Neural network guided motion correction in magnetic resonance imaging.

Abstract

Described herein is a medical system 100, 300 having 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 as input a trial motion trajectory 128. Execution of the machine-executable instructions causes a computing system 104 to: receive 200 measured k-space data 124 representing an object 318; perform 202 motion estimation of the object between a series of discrete acquisitions by solving an optimization problem to determine a calculated motion trajectory of the object in a predefined coordinate system, where the optimization problem is modified using the trajectory data; and reconstruct 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 more particularly to motion-compensated magnetic resonance imaging. [Background technology]

[0002] As part of the procedure to produce images inside a patient's body, a large static magnetic field is used by magnetic resonance imaging (MRI) scanners to align the nuclear spins of atoms. This large static magnetic field is called the B0 field or main magnetic field. Various quantities or properties of a subject can be spatially measured and imaged using MRI. Summary of the Invention [Problem to be solved by the invention]

[0003] The difficulty in performing magnetic resonance imaging is that acquiring k-space data is time consuming and the subject often moves, causing blurring and motion artifacts in the resulting magnetic resonance images.

[0004] Lundervold et al., "An overview of deep learning in medical imaging focusing on MRI," Z Med Phys 29 (2019) 102-127, is a review paper that discusses how deep learning has been applied to the MRI processing chain, from acquisition to retrieval, image segmentation, and disease prediction. Loktyushin et al., "Blind Retrospective Motion Correction of MR Images," Magnetic Resonance in Medicine 70 (2013) 1608, discloses motion correction based on an iterative search for the motion trajectory that yields the clearest image due to the steepest gradient entropy. That is, the iterative optimization is performed using the image gradient entropy metric as a cost function. [Means for solving the problem]

[0005] The present invention provides a medical system, a computer program and a method in the independent claims. Embodiments are set out in the dependent claims.

[0006] As mentioned above, subject motion during the acquisition of k-space data during an MRI acquisition can lead to blurring and image artifacts. There are various ways to correct for subject motion. One technique is to determine subject motion by formulating the motion estimation problem as a numerical optimization problem. First, subject motion can be assumed, and a trial image can be constructed. This trial image can be resampled to k-space and compared to the originally measured k-space data. Conventional optimization techniques can be used to numerically search for subject motion to minimize the difference between the resampled k-space data and the measured k-space data. A drawback of this approach is that it can be very numerically intensive.

[0007] There is also a risk of ending up in a local minimum and failing to properly solve the optimization problem. Embodiments can provide a means of accelerating the numerical search and minimize the probability of settling on a local minimum by using a motion estimation neural network to modify the optimization problem. In one example, the optimization is modified by adding a term to the cost function of the optimization problem that is a function of the probability that the trial motion trajectory is correct. The effect of this is to guide the numerical algorithm to the most likely solution for the subject's motion, which can be executed more quickly. The motion estimation neural network is configured to provide trajectory probabilities in response to receiving the trial motion trajectories as input.

[0008] According to the present invention, motion estimation involves solving, by a computing system, an optimization problem that minimizes the difference between measured k-space data and inverse-transformed k-space data from a current motion-corrected trial magnetic resonance image. That is, the optimization problem relates to optimizing data consistency between the measured k-space data and the inverse-transformed k-space data of the current motion-corrected trial magnetic resonance image, and motion correction is performed on a current trial motion trajectory. Motion estimation is performed iteratively by updating the current trial motion trajectory under the constraint that the trial motion trajectory be updated so that a subsequent correct trial motion trajectory has a higher probability value. In each iteration, subsequent motion-corrected trial magnetic resonance images are corrected using the updated trial motion trajectory. The probability distribution of the correct motion trajectory depends on subject (patient under examination) metadata and / or metadata associated with the MR acquisition sequence (e.g., scan type). A probability distribution of the likelihood of the accuracy 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 subsequent iterations of the optimization problem. Thus, the motion estimation network guides the motion compensated reconstruction algorithm to solve the optimization problem, leading to increasingly probable solutions by reinforcing more likely correct motion trajectories.

[0009] In another example, the motion estimation neural network is configured to output a proposed motion trajectory in response to receiving a trial motion trajectory as input, which is then used to modify or adjust the trial motion trajectory either before or after iterations of solving the optimization problem.

[0010] In one aspect, the present invention provides a medical system having 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 a subject or a motion trajectory of a subject in one iteration of an optimization problem. The trial motion trajectory has a predefined coordinate system. The predefined coordinate system is likely to be defined with respect to the motion problem itself. For example, if one is dealing with rigid body motion of a subject's skull during magnetic resonance imaging, it could be coordinates related to the rotation and motion of the skull. In another example, it could be a vector field that defines the motion of the subject as non-rigid body motion. In the following, an optimization problem is described, and the predefined coordinate system could be the coordinate system of the optimization problem.

[0011] The medical system further includes a computing system. Execution of the machine-executable instructions causes the computing system to perform the steps of receiving measured k-space data representative of a subject. The measured k-space data is divided into a series of discrete acquisitions. Typically, when magnetic resonance imaging data is acquired, it is acquired in shots or groups of k-space data. The measured k-space data represents these measured acquisitions or shots of magnetic resonance imaging data. A possible cause of image degradation and artifacts during magnetic resonance imaging is motion of the subject between the discrete acquisitions.

[0012] Execution of the machine-executable instructions further causes the computing system to perform the step of performing object motion estimation between the series of discrete acquisitions 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 a difference between the measured k-space data and a transform of the resampled k-space data of the motion-corrected trial magnetic resonance image as a function of the trial motion trajectory and the measured k-space data. Performing 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 determine object motion is one of the techniques that have been used in the past. The difference is that the optimization problem is modified by probability data.

