Systems and methods for MRI data processing

Abstract

Systems, methods, and apparatuses associated with processing complex-valued MRI data using machine learning (ML) models are described herein. The ML models can be learned based on synthetically generated MRI training data and by applying one or more meta-learning techniques. The MRI training data can be generated by adding phase information to real-valued MRI data and / or by converting single-coil MRI data to multi-coil MRI data based on coil sensitivity maps. The meta-learning process can include using a portion of the training data to conduct a first round of learning to determine updated model parameters and using a remaining portion of the training data to test the updated model parameters. A loss associated with the testing can then be determined and used to refine the model parameters. The ML models learned using these techniques can be employed for various tasks, including, for example, MRI image reconstruction and / or denoising.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of medical images. BACKGROUND

[0002] Magnetic resonance imaging (MRI) has become an important tool for disease detection, non-invasive diagnosis, and treatment monitoring. MRI works by collecting signals from a spatial frequency domain (often referred to as k-space) and generating images based on the collected signals. The k-space and / or images generated therefrom include complex-valued data, and thus, ideally, complex-valued data should be used for training an artificial neural network (ANN) to perform MRI data processing tasks such as MRI image reconstruction. However, in practice, medical MRI images available for training are typically stored in a real-valued format (such as Digital Imaging and Communications in Medicine (DICOM) format), in which only the magnitude of the complex-valued MRI data (e.g., MRI images) is preserved, and the phase information of the complex-valued data is discarded. Thus, currently available training data does not reflect the real world in a manner relevant to actual use cases, and artificial intelligence (AI) models trained using such data often lack accuracy and adaptability. Accordingly, there is a strong desire for systems, methods, and apparatuses having improved AI models for MRI data processing. SUMMARY

[0003] Described herein are systems, methods, and apparatuses associated with processing MRI data (e.g., reconstructing MRI images based on undersampled MRI data) using a machine learning (ML) model. The ML model can be implemented using an artificial neural network (ANN), and the ML model can be learned using an instance of the ANN through a training process that includes determining and storing initial parameters of the ML model, and processing a portion of a first MRI training dataset and a portion of a second MRI training dataset based on the initial parameters of the ML model. A first set of updated parameters of the ML model and a second set of updated parameters of the ML model can be determined based on the processing of the first MRI training dataset and the processing of the second MRI training dataset, respectively, and the training process can further include processing a remaining portion of the first MRI training dataset based on the first set of updated parameters of the ML model determined above to determine a first loss, processing a remaining portion of the second MRI training dataset based on the second set of updated parameters of the ML model determined above to determine a second loss, and updating the initial parameters of the ML model based on the first loss and the second loss (e.g., based on a sum or average of the first loss and the second loss).

[0004] In an example, the training process can further include processing a portion of the third MRI training dataset based on the initial parameters of the ML model to determine a third set of updated parameters of the ML model, processing a remaining portion of the third MRI training dataset based on the third set of updated parameters of the ML model to determine a third loss, and updating the initial parameters of the ML model further based on the third loss (e.g., based on a sum or average of the first loss, the second loss, and the third loss described herein).

[0005] In an example, at least one of the first MRI training dataset or the second MRI training dataset can include complex-valued MRI data. The complex-valued MRI data can be actual MRI data (e.g., collected from a clinical procedure), or they can be synthetically generated, e.g., based on real-valued MRI data and by adding phase values to the real-valued MRI data. The phase values can be derived from the MRI images, or as a function of one or more spatial locations associated with the real-valued MRI data.

[0006] In an example, at least one of the first MRI training dataset or the second MRI training dataset can include multi-coil MRI data that can be generated based on single-coil MRI data. For example, the multi-coil MRI data can be generated by applying one or more coil sensitivity maps to the single-coil MRI data, where the one or more coil sensitivity maps can be derived based on a spatial distribution function or a multi-coil MRI image. BRIEF DESCRIPTION OF DRAWINGS

[0007] The examples disclosed herein can be understood more readily by reference to the following detailed description, when taken in connection with the accompanying drawings, and wherein:

[0008] Figure 1 FIG. 1 is a simplified block diagram illustrating an example of processing MRI data using a ML model in accordance with one or more embodiments described herein.

