Methods and systems for synthesizing raw multichannel data

Abstract

Methods of synthesizing raw multichannel data are provided. The subject methods include receiving initial magnitude image data and producing phase image data from the initial magnitude image data using a generative model to synthesize the raw multichannel data. Systems and computer-readable media for practicing methods of the invention are also provided.

Description

[0001] Atty. Docket: UCSF-745WO METHODS ANDSYSTEMS FORSYNTHESIZINGRAWMULTICHANNELDATACROSS-REFERENCE TORELATEDAPPLICATIONSThis application claims the benefit of U.S. Provisional Patent Application No. 63 / 535,270, filed August 29, 2023, which application is incorporated herein by reference in its entirety. INTRODUCTION Magnetic resonance imaging (MRI) is a non-invasive medical imaging technique that is widely used in the clinical diagnosis and pathological analysis. In principle, MRI techniques use the interaction between radio frequency (RF) pulses, a strong magnetic field, and body tissues to generate images of the organs from inside a body. In most medical applications, hydrogen nuclei (which consist solely of a proton) that are in tissues create a signal that is processed to form images of the body. Only a small part of the hydrogen nuclei contributes to the measured signal due to their different alignment in the magnetic field. The protons are capable of absorbing energy when exposed to a short RF pulse (electromagnetic energy) at their resonance frequency. After absorbing energy from the RF pulse, the nuclei are promoted to the excited state where they only stay for a short time period, and then return to their initial state of equilibrium (so-called decay) by releasing energy. This transmission of energy by the nuclei as they return to their initial state is what is observed as the MRI signal. The subtle differences of that signal from different tissues combined with advanced signal processing algorithms implemented on modern computing devices is what enables various organs to be distinguished. Any imaging plane, or slice, can be projected, and then stored or printed for further diagnosis and treatment. The duration of an MRI scan is proportional to the number of data points acquired in the spatial frequency domain (i.e., “k-space”). Accordingly, one way of reducing the duration of the scan is to acquire fewer data points. For example, fewer samples may be acquired in the frequency encoding direction, the phase encoding direction, or both the frequency and phase encoding directions. However, when fewer data points are obtained than what is required by the spatial Nyquist criteria (this is often termed “under-sampling” k-space), the MR image generated from the collected data points by an inverse Fourier transform contains artifacts due to aliasing. As a result, although scanning time is reduced by under-sampling in the spatial frequency domain, the resulting MRI images have poor quality and may be unusable, as the introduced artifacts may severely degrade image quality, fidelity, and interpretability. The factor by which data is undersampled is known as the acceleration factor Atty. Docket: UCSF-745WO (AF). If AF is higher, data acquisition will be higher. However, as the distance between neighboring k-space lines increases, the field of view (FOV) decreases. This results in an aliased image, i.e., an image comprising an artifact caused by the scanned body part being larger than the FOV. Deep learning-based MRI reconstruction methods show promise in faithfully reconstructing MR images from undersampled k-space, but such methods are usually hampered by a lack of paired and diverse training data posing a barrier for effective clinical translation of these technologies. Current deep learning MRI reconstruction techniques use datasets [1] created at academic medical centers containing paired images and raw k-space MRI data and have enabled major advances in MRI reconstruction methods. However they are limited in several ways. Magnitude images contained in these datasets are preprocessed which can lead to biased results for MRI reconstruction [2] and are hard to standardize. Furthermore, these publicly available datasets are typically limited in anatomy, acquisition parameters and typically have limited pathology information. Recent studies have shown that these limitations can result in hallucinations of structures or artifacts during deep learning based MRI reconstruction [3, 4] limiting the generalization potential of these methods and their use clinically. However, one cannot simply use other clinical image datasets for MRI reconstruction as they do not contain the raw k-space MRI data and are a very lossy representation of the raw data. This is because typically only a magnitude image is stored while the image phase and multicoil information is discarded. Furthermore, MRI data are acquired from multi- channel RF coils, but clinical images show a coil-combined image and, thus, the