[0013] Typically, when solving an optimization problem, trajectories are iteratively refined by either naive sampling of the trajectory space or gradient descent of a data consistency term to minimize the difference between measured k-space data and resampled k-space data (data consistency). The drawback of this approach is that convergence can be very computationally intensive and slow. A motion estimation neural network can be used to guide the optimization problem so that the optimization problem follows or progresses to the most likely solution. For example, during a particular type of magnetic resonance imaging examination, there may be very typical movements of the subject. For example, respiratory movements or coughing may result in a particular type of movement in the subject. Instead of searching the entire solution space, a motion estimation neural network is used to guide or prioritize more likely solutions during the solution of the optimization problem. This can result in a significantly reduced computational load.

[0014] Execution of the machine-executable instructions further causes the computing system to reconstruct a final motion-corrected magnetic resonance image from the k-space data and the calculated motion trajectory in a predefined coordinate system. This final reconstruction may be performed after motion estimation is completed or may be performed during the course of performing motion estimation. For example, solving for the calculated motion trajectory may include computing trial images. Once an optimal solution is found or the optimization problem is terminated, the final or best image may be used and assigned as the final motion-corrected magnetic resonance image.

[0015] In another embodiment, the trajectory data includes trajectory probability data and the optimization problem includes a cost function that is a function of the trajectory probability. The optimization problem includes a cost function that is a function of the trajectory probability. The function of the motion estimation neural network is to provide this probability, which serves as a weighting function.

[0016] Here are three examples:

[0017] 1) Segmented orbit parameterization Assuming a rigid body motion model, the generalized motion compensated reconstruction can be formulated as follows: TIFF2025528062000002.tif828 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 body motion transformation matrix.

[0018] The patient's motion trajectory is <t2<···<t n A set of time points that satisfy TIFF2025528062000003.tif616 It is assumed that the signal is divided into multiple segments by

[0019] A piecewise approximation of the patient's motion trajectory is realized using a general function for each segment, for example using an mth order polynomial: TIFF2025528062000004.tif1850 where α ij is the j-th coefficient of the i-th segment.

[0020] The motion trajectory can then be completely described by combining these coefficients as well as the time segments into a single vector. K=(K1,...,K n ) T where K i =(t i ,α i0 ,...,α im )

[0021] The motion estimation problem can then be reformulated as follows: TIFF2025528062000005.tif1065 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 optimization in a low-dimensional search space spanned by K.

[0022] The regularization parameter λ governs the influence of trajectory probability on the optimization problem; the larger λ, the more constrained the search is to high-probability regions of the search space. In practice, λ can be increased over time as more available training data improves probability estimation.

[0023] It should be noted that the polynomial of the motion trajectory is just an example, and in practice, various functions can be used.

[0024] The effect of individual metadata fed into the neural network on the movement trajectory can potentially change the probability significantly. To account for this variability, the input data is first processed by one or several fully connected layers that encode the information content into a latent code. Optionally, this code is then further processed using one-dimensional convolutional layers to generate the required output data (in this embodiment, K i The coefficients) are again generated using fully connected layers. 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.

[0025] Once certain performance criteria are reached, the parameters of the trained network (i.e., its weights) can then be shared with other sites, enabling a distributed learning setup. In this way, data from diverse patient groups across multiple sites can be leveraged to improve network performance.

[0026] 2) Complete trajectory learning Instead of using a set of predefined functions for the (segmented) motion trajectories, the mapping TIFF2025528062000006.tif722 is learned by the neural network. In other words, the neural network is trained to provide both the (complete) motion trajectory and the associated probabilities. The motion estimation problem is then solved as TIFF2025528062000007.tif959 That is, motion estimation is performed entirely in the latent space of the network, which is spanned by β.

[0027] 3) Full orbital parameterization If we can assume that a function closely approximates the motion trajectory in a straightforward manner, for example, in the case of a polynomial, we obtain: TIFF2025528062000008.tif1127

[0028] Optimization problems, TIFF2025528062000009.tif958 The solution, i.e., the motion estimation, is performed in the parameter space given by the above function.

[0029] In another embodiment, motion estimation and reconstruction of the final motion-corrected magnetic resonance image are performed simultaneously as a generalized rigid motion corrected or non-rigid motion corrected reconstruction.

[0030] An advantage of the described medical system is the reduced computational load. Typically, these optimization problems are reserved for generalized rigid motion-compensated reconstruction. However, the probability function advantageously guides the optimization toward a specific solution, making non-rigid motion-compensated reconstruction feasible as well.

[0031] In another embodiment, the calculated motion trajectory is formulated as a segmented and parameterized trajectory.

[0032] In another embodiment, the motion trajectory is formulated as a polynomial.

[0033] In another embodiment, the motion trajectory is formulated as a fully parameterized trajectory.

[0034] In another embodiment, the motion trajectory is formulated as a series of harmonic functions.

[0035] In another embodiment, the calculated motion trajectory is formulated as a time-dependent deformation vector field.

[0036] In another embodiment, the motion estimation neural network is a sequence of fully connected layers.

[0037] In another embodiment, the motion estimation neural network has multiple one-dimensional convolutional layers followed by at least one fully connected layer. A sequence of multiple one-dimensional convolutional layers followed by multiple fully connected layers, or at least one fully connected layer, works well because these neural networks are very flexible and can allow for accurate calculation of trajectory probabilities.

[0038] In another embodiment, the motion estimation neural network is further configured to output both a calculated motion trajectory and a trajectory probability in response to receiving the input vector. In this embodiment, the motion estimation neural network not only provides a trajectory probability for the weighting function, but also a calculated motion trajectory that can be used in the next iteration of the optimization problem. In certain examples, this can provide an acceleration, and in some cases, a more accurate determination of the object's motion.

[0039] In another embodiment, the motion estimation neural network is formed from multiple convolutional layers followed by additional convolutional layers to output the calculated motion trajectories, followed by at least one fully connected layer to output the trajectory probabilities.