[0009] Figure 2 FIG. 2 is a simplified block diagram illustrating an example of reconstructing an MRI image based on under-sampled data using a pre-trained ML model in accordance with one or more embodiments described herein.

[0010] Figure 3 FIG. 3 is a flow diagram illustrating an example operation that can be associated with training of a ML model in accordance with one or more embodiments described herein.

[0011] Figure 4 FIG. 4 is a flow diagram illustrating an example of a meta-learning process in accordance with one or more embodiments described herein.

[0012] Figure 5is a simplified block diagram illustrating example components of a device that can be configured to perform the tasks described in accordance with one or more embodiments provided herein. DETAILED DESCRIPTION

[0013] The present disclosure is illustrated by way of example and not limitation in the figures of the accompanying drawings.

[0014] Figure 1 Examples are illustrated of processing MRI data using deep learning based techniques, such as machine learning (ML) models. As shown, MRI data 102 associated with an anatomical structure, such as a human brain, can be collected from a spatial frequency domain, referred to herein as k-space (or k-space data / information). MRI data can inherently be complex-valued (e.g., because they are measurements of rotating magnetization in the human body), and as such, can include real and imaginary parts. An ML model 104 can be trained to process the MRI data 102 and produce a result, such as an MRI image 106, that can be used for disease detection, non-invasive diagnosis, and / or treatment monitoring. The ML model can be implemented using an artificial neural network (ANN), such as a convolutional neural network (CNN), and the ML model (e.g., parameters of the ML model) can be learned through a training process, based on real data or synthetically generated (e.g., computer simulated based on real data). The ML model can be trained to perform different tasks, including, for example, MRI image reconstruction, denoising, contrast enhancement, etc., and the data simulation and model training techniques described herein can be applied to any of these models and / or tasks.

[0015] Figure 2 Examples are illustrated of using pre-trained ML models for MRI image reconstruction. As shown, when data is collected from k-space 202 for these tasks, a sampling mask (e.g., 204 shown in the figure) can be used to undersample the k-space in order to speed up the data collection and image generation process. For example, the sampling mask 204 can include values corresponding to a plurality of locations of the k-space, and the values can indicate whether data can be collected from each of the locations (e.g., a value of “1” can indicate data collection at a location, while a value of “0” can indicate no data collection at the location). The undersampling operation can result in undersampled MRI data 206 being collected, and the undersampled data can be converted into an MRI image (e.g., 208 shown in the figure) via an inverse fast Fourier transform (IFFT). Since MRI data and MRI images can be converted back and forth using an IFFT (e.g., from data to image) or a FFT (e.g., from image to data), the term “MRI data” can be used interchangeably with the term “MRI image” herein.

[0016] Since the MRI image 208 can be generated from the undersampled MRI data 206, the image can lack detail (e.g., as compared to a fully-sampled MRI image) and / or can contain artifacts (e.g., aliasing artifacts) caused by the undersampling. To recover the missing detail and / or remove the artifacts, the ML model 210 can be used to reconstruct an MRI image (e.g., 212 shown in the figure) based on the undersampled image 208. The reconstructed MRI image 212 can be characterized by improved quality (e.g., having the same or approximately similar quality as when an image is generated based on fully-sampled k-space data) as compared to the undersampled image 208, and can be used to facilitate one or more downstream tasks, such as Tl mapping, T2 mapping, etc.