multi- channel information is lost. Phase information contains contrast from chemical shift, magnetic susceptibility differences, inhomogeneities in the main magnetic field, RF coils used, fat / water separation and tissue interfaces, and blood flow [6, 7, 8, 9, 10]. Additionally, recent studies have shown that using complex-valued neural networks with complex activation functions for MRI reconstruction [11, 12] that include phase information during training produce higher quality reconstructed images. Current techniques for generating synthetic MRI data typically focus on generating multiple synthetic magnitude images of different contrasts using specific acquisition sequences [13, 14, 15, 16, 17, 18] or parameter maps using an analytical signal model [19, 20]. More recent studies such as [21, 22] have included methods to generate synthetic image phase by emulating physical models, and have focused on fine tuning training datasets consisting mostly of natural images. No methods have attempted to synthesize MRI phase maps that include all the phase information listed above. Atty. Docket: UCSF-745WO SUMMARY The present inventors have realized that there would be significant advantages in leveraging the diversity of pre-existing images from clinical MRI scans as they contain a range of patient populations, anatomy, pathology, image contrast, acquisition parameters, MRI scanners used, and more. This would be particularly useful for multi-task networks [5] that perform both image reconstruction and a downstream task such as segmentation or classification to improve the performance. It was discovered that training on more diverse and representative datasets would improve the utility of deep learning models when reconstructing undersampled images, especially for rare anatomies and pathologies, and could potentially allow greater clinical adoption. As such, methods and systems for synthesizing raw multichannel data having the ability to realize the above-described advantages are desirable. Embodiments of the present invention satisfy these and other desires. Aspects of the disclosure include methods. Methods of interest include receiving initial magnitude image data (e.g., magnetic resonance imaging (MRI) image data, synthetic aperture radar (SAR) data, time-resolved optical microscopy data, hyperspectral imaging data) and producing phase image data from the initial magnitude image data using a generative model to synthesize the raw multichannel data. In select cases where the initial magnitude image data is MRI image data, the raw multichannel data is k-space data. In some instances, methods include reconstructing an image based on the synthesized raw multichannel data. In select implementations, the initial magnitude image data is received from a plurality of signal receivers (e.g., radiofrequency coil receivers). In some cases, methods include generating sensitivity profiles for the plurality of signal receivers. Methods in some cases also involve combining the sensitivity profiles with the initial magnitude image data and the phase image data. Embodiments of the subject methods may include generating the sensitivity profiles using eigenvector-derived maps. Additional embodiments of the methods include analytically converting the initial magnitude image data and the phase image data to real and imaginary components. In some instances, methods include combining the sensitivity profiles with the real and imaginary components. In certain cases, the generative model is a deep learning-based generative model configured to leverage a dataset (e.g., concurrent dataset or historical dataset) of prior images or raw data. In select instances, the generative model comprises a discriminator (e.g., PatchGAN discriminator) configured to judge the realism of the synthesized raw multichannel data. In embodiments, the generative model is a generative adversarial network (GAN). In select versions, the generative model is a conditional deep learning-based generative model (e.g., cGAN). Generative models according to embodiments of the methods include one or more loss Atty. Docket: UCSF-745WO functions, for example, a loss function derived by a probabilistic model. In some embodiments, methods include generating synthetic MRI phase images from input MRI magnitude images. Corresponding radiofrequency coil sensitivity maps are derived and then used to generate synthetic multi-channel data. The resulting synthetic multi-coil MRI data, including synthesized image phase. Non-transitory computer-readable media and systems configured to perform the subject methods are also provided. Systems of interest include a processor and a non- transitory computer-readable medium of the invention comprising instructions stored thereon, which when executed by the processor, cause the processor to perform the subject methods. In some embodiments, systems include an instrument comprising a plurality of signal receivers, such as an MRI. BRIEFDESCRIPTION OF THEFIGURESThe invention