[0040] In another embodiment, the motion estimation neural network is formed from multiple convolutional layers followed by additional convolutional layers to output the calculated motion trajectories, followed by at least one pooling layer and at least one fully connected layer to output the trajectory probabilities.

[0041] In another embodiment, the motion estimation neural network is formed from an input layer followed by multiple convolutional layers to output calculated motion trajectories, which are further connected to at least one fully connected layer to output trajectory probabilities.

[0042] In another embodiment, the trajectory data includes a proposed motion trajectory in a predefined coordinate system, and correcting the optimization problem using the trajectory data includes updating the trial motion trajectory to be a weighted sum of the corrected motion trajectory and the trial motion trajectory.

[0043] Using the notation explained above, the optimization problem can be formulated as follows: TIFF2025528062000010.tif1149 Now, between iterations, the vector K is K = αK + βN(K) is updated by

[0044] where α and β are weighting coefficients and N(K) is the proposed motion trajectory, i.e., the vector K is input to the motion estimation neural network. In this formula, a weighted sum of the trial motion trajectory and the proposed motion trajectory is performed.

[0045] In another embodiment, the motion estimation neural network is a sequence of one-dimensional convolutional layers, where a preferred coordinate system parameterizes the rigid body motion of the object and the motion estimation neural network outputs a proposed motion trajectory.

[0046] In another embodiment, where a predefined coordinate system parameterizes the rigid body motion of the object and the motion estimation neural network outputs a proposed motion trajectory, the motion estimation neural network is a sequence of fully connected layers.

[0047] In another embodiment, where a predefined coordinate system parameterizes the rigid body motion of the object and the motion estimation neural network outputs a proposed motion trajectory, the motion estimation neural network is a sequence of layers including both 1D convolutional layers and fully connected layers.

[0048] In another embodiment, the motion estimation neural network is a sequence of 3D convolutional layers, where a preferred coordinate system parameterizes the deformation vector field and the motion estimation neural network outputs a proposed motion trajectory.

[0049] In another embodiment, where a preferred coordinate system parameterizes the deformation vector field and the motion estimation neural network outputs a proposed motion trajectory, the motion estimation neural network is a sequence of 2D convolutional layers for each slice of the 3D volume.

[0050] 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 has a proposed training motion trajectory. The training motion trajectory data can be obtained by solving the above optimization problem without updating the trial motion trajectory between iterations. Starting with the trial motion trajectory, it can be set equal to the training trial motion trajectory, and then the trajectory from the completed numerical optimization can be used as the proposed training motion trajectory. After many pairs including training trial motion data and proposed training motion trajectories are collected, the motion estimation neural network can be trained using a deep learning protocol, for example, using the training trial motion trajectories as input to the neural network and the proposed training motion trajectories as ground truth data.

[0051] In another embodiment, execution of the machine-executable instructions further causes the computing system to receive acquisition metadata describing measured k-space data and / or an 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, the motion estimation neural network can be selected, which is most likely to provide a more accurate motion estimation.

[0052] In another embodiment, the motion estimation neural network is further configured to receive acquisition metadata as input. Inputting the trial motion trajectory into the motion estimation neural network further comprises inputting at least a portion of the acquisition metadata into the motion estimation neural network. This may be beneficial because it allows for more detailed tuning of the trajectory data with respect to specific acquisition conditions, subject position, or subject age and gender.

[0053] In another embodiment, execution of the machine-executable instructions further causes the computing system to receive training k-space data. Execution of the machine-executable instructions further causes the computing system to receive training trajectory probability data and preferably training motion trajectory data. For example, there are embodiments in which only training trajectory probability data is output, and embodiments in which training motion trajectory data is also output by the neural network. In some cases, the training k-space data can further include acquisition metadata, depending on whether the neural network is trained to receive additional acquisition metadata. Execution of the machine-executable instructions further causes the computing system to train a motion estimation neural network using the training k-space data and training motion trajectory probability data, and preferably the training motion trajectory data. In this case, the k-space data and possibly acquisition metadata are known in advance, as are the trajectory probability data and possibly the training motion trajectory data. The training data can then be used to train the motion estimation neural network, for example, using a deep learning algorithm.

[0054] 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 trajectory. Using a loss function that includes a function as a derivative of the trial motion trajectory can be beneficial because it can make the output of the motion estimation neural network more stable.

[0055] In another embodiment, the training trajectory probability data and / or preferably the training motion trajectory data are determined using any one of a numerical solution of an optimization problem, a navigator, self-navigation data from k-space data, optical data such as camera data, motion data from fiducial markers, and combinations thereof. This embodiment can be beneficial because the measured motion of the object can be used to assist in training the motion estimation neural network.

[0056] In another embodiment, the medical system further comprises a magnetic resonance imaging system, wherein the memory further stores pulse sequence commands configured to control the magnetic resonance imaging system to acquire the measured k-space data, and execution of the machine-executable instructions further causes the computing system to perform the step of controlling the magnetic resonance imaging system with the pulse sequence commands to acquire the measured k-space data.

[0057] In another aspect, the present invention provides a computer program product having machine-executable instructions and a motion estimation neural network. The motion estimation neural network is configured to output trajectory data in response to receiving as input a trial motion trajectory. The trial motion trajectory has a predefined coordinate system. Execution of the machine-executable instructions causes a computing system to perform the steps of receiving measured k-space data representing an object. The measured k-space data is divided into a series of discrete acquisitions. Execution of the machine-executable instructions further causes the computing system to perform the steps of performing motion estimation of the object between the series of discrete acquisitions 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 a difference between the measured k-space data and a transform of the resampled k-space data and a motion-corrected trial magnetic resonance image as a function of the trial motion trajectory and the measured k-space data.