[0017] The ML models described herein (e.g., Figure 1 the ML model 104 and / or Figure 2 the ML model 210) can be implemented and / or learned using an artificial neural network (ANN). For example, the ML model can be learned (e.g., during training) using a first instance of an ANN, and can be implemented (e.g., at inference time or runtime) using a second instance of the ANN. Depending on the task the ANN is trained to perform, the ANN can have different structures. For example, to perform image reconstruction and / or de-noising, the ANN can include a convolutional neural network (CNN), and if the reconstruction and / or de-noising involves multiple contrasts, the ANN can include a recurrent neural network (RNN) that includes one or more RNN blocks or units (e.g., sub-networks), each of which can be configured to process a corresponding one of the multiple contrasts.

[0018] A CNN used to perform the tasks or functions described herein can include multiple convolution and / or transposed convolution layers. Each convolution layer, in turn, can include multiple convolution kernels or filters having respective weights (e.g., corresponding to parameters of the ML model implemented by the neural network) that can be configured to extract features from an input image (or data). The convolution operation can be followed by batch normalization and / or an activation function (e.g., such as a rectified linear unit (ReLu) activation function), and the features extracted by each convolution layer can be down-sampled through one or more pooling layers and / or one or more fully connected layers to obtain a representation of the features, e.g., in the form of a feature map or a feature vector. In an example, the features extracted by the convolution layers can be passed to one or more up-pooling layers and / or one or more transposed convolution layers. Through these layers, the extracted features can be up-sampled and further processed (e.g., via multiple de-convolution operations) to derive one or more up-scaled or dense feature maps or feature vectors. The dense feature maps or vectors can then be used to generate a reconstructed or de-noised MRI image (e.g., Figure 1 the image 106 of Figure 2 the image 212 of

[0019] Figure 3 Example operations that can be associated with training an ML model described herein (e.g., an ANN implementing the ML model) are illustrated. As shown, the training operations can include initializing parameters of the ML model or neural network (e.g., weights associated with individual filters or kernels of the neural network) at 302. The parameters can be initialized, for example, based on samples collected from one or more probability distributions or parameter values of another ML model or neural network having a similar architecture. The training operations can also include providing training data (e.g., undersampled MRI images or undersampled MRI data) to the ML model or neural network at 304, and causing a task (e.g., predicting a reconstructed MRI image) to be performed at 306 using the ML model or neural network based on the provided training data.

[0020] At 308, a loss associated with performance of the task (e.g., a reconstruction loss) can be determined, for example, by comparing a result produced by the ML model or neural network (e.g., a reconstructed image) to a gold standard (e.g., a fully-sampled MRI image). The loss can be determined using a suitable loss function, such as a loss function based on mean squared error (MSE), structural similarity index measurement (SSIM), LI norm, peak signal-to-noise ratio (PSNR), etc. And once the loss is determined, the loss can be evaluated at 310 to determine whether one or more training termination criteria have been satisfied. For example, the training termination criteria can be considered to be satisfied if the loss described above is below a predetermined threshold, if a change in the loss between two training iterations (e.g., between successive training iterations) falls below a predetermined threshold, etc. If it is determined at 310 that the training termination criteria have been satisfied, the training can end. Otherwise, the loss can be backpropagated through the neural network at 312 (e.g., based on gradient descent associated with the loss) before the training returns to 306.

[0021] For the sake of simplicity of illustration, the training steps are depicted and described herein in a particular order. However, it should be appreciated that the training operations can occur in various orders, simultaneously, and / or with other operations not presented or described herein. Moreover, it should be noted that not all operations that can be included in a training process are depicted and described herein, and not all of the example operations need to be performed.