may be best understood from the following detailed description when read in conjunction with the accompanying drawings. Included in the drawings are the following figures: FIG. 1 presents a flowchart for practicing a method of the invention according to certain embodiments. FIG.2 depicts a system for synthesizing raw multichannel data according to certain embodiments of the invention. FIG. 3A-3B illustrate a synthetic raw data generation (FIG. 3A) and image reconstruction pipeline (FIG.3B). FIG.4A-4B depict representative ground truth magnitude, ground truth phase, and synthetic phase images generated from a conditional GAN using a 16-coil model (FIG.4A) and a 20-coil model (FIG.4B). FIG. 5A-5B depict sample image comparisons at 4x (FIG. 5A) and 8x (FIG. 5B) acceleration factors for the 20-coil dataset. FIG.6A-6B depict sample image comparisons at 4x (FIG.6A) and 8x (FIG.6B) for the 16 coil dataset. FIG. 7A-7B illustrate performance of ground truth-trained and synthetically trained Variational Network reconstruction models at different acceleration factors for 16-coil (FIG. 7A) and 20-coil (FIG.7B) datasets. FIG.8 illustrates the generation of multiple synthetic MR phase images from a single MR magnitude image using a method based on BicycleGAN. FIG. 9A-9B illustrate the use of an RF coil library method which generates the synthetic raw k-space data from the outputs of FIG.8. Atty. Docket: UCSF-745WO DETAILED DESCRIPTION Before the methods, systems and computer-readable media of the present disclosure are described in greater detail, it is to be understood that the methods, systems and computer-readable media not limited to particular embodiments described, as such may, of course, vary. For example, it is to be understood that while the aspects of the invention are described with reference to applications in MRI technology, the invention is not limited to MRI applications. As will be described in greater detail below, the present invention is also relevant to at least synthetic aperture radar (SAR), time-resolved optical microscopy, hyperspectral imaging, self-driving car technology, and the like. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting, since the scope of the methods, systems and computer- readable media will be limited only by the appended claims. Where a range of values is provided, it is understood that each intervening value, to the tenth of the unit of the lower limit unless the context clearly dictates otherwise, between the upper and lower limit of that range and any other stated or intervening value in that stated range, is encompassed within the methods, systems and computer-readable media. The upper and lower limits of these smaller ranges may independently be included in the smaller ranges and are also encompassed within the methods, systems and computer-readable media, subject to any specifically excluded limit in the stated range. Where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in the methods, systems and computer-readable media. Certain ranges are presented herein with numerical values being preceded by the term “about.” The term “about” is used herein to provide literal support for the exact number that it precedes, as well as a number that is near to or approximately the number that the term precedes. In determining whether a number is near to or approximately a specifically recited number, the near or approximating unrecited number may be a number which, in the context in which it is presented, provides the substantial equivalent of the specifically recited number. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the methods, systems and computer-readable media belong. Although any methods, systems and computer-readable media similar or equivalent to those described herein can also be used in the practice or testing of the methods, systems and computer-readable media, representative illustrative methods, systems and computer-readable media are now described. Atty. Docket: UCSF-745WO All publications and patents cited in this specification are herein incorporated by reference as if each individual publication or patent were specifically and individually indicated to be incorporated by reference and are incorporated herein by reference to disclose and describe the materials and / or methods in connection with which the publications are cited. The citation of any publication is for its disclosure prior to the filing date and should not be construed as an admission that the present methods, systems and computer-readable media are not entitled to antedate such publication, as the date of publication provided may be different from the actual publication date which may need to be independently confirmed. It is noted that, as used herein and in the appended claims, the singular forms “a”, “an”, and “the” include plural referents unless the context clearly dictates otherwise. It is further noted that the claims may be drafted to exclude any optional element. As such, this statement