[0058] Performing motion estimation includes receiving trajectory data in response to inputting trial motion trajectories into a motion estimation neural network. The optimization problem is then modified using the trajectory data. Execution of the machine-executable instructions further causes the computing system to perform the step of reconstructing a final motion-corrected magnetic resonance image from the k-space data and the calculated motion trajectories in a predefined coordinate system.

[0059] 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 a subject. The measured k-space data is divided into a series of discrete acquisitions. The method further includes performing motion estimation of the subject between the series of discrete acquisitions by solving an optimization problem to determine a calculated motion trajectory of the subject in a suitable coordinate system. The optimization problem is formulated to minimize a difference between the measured k-space data and a transformation of resampled k-space data of a motion-corrected trial magnetic resonance image as a function of the trial motion trajectory and the measured k-space data.

[0060] 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 optimization problem is then modified using the trajectory data. The method further includes reconstructing a final motion-corrected magnetic resonance image from the k-space data and the calculated motion trajectory in the predefined coordinate system.

[0061] It should be understood that one or more of the foregoing embodiments of the present invention may be combined, provided the combined embodiments are not mutually exclusive. As will be appreciated by those skilled in the art, aspects of the present invention may be embodied as an apparatus, a method, or a computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware form, an entirely software form (including firmware, resident software, microcode, etc.), or a combination of software and hardware forms, all of which may be 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 medium(s) having computer-executable code embodied thereon.

[0062] Any combination of one or more computer-readable media may be utilized. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. As used herein, "computer-readable storage medium" encompasses any tangible storage medium capable of storing instructions executable by a processor or computing system of a computing device. The computer-readable storage medium may also be referred to as a computer-readable non-transitory storage medium. The computer-readable storage medium may also be referred to as a tangible computer-readable medium. In some embodiments, the computer-readable storage medium may also store data accessible by the 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 memory, read-only memory (ROM), optical disks, magneto-optical disks, and computing system register files. Examples of optical disks include compact discs (CDs) and digital versatile discs (DVDs), such as CD-ROM, CD-RW, CD-R, DVD-ROM, DVD-RW, or DVD-R discs. The term computer-readable storage medium also refers to various types of storage media that can be accessed by a computer device over a network or communication link. For example, data can be retrieved via a modem, over the Internet, or over a local area network. Computer-executable code embodied on a computer-readable medium can be transmitted using any suitable medium, including, but not limited to, wireless, wired, fiber optic cable, RF, etc., or any suitable combination of the foregoing.

[0063] A computer-readable signal medium may include, for example, a propagated data signal having computer-executable code embodied therein, 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, and such computer-readable medium is not a computer-readable storage medium, but is capable of communicating, propagating, or transporting a program for use by or in connection with an instruction execution system, apparatus, or device.

[0064] "Computer memory" or "memory" is one 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 be computer memory, or vice versa.

[0065] As used herein, a "computing system" encompasses electronic components capable of executing programs, machine-executable instructions, or computer-executable code. References to a computing system, including examples of a "computing system," should be interpreted as including two or more computing systems or processing cores, as the case may be. A computing system may be, for example, 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 referring to a collection or network of computing devices, possibly each having a processor or computing system. Machine-executable code or instructions can be executed by multiple computing systems or processors, which may be within the same computing device or distributed across multiple computing devices.

[0066] Machine-executable instructions or computer-executable code may comprise instructions or programs that cause a processor or other computing system to perform aspects of the present invention. Computer-executable code for performing operations for aspects of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages, such as the "C" programming language or similar programming languages, compiled into machine-executable instructions. In some examples, the computer-executable code may be in the form of a high-level language or pre-compiled, and may also be used in conjunction with an interpreter that generates machine-executable instructions on the fly. In other examples, the machine-executable instructions or computer-executable code may be in the form of a program for a programmable logic gate array.

[0067] The computer executable code may run entirely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter situation, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., via the Internet using an Internet Service Provider).

[0068] Aspects of the present invention will be described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block or portion of a block in the flowcharts, diagrams, and / or block diagrams, where applicable, can be implemented by computer program instructions in the form of computer-executable code. It will further be understood that combinations of blocks in different flowcharts, diagrams, and / or block diagrams can be combined, if not mutually exclusive. These computer program instructions can be provided to a general-purpose computer, special-purpose computer, or other programmable data processing device computing system to generate a machine such that the instructions, when executed via the computer or other programmable data processing device computing system, result in means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0069] These machine-executable instructions or computer program instructions can be stored on a computer-readable medium that can instruct a computer, other programmable data processing apparatus, or other device to function in a particular manner, and the instructions stored on the computer-readable medium can produce an article of manufacture including instructions that implement the function / acts specified in a block or blocks of the flowcharts and / or block diagrams.

[0070] The machine-executable instructions or computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to generate a computer-implemented process such that a series of operational steps executed on the computer, other programmable apparatus, or other device provide a process for implementing the functions / operations specified in the flowchart and / or block diagram block or blocks.

[0071] 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" is also referred to as a "human interface device," and a user interface can provide information or data to an operator and / or receive information or data from an operator. A user interface can allow a computer to receive input from an operator and provide output from the computer to a user. In other words, a user interface can allow an operator to control or manipulate a computer, and an interface can allow a computer to show the effects of the operator's control or manipulation. The display of data or information on a display or graphical user interface is an example of providing information to an operator. Receiving data via a keyboard, mouse, trackball, touchpad, pointing stick, graphics tablet, joystick, gamepad, webcam, headset, pedals, wired gloves, remote control, and accelerometer are all examples of user interface components that allow information or data to be received from an operator.

[0072] As used herein, a "hardware interface" includes an interface that allows a computing system of a computer system to interact with and / or control external computing devices and / or equipment. A hardware interface may allow a computing system to send control signals or instructions to external computing devices and / or equipment. A hardware interface may also allow a computing system to exchange data with external computing devices and / or equipment. 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 local area network connection, a TCP / IP connection, an Ethernet connection, a control voltage interface, a MIDI interface, an analog input interface, and a digital input interface.

