities or properties of an object spatially and to image it. The difficulty in performing magnetic resonance imaging is that time is required to acquire k-space data, and typically the object will move, causing blurring and motion artifacts in the resulting magnetic resonance image.

[0003] The journal publication Lundervold et al., 'An overview of deep learning in medical imaging focusing on MRI,' Z Med Phys 29 (2019) 102-127 is a review article discussing how deep learning is applied to the MRI processing chain. This includes acquisition to retrieval, image segmentation, and disease prediction. The paper 'Blind Retrospective Motion Correction of MR Images' by Loktyushin et al. in Magnetic Resonance in Medicine 70 (2013) 1608 discloses motion correction based on an iterative search for motion trajectories to produce the clearest image by the entropy of the steepest gradient. That is, the iterative optimization is done using the image gradient entropy metric as the cost function. Summary of the invention

[0004] The invention provides a medical system, a computer program and a method in the independent claims. Embodiments are given in the dependent claims.

[0005] As described above, object motion during the acquisition of k-space data during MRI acquisition can cause blurring and image artifacts. There are many ways to correct for object motion. One technique is to determine the object motion by formulating the motion estimation problem as a numerical optimization problem. Initially, the motion of the object can be assumed and a test image constructed. The test image can be resampled back into k-space and compared with the originally measured k-space data. Normal optimization techniques can be used to perform a numerical search for object motion to minimize the difference between the resampled k-space data and the measured k-space data. The difficulty in this approach is that it can be very numerically intensive.

[0006] There is also a risk of stabilizing to a local minimum and not solving the optimization problem correctly. Embodiments may provide means for accelerating the numerical search, and for minimizing the probability of stabilizing to a local minimum by modifying the optimization problem using a motion estimation neural network. In one example, the optimization is modified by adding a term to a cost function of the optimization problem, the cost function of the optimization problem being a function of the probability that the trial motion trajectory is correct. The effect of this is that the numerical algorithm is guided to the most likely solution for the object's motion, and this can be done more quickly. The motion estimation neural network is configured to provide trajectory probabilities in response to receiving a trial motion trajectory as input.

[0007] According to the present invention, motion estimation involves solving an optimization problem of minimizing by a computing system the difference between measured k-space data and inversely transformed k-space data from a current motion-corrected trial magnetic resonance image. That is, the optimization problem involves optimizing the data consistency between the measured k-space data and the inversely transformed k-space data of the current motion-corrected trial magnetic resonance image, wherein the current trial motion trajectory is motion-corrected. Motion estimation is performed in an iterative manner by updating the current trial motion trajectory under the constraint that the trial motion trajectory is updated to a high probability value that the subsequent trial motion trajectory is correct. The subsequent motion-corrected trial magnetic resonance images in the iteration are corrected with the updated trial motion trajectory. The probability distribution of the correctness of the motion trajectory depends on the object (patient to be examined) metadata and / or metadata associated with the MR acquisition sequence (e.g., scan type). The probability distribution of the correctness probability of the trial motion correction is returned by a motion estimation neural network. The motion estimation neural network can return a subsequent motion trajectory from the current motion trajectory, which can be used in the next iteration of the optimization problem. Thus, the motion estimation network guides a motion-compensated reconstruction algorithm to solve the optimization problem so as to drive to increasingly probable solutions by emphasizing motion trajectories that are more likely to be correct.

[0008] In another example, the motion estimation neural network is configured to output a suggested motion trajectory in response to receiving a trial motion trajectory as input. The suggested motion trajectory is then used to modify or adjust the trial motion trajectory before or after an iteration of solving the optimization problem.

[0009] In one aspect, the present invention provides a medical system comprising a memory storing machine executable instructions and a motion estimation neural network. The motion estimation neural network is configured to output trajectory data in response to receiving a trial motion trajectory as input. The trial motion trajectory is essentially a proposed motion trajectory of an object or a motion trajectory of an object in one iteration of an optimization problem. The trial motion trajectory has a predefined coordinate system. The predefined coordinate system may be defined based on the motion problem itself. For example, if the rigid motion of the skull of an object is processed during magnetic resonance imaging, it may be a coordinate related to the rotation and motion of the skull. In other cases, it may be a vector field that defines the motion of the object as a non-rigid motion. The optimization problem is described below, and the predefined coordinate system will likely be the coordinate system of the optimization problem.

[0010] The medical system also includes a computing system. Execution of the machine executable instructions causes the computing system to receive measured k-space data describing the object. The measured k-space data is divided into a sequence of discrete acquisitions. Typically, when acquiring magnetic resonance imaging data, it is acquired in excitations or groups of k-space data. The measured k-space data represents these measured acquisitions or excitations of magnetic resonance imaging data. A possible cause of image degradation and artifacts during magnetic resonance imaging is the movement of the object between discrete acquisitions.

[0011] Execution of the machine executable instructions also causes the computing system to perform motion estimation of the object between discrete acquisitions of the sequence by solving an optimization problem to determine a calculated motion trajectory of the object in a predefined coordinate system. The optimization problem is formulated to minimize the difference between the transformation of the measured k-space data and the resampled k-space data of the motion-corrected trial magnetic resonance image based on the trial motion trajectory and the measured k-space data. Performing the motion estimation includes receiving trajectory data in response to inputting the trial motion trajectory into a motion estimation neural network. The optimization problem is modified using the trajectory data from the motion estimation neural network. Using an optimization problem to solve for the motion of the object is a technique that has been used previously. The difference is that the optimization problem is modified by probability data.

[0012] Typically, when solving an optimization problem, the trajectory is iteratively refined to minimize the difference between the measured k-space data and the resampled k-space data (data consistency) by naive sampling of the trajectory space or by gradient descent of the data consistency term. The difficulty with this approach is that it can be very computationally intensive and converge slowly. A motion estimation neural network can be used to guide the optimization problem so that it follows or goes to the most likely solution. For example, during a particular type of magnetic resonance imaging examination, there may be very typical motion of the object. For example, respiratory motion or coughing may cause a particular type of motion of the object. Instead of searching the entire solution space, a motion estimation neural network is used to guide or strongly support more likely solutions during the solution of the optimization problem. This can result in a greatly reduced computational burden.

[0013] Execution of the machine executable instructions also causes the computing system to reconstruct a final motion corrected magnetic resonance image based on the k-space data and the calculated motion trajectory in the predefined coordinate system. The final reconstruction can be performed after the motion estimation is completed, or can be performed during the process of performing the motion estimation. For example, the solution of the calculated motion trajectory can involve the calculation of trial images. Once the optimal solution is found or the optimization problem is completed, the final or best image can be used and assigned as the final motion corrected magnetic resonance image.