is intended to serve as antecedent basis for use of such exclusive terminology as “solely,” “only” and the like in connection with the recitation of claim elements, or use of a “negative” limitation. It is appreciated that certain features of the methods, systems and computer-readable media, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the methods, systems and computer-readable media, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable sub- combination. All combinations of the embodiments are specifically embraced by the present disclosure and are disclosed herein just as if each and every combination was individually and explicitly disclosed, to the extent that such combinations embrace operable processes and / or compositions. In addition, all sub-combinations listed in the embodiments describing such variables are also specifically embraced by the present methods, systems and computer-readable media and are disclosed herein just as if each and every such sub- combination was individually and explicitly disclosed herein. As will be apparent to those of skill in the art upon reading this disclosure, each of the individual embodiments described and illustrated herein has discrete components and features which may be readily separated from or combined with the features of any of the other several embodiments without departing from the scope or spirit of the present methods, systems and computer-readable media. Any recited method can be carried out in the order of events recited or in any other order that is logically possible. METHODSThe present disclosure provides computer-implemented methods for synthesizing raw multichannel data. By “raw multichannel data” it is meant data germane to multiple signal Atty. Docket: UCSF-745WO receiver pathways that has not been preprocessed for use in another application such as image reconstruction. For example, in some embodiments of the invention applicable to MRI imaging, the raw multichannel data is k-space data. The term “k-space” is used herein in its conventional sense to describe an image space in which signals are stored during data acquisition as a function of time and phase from an MRI sequence. “Phase” is used to describe a position relative to a part of a cycle in a periodic function. In embodiments, raw multichannel data synthesized by the invention includes phase information relevant to one or more of: contrast from chemical shift, magnetic susceptibility differences, inhomogeneities in the main magnetic field, signal receivers (e.g., RF coils) used, fat / water separation and tissue interfaces, and blood flow. To describe these concepts mathematically, the signal acquired from a 2D MRI slice (assuming that T2decay can be neglected) in the spatial frequency domain, or k-space, can be expressed as: ^ ^ ^^^^, ^^^ = ^ ^ ^^^, ^^^^^^^^^^^^^^^^^^^^ ^ ^ where ^^^, ^^is the signal generated at the position^^, ^^. This is a complex quantity which is equivalent to: ^^^, ^^ = ^^^^, ^^ + ^^^^^, ^^ where ^^^^, ^^is the real component of the signal and ^^^^, ^^is the imaginary component of the signal. The goal of MRI reconstruction is to recover ^^^, ^^from ^^^^, ^^^. The MR signal, ^^^, ^^, is generated by the rotation of the transverse components of the net magnetization. The signal is complex-valued because it is a measurement of both the x and y components of the net magnetization. The majority of MRI scans are interpreted based on the magnitude of the signal, |^^^, ^^|, which corresponds to the amplitude of the transverse magnetization. There is also information encoded in the phase (also known as angle) of the signal, ∠^^^, ^^, which corresponds to the rotation angle of the transverse magnetization. This includes chemical shift, magnetic susceptibility differences, inhomogeneities in the main magnetic field, RF coil profiles, fat / water separation, tissue interfaces, and blood flow. Machine learning is proving to be transformative for phase-based Fourier imaging modalities such as MRI in at least two major areas. First, it is enabling automation and improvement of many image processing and analysis tasks such as image segmentation, image identification, detection of abnormalities and classification of abnormalities. Second, it Atty. Docket: UCSF-745WO is enabling faster MRI scans by using data-driven, neural network models to reconstruct images from smaller amounts of MRI raw data, meaning less time is required to collect data. Furthermore, there are exciting new opportunities to combine improvements in both of these areas through techniques such as multi-task learning, which start with MRI raw data and produce both images and analyses results. Success in these machine learning approaches is arguably primarily determined by the availability of large amounts of high-quality data. There are large amounts of images available in clinical imaging archives as well as resulting diagnoses and other annotations, but the MRI raw data is harder to gather since it is deleted shortly