[0073] As used herein, a "display" or "display device" encompasses an output device or user interface adapted to display images or data. A display can output visual, auditory, 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, vector displays, 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.

[0074] Medical imaging data is defined herein as recorded measurements obtained by a tomographic medical imaging system that represent an object. Medical imaging data can be reconstructed into a medical image. A medical image is defined herein as a reconstructed two-dimensional or three-dimensional visualization of anatomical data contained within the medical imaging data. This visualization can be performed, for example, using a computer.

[0075] K-space data is defined herein as the recorded measurements of radio frequency signals emitted by atomic spins using the antenna of a magnetic resonance machine during a magnetic resonance imaging scan. Magnetic resonance data is an example of tomographic medical imaging data.

[0076] 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 magnetic resonance imaging data. This visualization can be performed, for example, by a computer. [Brief explanation of the drawings]

[0077] [Figure 1] FIG. 1 is a diagram illustrating an example of a medical system. [Figure 2] 2 is a flow chart illustrating a method of using the medical system of FIG. 1; [Figure 3] FIG. 1 is a diagram illustrating an example of a medical system. [Figure 4] 4 is a flow chart illustrating a method of using the medical system of FIG. 3. [Figure 5] 1 is a flowchart illustrating a method for training a motion estimation neural network. [Figure 6] FIG. 1 is a diagram showing an example of a medical system implementation. [Figure 7] FIG. 1 shows an example implementation of a motion estimation neural network. [Figure 8] FIG. 10 illustrates another implementation of a motion estimation neural network. [Figure 9] FIG. 10 illustrates another implementation of a motion estimation neural network. [Figure 10] FIG. 10 illustrates another implementation of a motion estimation neural network. DETAILED DESCRIPTION OF THE INVENTION

[0078] Preferred embodiments of the present invention will now be described, by way of example only, with reference to the drawings in which:

[0079] Like numbered components in these figures are either equivalent components or perform the same function. An aforementioned component is not necessarily described in a subsequent figure if the functionality is equivalent.

[0080] FIG. 1 illustrates an example medical system 100. The medical system 100 is shown as having a computer 102. The computer 102 is intended to represent one or more computers or computing systems in one or more locations. The computer 102 is shown as having a computing system 104. The computing system 104 may represent one or more computing systems or computing cores in one or more locations. The computing system 104 is shown in communication with an optional hardware interface 106. The optional hardware interface 106 may enable the computing system 104 to control and operate other components, such as a magnetic resonance imaging system. The computing system 104 is further shown in communication with an optional user interface 108, which may enable a user to operate and / or control the medical system 100. The computing system 104 is further shown in communication with a memory 110. The memory 110 is intended to represent various types of memory accessible by the computing system 104. For example, memory 110 may represent a non-transitory storage medium.

[0081] The memory 110 is shown as including 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 further shown as including a motion estimation neural network 122. The memory 110 is further shown as including measured k-space data 124. The measured k-space data 124 may describe an object and is divided into a sequence of discrete acquisitions or shots. The memory 110 is further shown as including an optimization module 126 that is used to solve for the calculated motion trajectory 134.

[0082] The optimization module 126 modifies 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 further shown as containing a calculated motion trajectory 134 solved by the optimization module 126. The memory 110 is further 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.

[0083] 2 shows a flowchart illustrating a method of operation of the medical system 100 of FIG. 1. First, in step 200, measured k-space data 124 is received. As previously described, the measured k-space data 124 represents an object and is divided into a series of discrete acquisitions. Next, in step 202, object motion estimation is performed by solving an optimization problem using an optimization module 126 to determine the motion between the series of discrete acquisitions 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 measured k-space data 124 and a transform of the resampled k-space data of a motion-corrected trial magnetic resonance image as a function of the trial motion trajectory and the measured k-space data.

[0084] Performing motion estimation includes receiving trajectory data 130 in response to inputting trial motion trajectories 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 during the interaction that updates or modifies 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.

[0085] Figure 3 shows another example of a medical system 300. The medical system 300 shown in Figure 3 is similar to the medical system 100 of Figure 1, except that it further includes a magnetic resonance imaging system 302 controlled by the computing system 104.

[0086] The magnetic resonance imaging system 302 includes a magnet 304. The magnet 304 is a cylindrical superconducting magnet with a bore 306 extending therethrough. Different types of magnets can be used. For example, both segmented cylindrical magnets and so-called open magnets can be used. A segmented cylindrical magnet is similar to a standard cylindrical magnet except that the cryostat is divided into two sections to allow access to the magnet's isosurface. Such magnets can be used, for example, in conjunction with charged particle beam therapy. An open magnet has two magnet sections, one above the other, with a space between them large enough to accommodate a subject. The arrangement of the two magnet sections resembles a Helmholtz coil. Open magnets are popular because the subject is less enclosed. Inside the cryostat of the cylindrical magnet is a collection of superconducting coils.

[0087] Within the bore 306 of the cylindrical magnet 304 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. K-space data is typically acquired for the field of view 309. A region of interest may be identical to the field of view 309 or may be a subvolume of the field of view 309. A subject 318 is shown supported by a subject support 320 such that at least a portion of the subject 318 is within the imaging zone 308 and the field of view 309.

[0088] Also within the magnet bore 306 is a set of magnetic field gradient coils 310 used for preliminary k-space data acquisition for spatially encoding 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 exemplary. Typically, the magnetic field gradient coils 310 have three separate coil sets for spatial encoding in three orthogonal spatial directions. The magnetic field gradient power supply supplies current to the magnetic field gradient coils 310. The current supplied to the magnetic field gradient coils 310 is controlled as a function of time and can be ramped or pulsed.