[0022] As described herein, the ML model 102 or 104 is provided with training data in actual use cases (e.g., undersampled MRI images or undersampled MRI data) that are different from the training data used to train the ML model 102 or 104. For example, the training data used to train the ML model 102 or 104 can include MRI images or MRI data that are fully-sampled, while the training data provided to the ML model 102 or 104 in actual use cases can include MRI images or MRI data that are undersampled. Figure 1 Figure 2 ​MRI data (e.g., collected from k-space) can inherently be complex-valued. As such, training of the ML model should ideally also be performed using complex-valued data to simulate real-world scenarios (e.g., such as phase-sensitive image processing tasks). In practice, however, MRI images that can be used for model training are often stored in real-valued formats (such as Digital Imaging and Communications in Medicine (DICOM) formats), where only the magnitude of the complex-valued MRI data (e.g., MRI images) can be preserved. Additionally, while modern MRI scanning technology can utilize multiple coils to simultaneously collect data from each coil, the final saved DICOM images can be coil-combined and only resemble single-coil images. Thus, ML models trained using these real-valued single-coil data can not be able to handle the complexities and diversities associated with real-world complex-valued data. To improve the accuracy and adaptability of the ML model, complex-valued multi-coil training data can be synthetically generated (e.g., using computer simulations) based on the real-valued single-coil data, for example, and used to train the ML models described herein. When actual complex-valued training data (e.g., collected from clinical procedures) is available, the synthetically generated MRI data can also be used together with the actual MRI data to train the ML model (e.g., the ML model can be trained using a mix of actual and synthetically generated MRI data).

[0023] In an example, complex-valued MRI training data (e.g., MRI images) can be synthetically generated by adding phase information (e.g., artificial phase information) to real-valued MRI data or images. For example, a first complex-valued MRI training data set can be generated by adding respective first phase values to first real-valued MRI data (e.g., at one or more first spatial locations associated with the first real-valued MRI data), and a second complex-valued MRI training data set can be generated by adding respective second phase values to second real-valued MRI data (e.g., at one or more second spatial locations associated with the second real-valued MRI data). To illustrate, a real-valued MRI image can be represented as m(x,y,z) = |M(x,y,z)|. By adding a phase θ(x,y,z) at each spatial location (x,y,z), the real-valued image can be converted to a complex-valued image based on the following:

[0024] m(x,y,z) = |M(x,y,z)| * exp(jθ(x,y,z))

[0025] where j can represent the imaginary unit of a complex number.

[0026] The spatial distribution of the phase θ(x,y,z) can be parametric or non-parametric. In a parametric example, the phase value at a spatial location (x,y,z) can be determined as a function (e.g., a first-order linear function) of the spatial location, such as the following:

[0027] θ(x, y, z) = ax + by + cz

[0028] where a, b, and c can be determined by fitting a function to existing phase data. In a non-parametric example, phase values at a location (x, y, z) can be determined (e.g., extracted) from one or more existing complex-valued images and applied to a real-valued (e.g., magnitude-only) image. For example, a plurality of existing complex-valued images can be averaged, and the phase values of the averaged image can be added to the real-valued image. In an example, phase values can also be synthesized based on the image m(x, y, z). The synthesis can be performed using conventional methods (such as smoothing) or using deep learning-based methods in which a neural network can be trained to generate plausible phases based on real-valued (e.g., magnitude-only) images.

[0029] Multi-coil MRI data (e.g., multi-coil MRI images) can be generated (e.g., synthesized) based on single-coil MRI data (e.g., single-coil MRI images). For example, a multi-coil MRI image (e.g., for n coils) can be synthetically generated based on a single-coil MRI image and a set of coil sensitivity maps (e.g., simulated or synthesized coil sensitivity maps). Let m(x, y, z) represent image data at a location (x, y, z), and let C(x, y, z, p) represent a coil sensitivity map for the pth coil, then MRI data for the pth coil at the location (x, y, z) can be computed based on:

[0030] m(x, y, z, p) = C(x, y, z, p) * |M(x, y, z)| * exp(j0(x, y, z))

[0031] where j, |M(x, y, z)|, and exp(j0(x, y, z)) can represent the above values. Thus, by simulating a set of first coil sensitivity maps associated with a plurality of first coils, a first multi-coil dataset can be generated based on a single-coil dataset, and by simulating a set of second coil sensitivity maps associated with a plurality of second coils, a second multi-coil dataset can be generated based on the single-coil dataset.