[0014] In another embodiment, the trajectory data comprises trajectory probability data, wherein the optimization problem comprises a cost function as a function of the trajectory probability. The optimization problem then comprises a cost function as a function of the trajectory probability. The function of the motion estimation neural network is to provide this probability working as a weighted function.

[0015] Three specific examples are described below:

[0016] 1) Segmented trajectory parameterization

[0017] Assuming a rigid motion model, the generalized motion compensated reconstruction can be formulated as follows:

[0018]

[0019] Where y is the acquired k-space data, x is the motion-free image, A is the sampling matrix, F is the discrete Fourier transform, S is the coil sensitivity matrix, and T is the rigid motion transformation matrix.

[0020] Assume that the patient's motion trajectory is represented by a set of time points Divide into multiple segments that meet the condition

[0021] t1 <t2<…<t n

[0022] A piecewise approximation of the patient's motion trajectory is achieved using a general functional form for each segment (eg, using an mth order polynomial).

[0023]

[0024] where α ij is the j-th order coefficient of the ith segment.

[0025] The motion trajectory can then be fully described by combining these coefficients along with the time division into a single vector.

[0026] K=(K1,…,K n ) T

[0027] Where K i =(t i ,α i0 ,…,α im ).

[0028] The motion estimation problem can then be reformulated as

[0029]

[0030] where the probability distribution p(K) is given by a neural network that uses patient and scan metadata as input variables. In this way, motion estimation is simplified by performing an optimization in a low-dimensional search space spanned by K.

[0031] The regularization parameter λ defines the effect of trajectory probabilities on the optimization problem: the larger λ is, the more the search will be constrained to high-probability regions of the search space. In practice, λ can be increased over time as more available training data improves the probability predictions.

[0032] Note that the polynomial form of the motion trajectory is used here only as an example, and various functional forms may be used in practice.

[0033] The impact of individual metadata fed to the neural network on the motion trajectory may drastically change the probability. To account for this variability, the input data is first processed by one or several fully connected layers, which encode the information content into a latent code. Optionally, the code is then further processed using a 1D convolutional layer, and the desired output data (e.g., K in this example) is generated using fully connected layers again. i coefficients). To avoid overfitting, the depth of the network and the size of the individual layers are chosen depending on the size of the available dataset.

[0034] Once a certain performance criterion is reached, the parameters of the trained network (i.e., its weights) can be shared with other sites to allow for a distributed learning setting. In this way, data from different patient groups across multiple sites can be leveraged to improve network performance.

[0035] 2) Full trajectory learning

[0036] Instead of using a set of predefined functional forms for (segmented) motion trajectories, we map

[0037] is learned by a neural network. In other words, the network is trained to provide (complete) motion trajectories and associated probabilities. The motion estimation problem is then given by:

[0038]

[0039] That is, the motion estimation is performed entirely in the latent space of the network spanned by β.

[0040] 3) Full trajectory parameterization

[0041] If one can assume some functional form that approximates the motion trajectory directly well enough, for example in the polynomial case:

[0042] θ(t)=∑ i α i t i

[0043] Leading to optimization problem

[0044]

[0045] That is, motion estimation is performed in the parameter space given by the above functional form.

[0046] In another embodiment, the motion estimation and the reconstruction of the final motion corrected magnetic resonance image are performed simultaneously as a generalized rigid motion corrected or non-rigid motion corrected reconstruction.

[0047] The advantage of the described medical system is that the computational burden is reduced. Conventionally, these optimization problems have been reserved for reconstruction with generalized rigid motion correction. However, since the probability function greatly reduces or guides the optimization to a specific solution, it now becomes feasible to also perform reconstruction with non-rigid motion correction.

[0048] In another embodiment, the calculated motion trajectory is formulated as a segmented and parameterized trajectory.

[0049] In another embodiment, the motion trajectory is formulated as a polynomial.

[0050] In another embodiment, the motion trajectory is formulated as a fully parameterized trajectory.

[0051] In another embodiment, the motion trajectory is formulated as a series of harmonic functions.

[0052] In another embodiment, the calculated motion trajectory is formulated as a time-dependent deformation vector field.

[0053] In another embodiment, the motion estimation neural network is a sequence of fully connected layers.

[0054] In another embodiment, the motion estimation neural network comprises a plurality of one-dimensional convolutional layers followed by at least one fully connected layer. A sequence of a plurality of fully connected layers or a plurality of one-dimensional convolutional layers followed by at least one fully connected layer works well because these neural networks are very flexible and can achieve accurate calculation of trajectory probabilities.

[0055] In another embodiment, the motion estimation neural network is further configured to output both the calculated motion trajectory and the trajectory probability in response to receiving the input vector. In this embodiment, the motion estimation neural network not only provides the trajectory probability for the weighting function, but also provides the calculated motion trajectory that can be used in the next iteration of the optimization problem. In some cases, this may result in a faster and even more accurate determination of the motion of the object.

[0056] In another embodiment, the motion estimation neural network is formed by a plurality of convolutional layers followed by additional convolutional layers to output the calculated motion trajectory. A plurality of convolutional layers are followed by at least one fully connected layer to output the trajectory probability.

[0057] In another embodiment, the motion estimation neural network is formed by a plurality of convolutional layers followed by additional convolutional layers to output the calculated motion trajectory. A plurality of convolutional layers are followed by at least one pooling layer and at least one fully connected layer to output the trajectory probability.

[0058] In another embodiment, the motion estimation neural network is formed by an input layer followed by a plurality of convolutional layers to output the calculated motion trajectory. The input layer is also connected to at least one fully connected layer to output the trajectory probability.

[0059] In another embodiment, the trajectory data includes a proposed motion trajectory in a predefined coordinate system. Modifying the optimization problem using the trajectory data includes updating the trial motion trajectory to a weighted sum of the modified motion trajectory and the trial motion trajectory.

[0060] Using the notation introduced previously, the optimization problem can be formulated as:

[0061]

[0062] where between iterations, the vector K is updated as follows:

[0063] K=αK+βN(K)

[0064] where α and β are weighting factors and N(K) is the proposed motion trajectory: the vector K input to the motion estimation neural network. In this equation, a weighted sum of the trial motion trajectory and the proposed motion trajectory is performed.

[0065] In another embodiment, if the preferred coordinate system parameterizes the rigid body motion of the object, the motion estimation neural network is a sequence of one-dimensional convolutional layers, and the motion estimation neural network outputs a proposed motion trajectory.

[0066] In another embodiment, if the preferred coordinate system parameterizes the rigid body motion of the object, the motion estimation neural network is a sequence of fully connected layers, and the motion estimation neural network outputs a proposed motion trajectory.