[0089] Adjacent to the imaging zone 308 is a radio frequency coil 314 that manipulates the orientation of magnetic spins within the imaging zone 308 and also receives radio transmissions from the spins within the imaging zone 308. A radio frequency antenna can have multiple coil elements. A radio frequency antenna can also be referred to as a channel or an 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 can be replaced with separate transmit and receive coils and separate transmitters and receivers. It is understood that the radio frequency coil 314 and the radio frequency transceiver 316 are exemplary. The radio frequency coil 314 is also intended to represent a dedicated transmit antenna and a dedicated receive antenna. Similarly, the transceiver 316 can also represent a separate transmitter and receiver. Additionally, the radio frequency coil 314 can have multiple receive / transmit elements, and the radio frequency transceiver 316 can 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 .

[0090] The memory 110 is further shown as having pulse sequence commands 330. The pulse sequence commands are commands or data that can be converted into commands that can control the magnetic resonance imaging system 302 to acquire the measured k-space data 124. The memory 110 is further shown as including acquisition metadata 332. This can be details obtained from the pulse sequence commands 330 as well as operator-entered data that describes details about the setup of the magnetic resonance imaging system 302 and / or the subject 318. The acquisition metadata 332 can also include information about the anatomical region of the subject 318 being imaged. The memory 110 is further shown as optionally including a database of motion estimation neural networks 334. For example, there can be different motion estimation neural networks for different anatomical regions of the subject. The acquisition metadata 332 or a portion of the acquisition data 332 can be used to query the database 334 to retrieve the motion estimation neural network 122.

[0091] FIG. 4 shows a flowchart illustrating a method for operating the medical system 300 of FIG. 3. The method begins in step 400, where the magnetic resonance imaging system 300 is controlled by 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 subject is received. The acquisition metadata 332 can be generated automatically from data from the pulse sequence command 330 and / or can be generated from data entered by an operator. The motion estimation neural network 122 can be further configured to receive the acquisition metadata as input. Alternatively, or in addition, the acquisition metadata 332, or a portion of the acquisition metadata, can be used to query a database of motion estimation neural networks to obtain the motion estimation neural network 122. After step 402, the method proceeds to steps 200, 202, and 204, as shown in FIG. 2.

[0092] FIG. 5 is a flowchart illustrating a method for training a motion estimation neural network. First, in step 500, training trial motion trajectories are received. Next, in step 502, training trajectory data is received. The combination of the training trial motion trajectories and the training trajectory data represents data that can be used to train the motion estimation neural network. For example, the training trial motion trajectories are input to 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 trajectories as input to the neural network, and the training trajectory probabilities are used as ground truth data. This can be performed, for example, using a deep learning training algorithm. The training process can also be performed as a vector or parallel process.

[0093] In the example, a motion estimation neural network 122 is used to predict a probability distribution of patient motion trajectories (trajectory probabilities 130) for a given scan type. The network receives as input metadata about both the patient and the MR sequence that may influence the resulting distribution. The network-predicted probability distribution is used to guide the motion-compensated reconstruction algorithm by constraining the search space to high-probability regions, which leads to improved convergence properties and reduced computation time. Training of the network is achieved using ground-truth motion trajectories obtained using an external sensor, e.g., an end-bore camera, or by (unguided) motion-compensated reconstruction.

[0094] 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 ghosts or blurs in the images, often degrading image quality to the point where medical analysis is impossible.

[0095] Due to the clinical importance of motion artifacts, many solutions have been proposed by the MR research community. In particular, motion-compensated reconstruction methods have been shown to often allow for a substantial reduction in motion artifact levels.

[0096] Motion-compensated reconstruction methods attempt to estimate accurate motion parameters as a function of scan time. However, even for simple rigid-body motion models, such as those commonly used for neuroscanning, the resulting optimization problem is typically high-dimensional and nonconvex. As a result, motion-compensated results often require long computation times, even when performed on a GPU, which can reach several hours in the presence of severe motion. In addition, the algorithms can become "stuck" in local minima, resulting in suboptimal results with residual motion artifacts.

[0097] In our example, we can overcome these limitations by reducing the solution space of the motion parameter estimation problem. Based on the assumption that the space of actual patient motion trajectories is much lower dimensional than the space of all possible motion trajectories, we describe a learning-based approach to infer corresponding constraints from patient data corrupted by clinical motion.

[0098] A general overview of some examples is shown in Figure 6 below. A neural network (motion estimation neural network 122) is used to predict the probability distribution (trajectory probability 130) of a patient's motion trajectories for a specific scan type (without loss of generality, we assume only one fixed-length MR sequence in the following). The network can receive input metadata that may affect this probability distribution (both information about the patient, such as age and previous diagnoses, and information about the MR sequence, such as expected scan time and acoustic characteristics). Training of the network is achieved using ground-truth motion trajectories obtained using an external sensor, e.g., an end-of-bore camera, or by (potentially time-consuming) motion-compensated reconstruction. In the latter case, successful convergence of the algorithm is confirmed, e.g., by visual inspection, to ensure the accuracy of the estimated trajectories.

[0099] During inference, the network-predicted probability distribution 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, giving faster and more robust reconstructions due to continuously refined probability estimates as more training data becomes available.

[0100] 6 illustrates an example implementation of a medical system. A motion estimation neural network 122 is shown receiving as input acquisition metadata 332 and trial motion trajectories 128 and, in response, outputting trajectory probabilities 130. The acquisition metadata 332 is shown to include patient metadata and / or scan metadata. The trajectory probabilities 130 are used together with measured k-space data 124 to calculate a final motion-corrected magnetic resonance image 136. The system can be additionally trained by comparing the trajectory probabilities 130 with training motion trajectory data 600. For example, training can be performed during deployment of the medical system or can be performed in advance, and the neural network 122 can be transferred or used at a different site.