[0032] In examples, a coil sensitivity map can be synthesized (e.g., simulated) using a spatial distribution function that can be parameterized. For example, a coil sensitivity map for a pth coil can be determined based on C(x, y, z, p) = 1 / r((x, y, z), (xp, yp, zp)), where r() can be a function for computing a distance between a location (x, y, z) of the pth coil and a center location (xp, yp, zp) (e.g., r((x, y, z), (xp, yp, zp)) = sqrt((x-xp)2 + (y-yp)2 + (z-zp)2). In examples, a coil sensitivity map can be extracted from existing multi-coil images and processed before being applied to a single-coil image. For example, a plurality of coil sensitivity maps can be computed based on existing multi-channel MRI data before being averaged or smoothed (e.g., based on a polynomial fit, by applying a filter, etc.).

[0033] Synthetically generated complex-valued MRI data can allow for training of ML models or artificial neural networks (e.g., such as MRI image reconstruction neural networks described herein) using actual data, such that the models or networks can be capable of processing actual MRI processing tasks at inference time (e.g., when the models or networks are deployed). To further enhance the adaptability of ML models or neural networks (e.g., to different data types), meta-learning based techniques can be employed during training of the ML models or neural networks, such as Figure 4 illustrated. It should be noted that the illustrated meta-learning techniques can be applied to training of ML models or neural networks for various tasks including MRI image reconstruction, image denoising, contrast enhancement, etc. It should also be noted that the illustrated meta-learning techniques can be applied in combination with (e.g., to supplement) training of ML models or neural networks for specific tasks, such as Figure 3 the illustrated training process.

[0034] As Figure 4As shown, during training of the ML model (e.g., a neural network used to implement the ML model), at 402, initial parameters Pinit (e.g., weights of the neural network) of the ML model can be determined and stored. The initial parameters can be determined, for example, based on one or more probability distributions or based on parameter values of another ML model or neural network having a similar architecture. At 404, training data used to facilitate meta-learning can be obtained. The training data can include actual complex-valued multi-coil MRI images (e.g., or k-space data) that can be obtained from clinical practice and / or synthetic data that can be generated, for example, using the data synthesis techniques described herein. For example, let φ represent parameters used in the data synthesis process described above (e.g., φ can include values of a, b, c, r(), (xp, yp, zp), etc. in the equations or formulas provided herein), by varying the values of φ, one or more sets of complex-valued multi-coil MRI images or k-space data {y0, y1,...} can be synthetically generated based on parameters {φ0, φ1,...} and real-valued single-coil MRI images or k-space data {x0, x1,...}, respectively.

[0035] At 406, the stored initial parameters Pinit can be assigned to the ML model, and a round of training can be performed using the initial parameters and a portion of the first training data set y0 (e.g., which can be synthetically generated using φ0 and x0 as described above). For example, the training data set y0 can include a plurality of complex-valued MRI images, and a first portion of the MRI images y0 training can be used for training, while a remaining portion of the MRI images y0 test can be reserved as test data for use in later stages of meta-learning. As a result of the training performed using y0 training, at 408, a set of updated model parameters Pupdate0 can be obtained, for example, by backpropagating a loss through the ML model (e.g., through the layers of the neural network) (e.g., via a single gradient descent step or multiple gradient descent steps), and the updated model parameters can be stored for use during later stages of meta-learning.