[0067] In another embodiment, if the preferred coordinate system parameterizes the rigid body motion of the object, the motion estimation neural network is a sequence of layers including both one-dimensional convolutional layers and fully connected layers, and the motion estimation neural network outputs a proposed motion trajectory.

[0068] In another embodiment, if the preferred coordinate system parameterizes the deformation vector field, the motion estimation neural network is a sequence of three-dimensional convolutional layers, and the motion estimation neural network outputs a proposed motion trajectory.

[0069] In another embodiment, if the preferred coordinate system parameterizes the deformation vector field, the motion estimation neural network is a sequence of two-dimensional convolutional layers for each slice of the three-dimensional volume, and the motion estimation neural network outputs a proposed motion trajectory.

[0070] The above neural network architecture can be trained by using training data including training trial motion data and training trajectory data. The training trajectory data includes trained suggested motion trajectories. The training motion trajectory data can be obtained by solving the above optimization problem without updating the trial motion trajectory between iterations. It is possible to start with the trial motion trajectory and set it equal to the training trial motion trajectory, and then use the trajectory from the completed numerical optimization as the training suggested motion trajectory. After many pairs including training trial motion data and training suggested motion trajectories have been collected, the motion estimation neural network can be trained, for example, using a deep learning protocol, with the training trial motion trajectory as input to the neural network and the training suggested motion trajectory as ground truth data.

[0071] In another embodiment, execution of the machine executable instructions further causes the computing system to receive acquisition metadata describing the measured k-space data and / or the object. Execution of the machine executable instructions further causes the computing system to use the acquisition metadata to select a motion estimation neural network from a database of motion estimation neural networks. For a particular acquisition type or acquisition geometry, a motion estimation neural network may be selected. This is likely to provide a more accurate motion estimate.

[0072] In another embodiment, the motion estimation neural network is further configured to receive acquisition metadata as input. The step of inputting the trial motion trajectory into the motion estimation neural network will also include inputting at least a portion of the acquisition metadata into the motion estimation neural network. This may be beneficial because it may enable more detailed customization of the trajectory data to specific acquisition conditions, the location of the subject, or even the age and gender of the subject.

[0073] In another embodiment, execution of the machine executable instructions also causes the computing system to receive training k-space data. Execution of the machine executable instructions also causes the computing system to receive training trajectory probability data and preferably training motion trajectory data. For example, there may be some embodiments in which only training trajectory probability data is output, and other embodiments in which there is training motion trajectory data that is also output by the neural network. In some cases, the training k-space data may also include acquisition metadata, depending on whether the neural network is trained to also receive this data. Execution of the machine executable instructions also causes the computing system to train the motion estimation neural network using the training k-space data and the training motion trajectory probability data and preferably the training motion trajectory data. In this case, the k-space data and possible acquisition metadata are known in advance, and the trajectory probability data and possible training motion trajectory data are known in advance. The training data can then be used to train the motion estimation neural network, for example using a deep learning algorithm.

[0074] In another embodiment, the motion estimation neural network is trained using a loss function that includes a function that is a derivative of the trial motion trajectories. Using a loss function that includes a function that is a derivative of the trial motion trajectories may be beneficial because it may result in a more stable output of the motion estimation neural network.

[0075] In another embodiment, the training trajectory probability data and / or preferably the training motion trajectory data are determined using any of the following: numerical solutions to optimization problems, navigators, self-navigation data from k-space data, optical data such as camera data, motion data from fiducial markers, and combinations thereof This embodiment may be beneficial because the measured motion of the object can be used to assist in training the motion estimation neural network.

[0076] In another embodiment, the medical system further comprises a magnetic resonance imaging system. The memory further stores pulse sequence commands configured to control the magnetic resonance imaging system to acquire measured k-space data. Execution of the machine executable instructions further causes the computing system to control the magnetic resonance imaging system using the pulse sequence commands to acquire measured k-space data.

[0077] In another aspect, the present invention provides a computer program comprising machine executable instructions and a motion estimation neural network. The motion estimation neural network is configured to output trajectory data in response to receiving a trial motion trajectory as input. The trial motion trajectory has a predefined coordinate system. Execution of the machine executable instructions causes a computing system to receive measured k-space data, the measured k-space data describing an object. The measured k-space data is divided into a sequence of discrete acquisitions. Execution of the machine executable instructions also causes the computing system to perform motion estimation of the object between discrete acquisitions of the sequence by iteratively solving an optimization problem to determine a calculated motion trajectory of the object in the predefined coordinate system. The optimization problem is formulated to minimize the difference between the transformation of the measured k-space data and the resampled k-space data of the motion-corrected trial magnetic resonance image according to the trial motion trajectory and the measured k-space data.

[0078] Performing motion estimation includes receiving trajectory data in response to inputting the trial motion trajectory into the motion estimation neural network. The trajectory data is then used to modify the optimization problem. Execution of the machine executable instructions also causes the computing system to reconstruct a final motion-corrected magnetic resonance image based on the k-space data and the calculated motion trajectory in the predefined coordinate system.

[0079] In another aspect, the present invention provides a method of medical imaging or a method of operating a medical system. The method includes receiving measured k-space data describing an object. The measured k-space data is divided into a sequence of discrete acquisitions. The method also includes performing motion estimation of the object between discrete acquisitions of the sequence by solving an optimization problem to determine a calculated motion trajectory of the object in a preferred coordinate system. The optimization problem is formulated to minimize the difference between the transformation of the measured k-space data and the resampled k-space data of a motion-corrected trial magnetic resonance image based on the trial motion trajectory and the measured k-space data.

[0080] Performing motion estimation includes receiving trajectory data in response to inputting a trial motion trajectory into a motion estimation neural network. The trial motion trajectory has a predefined coordinate system. The trajectory data is then used to modify the optimization problem. The method also includes reconstructing a final motion-corrected magnetic resonance image based on the k-space data and the calculated motion trajectory in the predefined coordinate system.

[0081] It should be understood that one or more of the aforementioned embodiments of the present invention may be combined as long as the combined embodiments are not mutually exclusive.

[0082] Those skilled in the art will appreciate that aspects of the present invention may be embodied as an apparatus, method, or computer program product. Thus, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, microcode, etc.), or an embodiment combining software and hardware aspects, which embodiments may be collectively referred to herein as a "circuit," "module," or "system." Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer-readable media having computer executable code embodied thereon.