[0101] Additional examples may include one or more of the following features:

[0102] Importantly, additional input data can be used to enable the neural network to generate a more refined subspace of predicted motion trajectories. In one embodiment, the network also receives corrupted k-space data as input, allowing for a rough estimation of realistic patient motion given the acquired data.

[0103] The learned probabilities can be transferred from one MR sequence to another, assuming the relevant metadata is similar (duration, sound characteristics, etc.).

[0104] To improve the convergence properties of the resulting motion estimation problem, additional constraints on the mapping learned by the neural network are introduced during training. As an example, in the second embodiment given above ("Full Trajectory Learning"), the equation: TIFF2025528062000011.tif937 is added to the loss function during network training to obtain the learned mapping, TIFF2025528062000012.tif621 The regularization parameter γ defines the resulting "smoothness" of the mapping. Adding such a constraint can help avoid local minima during motion estimation.

[0105] Figure 7 shows an example implementation of a motion estimation neural network 700. 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 either trajectory probabilities and / or proposed motion trajectories. The input vector 702 can be a trial motion trajectory 128, or a combination of both the trial motion trajectory 128 and position metadata 332. The neural network structure shown in Figure 7 is sometimes called a multi-layer perceptron.

[0106] FIG. 8 shows another implementation of a motion estimation neural network 800. An input vector 702 is input to a first convolutional layer 802. It is then passed 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 proposed motion trajectory. The fully-connected layer 704 outputs a trajectory probability 130. If it is desired to create a neural network 800 that does not output a calculated motion trajectory 134, this branch with the convolutional layer 800 and the output calculated motion trajectory 134 can simply be removed and deleted. In that case, the architecture becomes a series of convolutional layers 802 followed by a fully-connected layer 704.

[0107] 9 shows another implementation of a motion estimation neural network 900. The input vector 702 is fed into two separate branches. One branch enters a series of convolutional layers 802, which 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 output trajectory probabilities 130. Note that if the branch outputting the calculated motion trajectory 134 is removed, the neural network 900 reverts to that shown in FIG. 7 for network 700.

[0108] 10 shows another implementation of a motion estimation neural network 1000. An input vector 702 is first fed to a series of convolutional layers 802. The output of the series of convolutional layers can enter an output layer that outputs, for example, a calculated motion trajectory 134 or a proposed motion trajectory. The output of the series of convolutional layers 802 can also be fed to another branch that first enters a pooling or downsampling layer 1002, enters a convolutional layer 802, then enters an additional pooling layer 102, then further enters another convolutional layer 802, and finally enters a fully connected layer 704. The fully connected layer 704 outputs trajectory probabilities 130.

[0109] 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.

[0110] 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 means are recited in mutually different dependent claims does not indicate that a combination of these means cannot be used to advantage. A computer program can 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 can also be distributed in other forms, such as via the Internet or other wired or wireless telecommunications systems. Any reference signs in the claims should not be construed as limiting the scope of the claims. [Explanation of symbols]

[0111] 100 Medical Systems 102 Computer 104 Computing Systems 106 Hardware Interface 108 User Interface 110 memory 120 machine executable instructions 122 Motion Estimation Neural Network 124 measured k-space data 126 Optimization Module 128 Trial motion trajectory 130 Orbital Probability 132 Motion-corrected trial magnetic resonance images 134 Calculated motion trajectories 136 Final Motion-Corrected Magnetic Resonance Image 200 Receive k-space data representing the subject 202 Performing object motion estimation during a series of discrete acquisitions by solving an optimization problem to determine the object's calculated motion trajectory in a predefined coordinate system 204 Reconstructing the final motion-corrected magnetic resonance image from the measured k-space data and the calculated motion trajectory in a predefined coordinate system. 300 Medical Systems 302 Magnetic Resonance Imaging System 304 Magnet 306 Magnet Bore 308 Imaging Zone 309 viewing angle 310 Magnetic Gradient Coil 312 Magnetic field gradient coil power supply 314 High Frequency Coil 316 Transceiver 318 subjects 320 Subject Support 330 Pulse Sequence Commands 332 Acquisition Metadata 334 Motion Estimation Neural Network Database 400 Pulse sequence commands control the magnetic resonance imaging system to acquire measured k-space data. 402 receives measured k-space data and / or acquisition metadata representative of the object; the motion estimation neural network is further configured to receive the acquisition metadata as input. 404 Using the acquired metadata to select a motion estimation neural network from a database of motion estimation neural networks Receive 500 training trial movement trajectories 502 receives training trajectory probabilities and preferably trains the calculated motion trajectories; 504 Train a motion estimation neural network using the training trial motion trajectories and training trajectory probabilities and preferably the calculated motion trajectories for training. 600 training movement trajectory data 700 Example of motion estimation neural network implementation 702 input vectors 704 fully connected layers 800 Example of motion estimation neural network implementation 802 convolutional layers 900 Example of motion estimation neural network implementation 902 Pooling (downsampling) layer 1000 Example of motion estimation neural network implementation

Claims

1. 1. A medical system comprising: a memory storing machine-executable instructions and a motion estimation neural network, the motion estimation neural network being configured to output trajectory data representing a probability distribution of correct motion trajectories in response to receiving a trial motion trajectory as an input, the trial motion trajectory having a predefined coordinate system; 1. A computing system, wherein execution of the machine-executable instructions causes the computing processor to: receiving measured k-space data representative of a subject, the measured k-space data being divided into a series of discrete acquisitions; performing motion estimation of the object between the series of discrete acquisitions by solving an optimization problem to determine a calculated motion trajectory of the object in a predefined coordinate system, the optimization problem being formulated to iteratively minimize a difference between the measured k-space data and a transform of resampled k-space data of the motion-corrected trial magnetic resonance image as a function of the trial motion trajectory and the measured k-space data, performing the motion estimation including receiving trajectory data representing a probability distribution of correct trial motion trajectories in response to inputting the trial motion trajectory into the motion estimation neural network, and performing the motion estimation further including correcting the optimization problem using the trajectory data; reconstructing a final motion-corrected magnetic resonance image from the measured k-space data and the calculated motion trajectory in the predefined coordinate system; a computing system for executing the A medical system having:

2. 2. The medical system of claim 1, wherein the calculated motion trajectory is formulated as one of a segmented parameterized trajectory, a polynomial, a fully parameterized trajectory, a deformation vector field, and a set of harmonic functions.