[0036] At 410, a determination can be made as to whether the initial phase of meta-learning has been completed. For example, the determination can be made based on the number of generated training datasets (e.g., y0, yi, y2...). If there are more training datasets remaining, the above process can be repeated for each remaining training dataset. For example, for training dataset yi (which can be synthetically generated using phi and xi as described above), the stored initial parameters Pinit of the ML model can be reassigned to the ML model, and another round of training can be performed using the initial parameters and a portion of training dataset yi. Training dataset yi can include a plurality of complex-valued MRI images, and a first portion of the MRI images, yi training, can be used for training, while a remaining portion of the MRI images, yi test, can be reserved as test data for use in later stages of meta-learning. As a result of the training performed using yi training, a set of updated model parameters Pupdatei can be obtained, for example, by backpropagating a loss through the ML model (e.g., through the layers of a neural network), and the updated model parameters can be stored for use during later stages of meta-learning.

[0037] For ease of description, only two training datasets are mentioned above (e.g., y0 and yi). However, those skilled in the art will appreciate that meta-learning can be performed using more than two training datasets (e.g., including a third synthetically generated training dataset), and the above operations can be repeated for additional training datasets (e.g., including updating the ML model parameters based on the additional training datasets). Those skilled in the art will also appreciate that actual complex-valued MRI data can be used during the meta-learning process, for example, in addition to or instead of the synthetic data described herein.

[0038] Referring back to Figure 4If, at 410, it is determined that the initial phase of meta-learning has been completed (e.g., all training data sets have been processed), learning can proceed to 412, where the stored, updated ML model parameters (e.g., Pupdateo, Pupdatei, etc.) can be tested with training data that was reserved for testing (e.g., y0 test, yi test, etc.). For example, testing can be performed by assigning the updated model parameters (e.g., Pupdateo, Pupdatei, etc.) to the ML model and processing the test data (e.g., y0 test, yi test, etc.) using these parameters. As a result of the testing, a respective loss associated with processing the test data with the updated model parameters can be determined, e.g., based on a suitable loss function (e.g., MSE, SSIM, etc.) and a gold standard associated with the processing task (e.g., the gold standard can be a fully-sampled MRI image for MRI image reconstruction). The determined loss (e.g., a combination of losses) can then be used at 414 to update the initial parameters Pinit of the ML model to obtain final (e.g., refined) parameters Pfinal of the ML model. The update of 414 can be performed, e.g., by backpropagating the sum or average of the losses resulting from the testing (e.g., using test data y0 test, yi test, etc.) through the artificial neural network.

[0039] The systems, methods, and / or apparatus described herein can be implemented using one or more processors, one or more storage devices, and / or other suitable auxiliary apparatus such as display devices, communication devices, input / output devices, etc. Figure 5 FIG. 5 is a block diagram illustrating an example device 500 that can be configured to perform the image MRI data processing tasks described herein. As shown, the device 500 can include a processor (e.g., one or more processors) 502, which can be a central processing unit (CPU), a graphics processing unit (GPU), a microcontroller, a reduced instruction set computer (RISC) processor, an application-specific integrated circuit (ASIC), an application-specific instruction set processor (ASIP), a physics processing unit (PPU), a digital signal processor (DSP), a field programmable gate array (FPGA), or any other circuit or processor capable of executing the functions described herein. The device 500 can also include a communication circuit 504, a memory 506, a mass storage device 508, an input device 510, and / or a communication link 512 (e.g., a communication bus) through which the components shown in the figure can exchange information.

[0040] The communication circuitry 504 can be configured to transmit and receive information utilizing one or more communication protocols (e.g., TCP / IP) and one or more communication networks, including a local area network (LAN), a wide area network (WAN), the Internet, a wireless data network (e.g., Wi-Fi, 3G, 4G / LTE, or 5G network). The memory 506 can include a storage medium (e.g., a non-transitory storage medium) configured to store machine-readable instructions that, when executed, cause the processor 502 to perform one or more of the functions described herein. Examples of a machine-readable medium can include volatile or non-volatile memory, including, but not limited to, semiconductor memory (e.g., electrically programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM)) flash memory, etc.). The mass storage device 508 can include one or more magnetic disks such as one or more built-in hard disk drives, one or more removable disks, one or more magneto-optical disks, one or more CD-ROM or DVD-ROM disks, etc., on which instructions and / or data can be stored for operation of the processor 502. The input device 510 can include a keyboard, a mouse, a voice control input device, a touch-sensitive input device (e.g., a touch screen), etc., for receiving user input for the device 500.