[0083] Any combination of one or more computer-readable media can be utilized. Computer-readable media can be computer-readable signal media or computer-readable storage media. Computer-readable storage media as used herein encompass any tangible storage media that can store instructions that can be executed by a processor or computing system of a computing device. Computer-readable storage media can be referred to as computer-readable non-temporary storage media. Computer-readable storage media can also be referred to as tangible computer-readable media. In some embodiments, computer-readable storage media can also store data that can be accessed by a computing system of a computing device. Examples of computer-readable storage media include, but are not limited to, floppy disks, magnetic hard disk drives, solid-state hard disks, flash memory, USB thumb drives, random access memories (RAM), read-only memories (ROM), optical disks, magneto-optical disks, and register files of computing systems. Examples of optical disks include compact disks (CDs) and digital versatile disks (DVDs), such as CD-ROMs, CD-RWs, CD-Rs, DVD-ROMs, DVD-RWs, or DVD-R disks. The term computer-readable storage media also refers to various types of recording media that can be accessed by a computer device via a network or communication link. For example, data can be retrieved via a modem, via the Internet, or via a local area network. Computer executable code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0084] A computer readable signal medium may include a propagated data signal having computer executable code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including but not limited to electromagnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that may communicate, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0085] Computer memory or memory is an example of a computer-readable storage medium. Computer memory is any memory directly accessible to a computing system. Computer storage or storage is another example of a computer-readable storage medium. Computer storage is any non-volatile computer-readable storage medium. In some embodiments, computer storage may also be computer memory and vice versa.

[0086] As used herein, "computing system" encompasses an electronic component capable of executing a program or machine executable instructions or computer executable code. References to computing systems including examples of "computing system" should be interpreted as possibly including more than one computing system or processing core. A computing system may, for example, be a multi-core processor. A computing system may also refer to a collection of computing systems within a single computer system or distributed among multiple computer systems. The term computing system should also be interpreted as possibly referring to a collection or network of computing devices, each of which includes a processor or computing system. Machine executable code or instructions may be executed by multiple computing systems or processors, which may be within the same computing device, or may even be distributed across multiple computing devices.

[0087] Machine executable instructions or computer executable code may include instructions or programs that cause a processor or other computing system to perform an aspect of the present invention. Computer executable code for performing operations of various aspects of the present invention may be written in any combination of one or more programming languages ​​and compiled into machine executable instructions, including object-oriented programming languages ​​(such as Java, Smalltalk, C++, etc.) and conventional procedural programming languages ​​(such as "C" programming language or similar programming languages). In some cases, the computer executable code may be in the form of a high-level language or in a precompiled form and used in conjunction with an interpreter that generates machine executable instructions on the fly. In other cases, the machine executable instructions or computer executable code may be in the form of programming for a programmable logic gate array.

[0088] The computer executable code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (e.g., over the Internet using an Internet service provider).

[0089] Aspects of the present invention are described with reference to the flowchart schematic diagram and / or block diagram of the method, device (system) and computer program product according to an embodiment of the present invention.It should be understood that each frame or a part of a frame of a flow chart, diagram and / or block diagram can be implemented by a computer program instruction in the form of a computer executable code when applicable.It should also be understood that when not mutually exclusive, the combination of frames in different flow charts, diagrams and / or block diagrams can be combined.These computer program instructions can be provided to the computing system of a general-purpose computer, a special-purpose computer or other programmable data processing device to produce a machine, so that the instruction executed by the computing system of a computer or other programmable data processing device creates a unit for realizing the function / action specified in one or more frames of a flow chart and / or block diagram.

[0090] These machine-executable instructions or computer program instructions may also be stored in a computer-readable medium, which may direct a computer, other programmable data processing apparatus, or other device to operate in a specific manner so that the instructions stored in the computer-readable medium produce an article of manufacture, which includes instructions for implementing the functions / actions specified in one or more boxes of the flowchart and / or block diagram.

[0091] Machine-executable instructions or computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device, so that a series of operational steps are performed on the computer, other programmable apparatus, or other device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable apparatus provide a process for implementing the functions / actions specified in one or more boxes of the flowchart and / or block diagram.

[0092] As used herein, a "user interface" is an interface that allows a user or operator to interact with a computer or computer system. A user interface may also be referred to as a human interface device. A user interface may provide information or data to an operator and / or receive information or data from an operator. A user interface may enable input from an operator to be received by a computer, and may provide output from a computer to a user. In other words, a user interface may allow an operator to control or manipulate a computer, and the interface may allow a computer to indicate the effects of the operator's control or manipulation. Displaying data or information on a display or graphical user interface is an example of providing information to an operator. Receiving data through a keyboard, mouse, trackball, touchpad, pointing stick, graphic tablet, joystick, game controller, webcam, headset, pedal, wired gloves, remote controller, and accelerometer are all examples of user interface components that are capable of receiving information or data from an operator.

[0093] As used herein, a "hardware interface" includes an interface that enables a computing system of a computer system to interact with and / or control an external computing device and / or apparatus. A hardware interface may allow a computing system to send control signals or instructions to an external computing device and / or apparatus. A hardware interface may also enable a computing system to exchange data with an external computing device and / or apparatus. Examples of hardware interfaces include, but are not limited to, a universal serial bus, an IEEE 1394 port, a parallel port, an IEEE 1284 port, a serial port, an RS-232 port, an IEEE-488 port, a Bluetooth connection, a wireless LAN connection, a TCP / IP connection, an Ethernet connection, a control voltage interface, a MIDI interface, an analog input interface, and a digital input interface.

[0094] As used herein, a "display" or "display device" encompasses an output device or user interface suitable for displaying images or data. A display may output visual, audio, and / or tactile data. Examples of displays include, but are not limited to, computer monitors, television screens, touch screens, tactile electronic displays, Braille screens, cathode ray tubes (CRTs), memory tubes, bi-stable displays, electronic paper, vectorscopes, flat panel displays, vacuum fluorescent displays (VFs), light emitting diode (LED) displays, electroluminescent displays (ELDs), plasma display panels (PDPs), liquid crystal displays (LCDs), organic light emitting diode displays (OLEDs), projectors, and head mounted displays.

[0095] Medical imaging data is defined herein as recorded measurements made by a tomographic medical imaging system describing an object. Medical imaging data can be reconstructed into a medical image. A medical image ID is defined herein as a reconstructed two-dimensional or three-dimensional visualization of anatomical data contained within the medical imaging data. The visualization can be performed using a computer.

[0096] K-space data is defined herein as recorded measurements of radio frequency signals emitted by atomic spins using an antenna of a magnetic resonance apparatus during a magnetic resonance imaging scan. Magnetic resonance data is an example of tomographic medical image data.