3. The medical system of claim 1 or 2, wherein the optimization problem includes a cost function that is a function of the trajectory probabilities.

4. the motion estimation neural network comprises a sequence of a plurality of fully connected layers, a plurality of one-dimensional convolutional layers followed by at least one fully connected layer; The medical system according to claim 2 or 3.

5. The medical system of 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 of claim 5 , wherein the trial motion trajectories span a latent space of the motion estimation neural network.

7. a motion estimation neural network having a plurality of convolutional layers followed by an additional convolutional layer, the additional convolutional layer outputting the calculated motion trajectories, the plurality of convolutional layers followed by at least one fully connected layer, the fully connected layer outputting the trajectory probabilities; the motion estimation neural network has a plurality of convolutional layers followed by an additional convolutional layer, the additional convolutional layer outputs a calculated motion trajectory, the plurality of convolutional layers are followed by at least one pooling layer and at least one fully connected layer, the fully connected layer outputs the trajectory probability; and the motion estimation neural network has an input layer followed by a plurality of convolutional layers, the plurality of convolutional layers outputting the calculated motion trajectories, the input layer further connected to at least one fully connected layer, the fully connected layer outputting the trajectory probabilities; 7. The medical system according to claim 5, wherein the motion estimation neural network comprises any one of the following:

8. 7. The medical system of claim 1, wherein the trajectory data includes a proposed motion trajectory in the predefined coordinate system, and wherein correcting 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 motion estimation neural network a sequence of 1D convolutional layers where the predefined coordinate system parameterizes rigid body motion of the object; a sequence of fully connected layers where the predefined coordinate system parameterizes the rigid body motion of the object, or a layer sequence including both one-dimensional convolutional layers and fully connected layers where the predefined coordinate system parameterizes the rigid body motion of the object; a sequence of 3D convolutional layers where the predefined coordinate system parameterizes a deformation vector field; or a sequence of 2D convolution layers for each slice of a 3D volume where the predefined coordinate system parameterizes a deformation vector field; The medical system according to claim 8 , wherein the medical system is any one of the above.

10. Execution of the machine-executable instructions further causes the computing system to: further receiving acquisition metadata representative of 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; The medical system according to any one of claims 1 to 9,

11. Execution of the machine-executable instructions further causes the computing system to: selecting the motion estimation neural network from the database of motion estimation neural networks using the acquired metadata; The medical system according to claim 10 , wherein the medical system executes the following steps.

12. Execution of the machine-executable instructions further causes the computing system to: receiving a training trial movement trajectory; receiving training trajectory data; training the motion estimation neural network using the training trial motion trajectories and the training trajectory data, wherein the motion estimation neural network is trained with a loss function that includes a function that is a derivative of the trial motion trajectory; The medical system according to any one of claims 1 to 11, wherein the medical system executes the above.

13. The medical system further comprises a magnetic resonance imaging system, the memory further stores pulse sequence commands for controlling the magnetic resonance imaging system to acquire the measured k-space data, and execution of the machine-executable instructions further causes the computing system to: controlling the magnetic resonance imaging system using the pulse sequence commands to acquire the measured k-space data; The medical system according to any one of claims 1 to 12, wherein the medical system executes the above.

14. machine-executable instructions; a motion estimation neural network; wherein the motion estimation neural network is configured to output trajectory data representing a probability distribution of correct motion trajectories in response to receiving a trial motion trajectory as an input, the trial motion trajectory having a predefined coordinate system; Execution of the machine-executable instructions causes the computing system to: receiving measured k-space data representative of a subject, the measured k-space data being divided into a series of discrete acquisitions; performing motion estimation of the object between a series of discrete acquisitions by solving an optimization problem to determine a calculated motion trajectory of the object in the predefined coordinate system, the optimization problem being formulated to iteratively minimize a difference between a transformation of resampled k-space data of a motion-corrected trial magnetic resonance image and the measured k-space data as a function of the trial motion trajectory and the measured k-space data, performing the motion estimation including receiving trajectory data representing a probability distribution of correct motion trajectories in response to inputting the trial motion trajectory into the motion estimation neural network, and correcting the optimization problem further including correcting the optimization problem using the trajectory data; reconstructing a final motion-corrected magnetic resonance image from the measured k-space data and the calculated motion trajectory in the predefined coordinate system; A computer program that executes

15. 1. A medical imaging method comprising: receiving measured k-space data representative of a subject, the measured k-space data being divided into a series of discrete acquisitions; performing motion estimation of the object between the series of discrete acquisitions by solving an optimization problem to determine a calculated motion trajectory of the object in a predefined coordinate system, the optimization problem being formulated to minimize a difference between the measured k-space data and a transform of resampled k-space data of a motion-corrected trial magnetic resonance image as a function of the trial motion trajectory and the measured k-space data, performing the motion estimation including receiving trajectory data representing a probability distribution of correct motion trajectories in response to inputting the trial motion trajectory into the motion estimation neural network, the motion estimation neural network being configured to output the trajectory data in response to receiving the trial motion trajectory as input, the trial motion trajectory having a predefined coordinate system, and performing the motion estimation including correcting an optimization problem using the trajectory data; reconstructing a final motion-corrected magnetic resonance image from the measured k-space data and the calculated motion trajectory in the predefined coordinate system; A medical imaging method comprising:

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