[0041] It should be noted that the device 500 can operate as a standalone device or can be connected (e.g., networked or grouped) with other computing devices, including other devices in the system 100, to perform the functions described herein. Moreover, although only one example of each component has been shown in the Figure 5 It will be understood by those skilled in the art that the device 500 can include multiple instances of one or more of the components shown in the figures, even though only one example of each component is shown in the

[0042] Although the present disclosure has been described in terms of certain embodiments and generally associated methods, modifications, and alterations, and variations of embodiments and methods will be apparent to those skilled in the art. Accordingly, the above description of example embodiments does not restrict the present disclosure. Other changes, substitutions, and alterations are possible. Additionally, unless otherwise specifically stated herein, discussions utilizing terms such as “analyzing,” “determining,” “enabling,” “identifying,” “modifying,” or the like, refer to the actions and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (e.g., electronic) quantities within the computer system’s registers and memories into other data similarly represented as physical quantities within the computer system memories or other such information storage, transmission or display devices.

[0043] It is to be understood that the above description is intended to be illustrative, and not restrictive. Many other embodiments will be apparent to those of skill in the art upon reading and understanding the above description. The scope of the disclosure should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.

Claims

1. A method of processing magnetic resonance imaging, MRI, data, the method comprising: obtaining magnetic resonance imaging, MRI, data; and processing the MRI data using a machine learning, ML, model, wherein the ML model is learned through a training process, the training process comprising: determining and storing initial parameters of the ML model; processing a portion of a first MRI training data set based on the initial parameters of the ML model, wherein, as a result of processing the portion of the first MRI training data set, a first set of updated parameters of the ML model is determined; processing a portion of a second MRI training data set based on the initial parameters of the ML model, wherein, as a result of processing the portion of the second MRI training data set, a second set of updated parameters of the ML model is determined; processing a remaining portion of the first MRI training data set based on the first set of updated parameters of the ML model to determine a first loss; processing a remaining portion of the second MRI training data set based on the second set of updated parameters of the ML model to determine a second loss; and updating the initial parameters of the ML model based on the first loss and the second loss; at least one of the first MRI training data set or the second MRI training data set comprises complex-valued MRI data; the complex-valued MRI data is synthetically generated based on real-valued MRI data and by adding a phase value to the real-valued MRI data.

2. The method of claim 1, wherein, the phase value is derived from an MRI image or is a function of one or more spatial locations associated with the real-valued MRI data.

3. The method of claim 1, wherein, the at least one of the first MRI training data set or the second MRI training data set comprises multi-coil MRI data generated based on single-coil MRI data.

4. The method of claim 3, wherein, the multi-coil MRI data is generated by applying one or more coil sensitivity maps to the single-coil MRI data, wherein the one or more coil sensitivity maps are derived based on a spatial distribution function or a multi-coil MRI image.

5. The method of claim 1, wherein, the ML model is further learned by: processing a portion of a third MRI training data set based on the initial parameters of the ML model, wherein, from the processing, a third set of updated parameters of the ML model is determined; processing a remaining portion of the third MRI training data set based on the third set of updated parameters of the ML model to determine a third loss; and updating the initial parameters of the ML model further based on the third loss.

6. The method of claim 1, wherein, the initial parameters of the ML model are updated during the training process based on a sum or an average of the first loss and the second loss.

7. The method of claim 1, wherein, the MRI data comprises under-sampled MRI data, and wherein processing the MRI data comprises reconstructing an MRI image based on the under-sampled MRI data.

8. A computer program product comprising instructions which, when executed on a computer, cause the computer to carry out the method of any one of claims 1-7.

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