[0097] A Magnetic Resonance Imaging (MRI) image or MR image is defined herein as a reconstructed two-dimensional or three-dimensional visualization of anatomical data contained within the magnetic resonance imaging data. The visualization may be performed using a computer. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Preferred embodiments of the present invention will now be described by way of example only and with reference to the accompanying drawings, in which:

[0099] Figure 1 An example of a medical system is shown;

[0100] Figure 2 Shows instructions for use Figure 1 A flowchart of a method for a medical system;

[0101] Figure 3 An example of a medical system is shown;

[0102] Figure 4 Shows instructions for use Figure 3 A flowchart of a method for a medical system;

[0103] Figure 5 A flow chart illustrating a method of training a motion estimation neural network is shown;

[0104] Figure 6 An embodiment of a medical system is shown;

[0105] Figure 7 An implementation of a motion estimation neural network is shown;

[0106] Figure 8 Another embodiment of a motion estimation neural network is shown;

[0107] Fig. 9 Another implementation of a motion estimation neural network is shown; and

[0108] Fig.10 Another implementation of a motion estimation neural network is shown. DETAILED DESCRIPTION

[0109] Elements with the same number in these figures are equivalent elements or perform the same function. Elements that have been discussed previously will not necessarily be discussed in later figures if the function is equivalent.

[0110] Figure 1 An example of a medical system 100 is shown. The medical system 100 is shown to include a computer 102. Computer 102 is intended to represent one or more computers or computing systems at one or more locations. Computer 102 is shown to include a computing system 104. Computing system 104 may also represent one or more computing systems or computing cores at one or more locations. Computing system 104 is shown in communication with an optional hardware interface 106. The optional hardware interface 106 may enable computing system 104 to control and operate other components, such as a magnetic resonance imaging system. Computing system 104 is also shown in communication with an optional user interface 108, which may enable a user to operate and / or control medical system 100. Computing system 104 is also shown in communication with memory 110. Memory 110 is intended to represent various types of memory that computing system 104 may access. For example, memory 110 may represent a non-transitory storage medium.

[0111] The memory 110 is shown as containing machine executable instructions 120. The machine executable instructions 120 enable the computing system 104 to perform basic tasks, such as calculations, image processing, and control of other components (if present). The memory 110 is also shown as containing a motion estimation neural network 122. The memory 110 is also shown as containing measured k-space data 124. The measured k-space data 124 can describe the object and be divided into a sequence of discrete acquisitions or shots. The memory 110 is also shown as containing an optimization module 126 for solving the calculated motion trajectory 134.

[0112] The optimization module 126 varies the trial motion trajectory 128 and views the resulting motion corrected trial magnetic resonance image 132. The optimization module 126 uses the motion estimation neural network 122 and may have a cost function that includes a function that depends on the trajectory probability output by the motion estimation neural network 122 in response to receiving the trial motion trajectory 128. The memory 110 is also shown as containing the calculated motion trajectory 134 solved by the optimization module 126. The memory 110 is also shown as containing a final motion corrected magnetic resonance image 136 reconstructed using the measured k-space data 124 and the calculated motion trajectory 134.

[0113] Figure 2 Shows the instructions for operation Figure 1 Flowchart of a method of a medical system 100 of the present invention. First, in step 200, measured k-space data 124 is received. As previously described, the measured k-space data 124 describes an object and is divided into a sequence of discrete acquisitions. Next, in step 202, motion estimation of the object is performed by solving an optimization problem using an optimization module 126 to determine the motion between discrete acquisitions of the sequence to determine a calculated motion trajectory 134 of the object in a predefined coordinate system. The optimization problem is formulated to minimize the difference between the transformation of the measured k-space data 124 and the resampled k-space data of the motion-corrected trial magnetic resonance image based on the trial motion trajectory and the measured k-space data.

[0114] Performing motion estimation includes receiving trajectory data 130 in response to inputting the trial motion trajectory 128 into the motion estimation neural network 122. The optimization problem includes a cost function that is a function of the trajectory data (trajectory probability) or an intermediate step between interactions that update or modify the trial motion trajectory with the trajectory data (proposed motion trajectory). Finally, in step 204, a final motion-corrected magnetic resonance image 136 is reconstructed from the k-space data 124 and the calculated motion trajectory 134.

[0115] Figure 3 Another example of a medical system 300 is shown. Figure 3 The medical system 300 depicted in FIG. Figure 1 The medical system 100 in FIG. 1 , except that it further comprises a magnetic resonance imaging system 302 controlled by the computing system 104 .

[0116] The magnetic resonance imaging system 302 comprises a magnet 304. The magnet 304 is a superconducting cylindrical magnet having a hole 306 passing therethrough. It is also possible to use different types of magnets; for example, both a split cylindrical magnet and a so-called open magnet can also be used. A split cylindrical magnet is similar to a standard cylindrical magnet, except that the cryostat has been divided into two parts to allow access to the isoplane of the magnet, such a magnet can be used, for example, in conjunction with charged particle beam therapy. An open magnet has two magnet parts, one above the other, with a space between them large enough to receive an object: the arrangement of the two parts is similar to that of a Helmholtz coil. Open magnets are popular because the object is less restricted. Inside the cryostat of the cylindrical magnet, there is a collection of superconducting coils.

[0117] Within the bore 306 of the cylindrical magnet 304, there is an imaging zone 308 where the magnetic field is strong and uniform enough to perform magnetic resonance imaging. A field of view 309 is shown within the imaging zone 308. The acquired k-space data is typically identified with respect to the field of view 309. The region of interest may be the same as the field of view 309, or it may be a sub-volume of the field of view 309. An object 318 is shown supported by an object support 320 such that at least a portion of the object 318 is within the imaging zone 308 and the field of view 309.

[0118] There is also a set of magnetic field gradient coils 310 within the bore 306 of the magnet, which is used to acquire preliminary k-space data to spatially encode magnetic spins within the imaging zone 308 of the magnet 304. The magnetic field gradient coils 310 are connected to a magnetic field gradient coil power supply 312. The magnetic field gradient coils 310 are intended to be representative. Typically, the magnetic field gradient coils 310 include three separate sets of coils for spatial encoding in three orthogonal spatial directions. The magnetic field gradient power supply provides current to the magnetic field gradient coils. The current provided to the magnetic field gradient coils 310 is controlled as a function of time and can be ramped or pulsed.

[0119] Adjacent to the imaging zone 308 is a radio frequency coil 314 for manipulating the orientation of magnetic spins within the imaging zone 308 and for receiving radio transmissions from spins also within the imaging zone 308. The radio frequency antenna may contain multiple coil elements. The radio frequency antenna may also be referred to as a channel or antenna. The radio frequency coil 314 is connected to a radio frequency transceiver 316. The radio frequency coil 314 and the radio frequency transceiver 316 may be replaced by separate transmit and receive coils and separate transmitters and receivers. It should be understood that the radio frequency coil 314 and the radio frequency transceiver 316 are representative. The radio frequency coil 314 is also intended to represent a dedicated transmit antenna and a dedicated receive antenna. Similarly, the transceiver 316 may also represent a separate transmitter and receiver. The radio frequency coil 314 may also have multiple receive / transmit elements, and the radio frequency transceiver 316 may have multiple receive / transmit channels. The transceiver 316 and the gradient controller 312 are shown as being connected to the hardware interface 106 of the computer system 102.

[0120] The memory 110 is also shown as containing pulse sequence commands 330. Pulse sequence commands are commands or data that can be converted into commands that can control the magnetic resonance imaging system 302 to acquire measured k-space data 124. The memory 110 is also shown as containing acquisition metadata 332. This can be details acquired from the pulse sequence commands 330, as well as data entered by an operator describing the settings of the magnetic resonance imaging system 302 and / or details about the object 318. The acquisition metadata 332 may also contain information about the anatomical region of the object 318 being imaged. The memory 110 is also shown as optionally containing a database 334 of motion estimation neural networks. For example, there may be different motion estimation neural networks for different anatomical regions of the object. The acquisition metadata 332 or a portion of the acquisition metadata 332 can be used to query the database 334 to retrieve the motion estimation neural network 122.

[0121] Figure 4 Shows the instructions for operation Figure 3 Flowchart of a method of a medical system 300 of the present invention. The method begins at step 400, where the magnetic resonance imaging system 300 is controlled using a pulse sequence command 330 to acquire measured k-space data 124. Next, in step 402, acquisition metadata 332 describing the measured k-space data and / or the object is received. The acquisition metadata 332 can be automatically generated from data from the pulse sequence command 330 and / or can be generated from data input by an operator. The motion estimation neural network 122 can also be configured to receive the acquisition metadata as input. Alternatively or in addition, the acquisition metadata 332 or a portion of the acquisition metadata is used to query a database of the motion estimation neural network to obtain the motion estimation neural network 122. After step 402, the method continues as follows Figure 2 Steps 200, 202 and 204 are shown.

[0122] Figure 5 A flow chart illustrating a method of training a motion estimation neural network is shown. First, in step 500, a training trial motion trajectory is received. Next, in step 502, training trajectory data is received. The combination of the training trial motion trajectory and the training trajectory data represents data that can be used to train the motion estimation neural network. For example, the training trial motion trajectory is input into the motion estimation neural network, and the output is compared with the associated training trajectory data. In step 504, the motion estimation neural network is trained using the training trial motion trajectory as an input to the neural network, and the training trajectory probabilities are used as ground truth data. This can be done, for example, using a deep learning training algorithm. The training process can also be done as a vector or parallel process.

[0123] In an example, a motion estimation neural network 122 is used to predict a probability distribution of patient motion trajectories for a given scan type (trajectory probabilities 130). The network receives as input metadata that may affect the resulting distribution about the patient and about the MR sequence. The probability distribution predicted by the network is used to guide the motion compensated reconstruction algorithm by constraining the search space to high probability regions, thereby improving convergence characteristics and reducing computation time. Training of the network is achieved using ground truth motion trajectories, which are obtained using external sensors (e.g., in-bore cameras) or by (unguided) motion compensated reconstruction.

[0124] Image degradation due to subject motion during acquisition is a persistent problem in clinical applications of magnetic resonance imaging (MRI). The associated artifacts typically appear as ghosting or blurring in the image and often degrade image quality to the point where medical analysis is impossible.

[0125] Due to the clinical relevance of motion artifacts, many solutions have been proposed by the MR research community. In particular, motion compensated reconstruction methods have been shown to allow for a significant reduction in the level of motion artifacts in many cases.

[0126] Motion-compensated reconstruction methods attempt to estimate the exact motion parameters based on the scan time. However, even for the simple rigid motion model commonly adopted in neural scans, the resulting optimization problem is usually high-dimensional and non-convex. As a result, long computation times are usually required to obtain motion-compensated results, reaching several hours for severe motion even when the calculations are performed on a GPU. Furthermore, the algorithm may get "stuck" in a local minimum, i.e., obtain suboptimal results with residual motion artifacts.

[0127] Examples can overcome these limitations by reducing the solution space of the motion parameter estimation problem. Based on the assumption that the space of true patient motion trajectories has much lower dimensionality than the space of all possible motion trajectories, a learning-based approach is described to infer corresponding constraints from clinical motion-corrupted patient data.

[0128] Below Figure 6 A general overview of some examples is shown in . A neural network (motion estimation neural network 122) is used to predict a probability distribution (trajectory probability 130) of a patient's motion trajectory for a given scan type (without loss of generality, only a single MR sequence of fixed length is assumed in the following). The network can receive as input metadata that may affect this probability distribution, both about the patient - such as age, previous medical diagnosis, etc., and about the MR sequence - such as expected scan time and sound characteristics. Training of the network is achieved using ground truth motion trajectories, which are obtained using external sensors (e.g., in-bore cameras) or by (potentially time-consuming) motion-compensated reconstruction. In the latter case, successful convergence of the algorithm is confirmed to ensure the correctness of the estimated trajectory, for example by visual inspection.

[0129] During inference, the probability distribution predicted by the network is used to guide the motion compensated reconstruction algorithm by constraining the search space to high probability regions. Importantly, the entire system can be trained after deployment, resulting in increasingly faster and more robust reconstructions due to the ever-refined probability predictions as more training data becomes available.

[0130] Figure 6 An embodiment of a medical system is shown. A motion estimation neural network 122 is shown as receiving acquisition metadata 332 and trial motion trajectories 128 as input; in response, it outputs trajectory probabilities 130. The acquisition metadata 332 is shown as including patient metadata and / or scan metadata. The trajectory probabilities 130 are used together with the measured k-space data 124 to calculate a final motion-corrected magnetic resonance image 136. The system can additionally be trained by comparing the trajectory probabilities 130 to the training motion trajectory data 600. For example, it can be done during deployment of the medical system, or it can be done in advance and the neural network 122 can be transferred or used at a different site.

[0131] Additional examples may include one or more of the following features:

[0132] Importantly, additional input data can be used to enable the neural network to produce an even further refined subspace of predicted motion trajectories. In one embodiment, the network also receives corrupted k-space data as input, allowing a rough estimate of the true patient motion given the acquired data.

[0133] Given that the relevant metadata are similar (duration, sound characteristics, etc.), the learned probabilities can be transferred from one MR sequence to another.

[0134] Additional constraints on the mapping learned by the neural network are introduced during training to improve the convergence properties of the resulting motion estimation problem. As an example, for the second embodiment given above ("full trajectory learning"), the term and / or Added to the loss function to enhance the learned mapping The regularization parameter γ defines the resulting “smoothness” of the mapping. Adding such a constraint can help avoid local minima during motion estimation.

[0135] Figure 7 An example of an implementation of a motion estimation neural network 700 is shown. There is an input vector 702 that is fed into a series of fully connected layers 704. The final fully connected layer outputs trajectory data 130. The trajectory data can be trajectory probabilities and / or suggested motion trajectories. The input vector 702 can be a trial motion trajectory 128 or a combination of both the trial motion trajectory 128 and the position metadata 332. Figure 7 The neural network structure shown can be called a multilayer perceptron.

[0136] Figure 8 Another example of an implementation of a motion estimation neural network 800 is shown. An input vector 702 is input into a first convolutional layer 802. It is then input through a series of n convolutional layers 802. After this sequence, at least one additional convolutional layer 800 forms one branch, and at least one fully connected layer 704 forms a second branch. The convolutional layer 800 outputs a calculated or predicted motion trajectory 134 or a suggested motion trajectory. The fully connected layer 704 outputs a trajectory probability 130. If it is desired to form a neural network 800 that does not output a calculated motion trajectory 134, then the branch with the convolutional layer 800 and the output calculated motion trajectory 134 can be simply removed and deleted. The architecture would then be a series of convolutional layers 802 followed by a fully connected layer 704.

[0137] Fig. 9 Another example of an implementation of a motion estimation neural network 900 is shown. The input vector 702 is fed into two separate branches. One branch enters a series of convolutional layers 802, which then outputs a calculated motion trajectory 134 or a proposed motion trajectory. The input vector 702 is also separately fed into at least one or a series of fully connected layers 704, which then outputs a trajectory probability 130. Note that if the branch that outputs the calculated motion trajectory 134 is deleted, the neural network 900 reverts to Figure 7The content shown for network 700.

[0138] Fig.10 Another implementation of a motion estimation neural network 1000 is shown. The input vector 702 is first fed into a series of convolutional layers 802. The output of the convolutional layer can, for example, go to an output layer, which then outputs a calculated motion trajectory 134 or a suggested motion trajectory. The output of the series of convolutional layers 802 can then also be fed into another branch, which first enters a pooling or downsampling layer 102, enters a convolutional layer 802, is then fed into an additional pooling layer 102, is then fed into another convolutional layer 802 again, and finally enters a fully connected layer 704. This then outputs a trajectory probability 130.

[0139] 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.

[0140] By studying the drawings, the disclosure and the appended claims, those skilled in the art can understand and implement other changes to the disclosed embodiments when practicing the claimed invention. 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 can implement the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used advantageously. The computer program may be stored / distributed on a suitable medium, such as an optical storage medium or solid-state medium provided 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 telecommunications systems. Any reference numerals in the claims should not be interpreted as limiting the scope.

[0141] Reference numerals list

[0142] 100 Medical Systems

[0143] 102 Computer

[0144] 104 Computing System

[0145] 106 Hardware Interface

[0146] 108 User Interface

[0147] 110 Memory

[0148] 120 machine executable instructions

[0149] 122 Motion Estimation Neural Network

[0150] 124 Measured k-space data

[0151] 126 Optimization Module

[0152] 128 test motion trajectory

[0153] 130 trajectory probability

[0154] 132Motion-corrected test MRI images

[0155] 134 Calculated motion trajectory

[0156] 136 Final motion-corrected MRI

[0157] 200 Receiving measured k-space data describing an object

[0158] 202 performs motion estimation of the object between discrete acquisitions of the sequence by solving an optimization problem to determine a calculated motion trajectory of the object in a predefined coordinate system

[0159] 204 Reconstructing a final motion-corrected magnetic resonance image based on the measured k-space data and the calculated motion trajectory in the predefined coordinate system

[0160] 300 Medical System

[0161] 302 Magnetic Resonance Imaging System

[0162] 304 magnet

[0163] 306 magnet hole

[0164] 308 Imaging Area

[0165] 309 Field of View

[0166] 310 magnetic field gradient coil

[0167] 312 Magnetic Field Gradient Coil Power Supply

[0168] 314 RF Coil

[0169] 316 transceiver

[0170] 318 objects

[0171] 320 objects supported

[0172] 330 pulse sequence command

[0173] 332 Collect metadata

[0174] 334 Motion Estimation Neural Network Database

[0175] 400 Controlling the magnetic resonance imaging system with pulse sequence commands to acquire measured k-space data

[0176] 402 receiving acquisition metadata describing measured k-space data and / or an object, wherein the motion estimation neural network is further configured to receive the acquisition metadata as input

[0177] 404 Selecting a motion estimation neural network from a database of motion estimation neural networks using acquisition metadata

[0178] 500 Receive training test motion trajectory

[0179] 502 Receive training trajectory probabilities and preferably train calculated motion trajectories

[0180] 504 Train the motion estimation neural network using the training trial motion trajectories and the training trajectory probabilities and preferably the training calculated motion trajectories

[0181] 600 training motion trajectory data

[0182] Implementation of 700 Motion Estimation Neural Network

[0183] 702 Input vector

[0184] 704 fully connected layer

[0185] 800 Implementation of Motion Estimation Neural Network

[0186] 802 convolutional layers

[0187] Implementation of 900 Motion Estimation Neural Network

[0188] 902 pooling (downsampling) layer

[0189] Implementation of 1000 Motion Estimation Neural Network

Claims

1. A medical system (100, 300), comprising: a memory (110) storing machine executable instructions (120) and a motion estimation neural network (122, 700, 800, 900, 1000), wherein the motion estimation neural network is configured to output trajectory data (130) in response to receiving as input a trial motion trajectory (128), the trajectory data representing a probability distribution that the motion trajectory is correct, wherein the trial motion trajectory has a predefined coordinate system; A computing system (104), wherein execution of the machine executable instructions causes the computing system to: - receiving (200) measured k-space data (124) describing an object (318), wherein the measured k-space data is divided into a sequence of discrete acquisitions; - performing (202) motion estimation of the object between discrete acquisitions of the sequence to determine a calculated motion trajectory (134) of the object in the predefined coordinate system by solving an optimization problem, wherein the optimization problem is formulated to iteratively minimize a difference between the measured k-space data and a transformation of the resampled k-space data of a trial magnetic resonance image according to a trial motion trajectory and motion correction of the measured k-space data, wherein performing the motion estimation includes receiving the trajectory data representing a probability distribution that the trial motion trajectory is correct in response to inputting the trial motion trajectory into the motion estimation neural network, wherein performing the motion estimation also includes modifying the optimization problem using the trajectory data; and - reconstructing (204) a final motion-corrected magnetic resonance image (136) from the measured k-space data and the calculated motion trajectory in the predefined coordinate system.

2. The medical system according to claim 1, wherein: The calculated motion trajectory is formulated as any of: a segmented and parameterized trajectory, a polynomial, a fully parameterized trajectory, a deformation vector field, and a series of harmonic functions.

3. The medical system according to claim 1 or 2, wherein: The optimization problem includes a cost function as a function of trajectory probability.

4. The medical system according to claim 2 or 3, wherein: The motion estimation neural network is any of the following: - a sequence (600) of multiple fully connected layers (704); and - A plurality (800, 1000) of one-dimensional convolutional layers (802) followed by at least one fully connected layer (704).

5. The medical system according to claim 1 or 2, wherein: The motion estimation neural network is further configured to output both the calculated motion trajectory and the trajectory probability in response to receiving the trial motion trajectory.

6. The medical system according to claim 5, wherein: The trial motion trajectories span the latent space of the motion estimation neural network.

7. The medical system according to claim 5 or 6, wherein: The motion estimation neural network is any of the following: - a plurality (800) of convolutional layers (802) followed by additional convolutional layers (802) for outputting the calculated motion trajectory (134), wherein the plurality of convolutional layers are followed by at least one fully connected layer (704) for outputting the trajectory probability (130); and - a plurality (1000) of convolutional layers (802) followed by additional convolutional layers (802) for outputting the calculated motion trajectory (134), wherein the plurality of convolutional layers are followed by at least one pooling layer (1002) and at least one fully connected layer (704) for outputting the trajectory probability; and - an input layer (900) followed by a plurality of convolutional layers (802) for outputting the calculated motion trajectory (134), wherein the input layer is further connected to at least one fully connected layer (704) for outputting the trajectory probability.

8. The medical system according to any one of claims 1 to 6, wherein: The trajectory data includes a proposed motion trajectory in the predefined coordinate system, wherein modifying the optimization problem using the trajectory data includes updating the trial motion trajectory to be a weighted sum of the proposed motion trajectory and the trial motion trajectory.

9. The medical system according to claim 8, wherein: The motion estimation neural network is any of the following: - if the preferred coordinate system parameterizes the rigid body motion of the object, then a sequence of one-dimensional convolutional layers; - if the preferred coordinate system parameterizes the rigid body motion of the object, a sequence of fully connected layers (700); - if the preferred coordinate system parameterizes the rigid body motion of the object, a sequence of layers including both one-dimensional convolutional layers and fully connected layers; - if a coordinate system is preferred to parameterize the deformation vector field, then a sequence of 3D convolutional layers; as well as - If the preferred coordinate system parameterizes the deformation vector field, then a sequence of 2D convolutional layers for each slice of the 3D volume.

10. The medical system according to any one of the preceding claims, wherein: Execution of the machine-executable instructions further causes the computing system to receive (402) acquisition metadata (332) describing the measured k-space data and / or the object, wherein the motion estimation neural network is further configured to receive the acquisition metadata as input.

11. The medical system according to claim 10, wherein: Execution of the machine-executable instructions further causes the computing system to select (404) the motion estimation neural network from a database (334) of motion estimation neural networks using the acquisition metadata.

12. A medical system according to any one of the preceding claims, wherein: Execution of the machine executable instructions further causes the computing system to: - receiving (500) a training trial motion trajectory (600); - receiving (502) training trajectory data; - training (504) the motion estimation neural network using the training trial motion trajectories and the training trajectory data, wherein the motion estimation neural network is preferably trained with a loss function comprising a function that is a derivative of the trial motion trajectories.

13. A medical system according to any one of the preceding claims, wherein: The medical system also includes a magnetic resonance imaging system (302), wherein the memory further stores pulse sequence commands (330) configured to control the magnetic resonance imaging system to acquire the measured k-space data, wherein execution of the machine-executable instructions further causes the computing system to control (400) the magnetic resonance imaging system using the pulse sequence commands to acquire the measured k-space data.

14. A computer program comprising machine executable instructions (120) and a motion estimation neural network (122, 700, 800, 900, 1000), wherein: The motion estimation neural network is configured to output trajectory data (130) in response to receiving as input a trial motion trajectory (128), the trajectory data representing a probability distribution that the motion trajectory is correct, wherein the trial motion trajectory has a predefined coordinate system, wherein execution of the machine-executable instructions causes the computing system to: - receiving (200) measured k-space data (124) describing an object (318), wherein the measured k-space data is divided into a sequence of discrete acquisitions; - performing (202) motion estimation of the object between discrete acquisitions of the sequence to determine a calculated motion trajectory (134) of the object in the predefined coordinate system by solving an optimization problem, wherein the optimization problem is formulated to iteratively minimize a difference between the measured k-space data and a transformation of the resampled k-space data of a trial magnetic resonance image according to a trial motion trajectory and motion correction of the measured k-space data, wherein performing the motion estimation comprises receiving the trajectory data representing a probability distribution that the motion trajectory is correct in response to inputting the trial motion trajectory into the motion estimation neural network, wherein modifying the optimization problem further comprises modifying the optimization problem using the trajectory data; and - reconstructing (204) a final motion-corrected magnetic resonance image (136) from the measured k-space data and the calculated motion trajectory in the predefined coordinate system.

15. A method of medical imaging, wherein: The method comprises: - receiving (200) measured k-space data (124) describing an object (318), wherein the measured k-space data is divided into a sequence of discrete acquisitions; - performing (202) motion estimation of the object between discrete acquisitions of the sequence to determine a calculated motion trajectory (134) of the object in a predefined coordinate system by solving an optimization problem, wherein the optimization problem is formulated to minimize a difference between the measured k-space data and a transformation of the resampled k-space data of a trial magnetic resonance image according to a trial motion trajectory and motion correction of the measured k-space data, wherein performing the motion estimation comprises receiving trajectory data in response to inputting a trial motion trajectory (128) into a motion estimation neural network (122, 700, 800, 900, 1000), the trajectory data representing a probability distribution that the motion trajectory is correct, wherein the motion estimation neural network is configured to output the trajectory data in response to receiving the trial motion trajectory as input, wherein the trial motion trajectory has a predefined coordinate system, wherein performing the motion estimation further comprises modifying the optimization problem using the trajectory data; and - reconstructing (204) a final motion-corrected magnetic resonance image (136) from the measured k-space data and the calculated motion trajectory in the predefined coordinate system.

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