after the images are reconstructed. There have been some dedicated efforts to gather raw MRI data, particularly the fastMRI project. fastMRI is described in, e.g., Zbontar et al. (2018). fastMRI: An open dataset and benchmarks for accelerated MRI. arXiv preprint arXiv:1811.08839. However, this data does not include diagnoses, outcomes, or other annotations, and it was acquired in limited scenarios of brain and knees with just a few types of contrast. The synthetic raw multichannel data of the invention consequently leverages existing data (e.g., in clinical imaging archives) to improve imaging speed, image reconstruction, and other tasks. As such, in some cases, the invention may be employed to reduce the imaging time needed to obtain a clinically useful MRI image by 5% or more, such as 10% or more, such as 20% or more, such as 30% or more, such as 40% or more and including 50% or more. In addition, the invention may be employed in some cases to reduce the presence of artifacts in undersampled MRI image by 5% or more, such as 10% or more, such as 20% or more, such as 30% or more, such as 40% or more and including 50% or more. Aspects of the subject methods include receiving initial magnitude image data. By “magnitude image data” it is meant one or more images in which the greyscale intensity and / or color intensity of different portions of the image corresponds to the magnitude of signal. The magnitude image data may be obtained using any phase-based Fourier imaging modality. For example, in some cases, the initial magnitude image data is magnetic resonance imaging (MRI) data. In some such cases, the initial magnitude image data includes images that would be available in clinical imaging archives. Put another way, the initial magnitude image data may be images that had once been used in a clinical setting, or are otherwise comparable to such images. The source and format of the initial magnitude data may vary. In select instances, the initial magnitude image data is processed from raw k-space data. In other instances, the initial magnitude data is in a digital image format that is transferrable over a data interchange protocol. In some such instances, the initial magnitude data is DICOM®(Digital Imaging and Communications in Medicine) data, or the like. In alternative embodiments, the initial magnitude image data is synthetic aperture radar (SAR) Atty. Docket: UCSF-745WO data. In still other embodiments, the initial magnitude image data is time-resolved optical microscopy data. In yet other embodiments, the initial magnitude image data is hyperspectral imaging data. The magnitude image data may have been collected from any convenient number of signal receivers. In some embodiments, the number of signal receivers ranges from 1 to 128, such as 15 to 20, and including 16 to 20. After the initial magnitude data is received, methods of the invention include producing phase image data from the initial magnitude image data using a generative model to synthesize the raw multichannel data. The “phase image data” is data including the phase information discussed above. In other words, while the initial magnitude image data does not include phase information, the methods include using a machine learning model to produce synthesized phase data that the model has determined would be correlated with said phase data. The generative model may be any model configured to learn the distribution of phase image data in a training dataset and generate new phase image data points. The production of phase image data in the present methods may be described as “signal receiver agnostic” because it can be applied to images acquired with any number of signal receivers with the generative model learning a one-to-one mapping from magnitude to phase. In some cases, the generative model is trained using data from a training dataset. The training dataset may be a dataset of prior images and raw data. For example, in select instances, the dataset includes raw complex-valued k-space with both magnitude and phase information of brain scans. In addition, the dataset may be a concurrent dataset or a historical dataset. By “concurrent” dataset, it is meant that the dataset is representative of signals collected from scans that are contemporaneous with the training of the model. On the other hand, “historical” datasets are representative of signals collected from scans that occurred in the past and are stored. For example, in some cases, the dataset is obtained from fastMRI. In some cases, the dataset is a concurrent dataset. In other cases, the dataset is a historical dataset. In still other cases, the dataset includes both concurrent and historical data. The data within the datasets may have been collected from any convenient number of signal receivers. In some embodiments, the number of signal receivers ranges from 1 to 128, such as 15 to 20, and including 16 to 20. In some embodiments, datasets include data collected from 16 signal receivers. In additional cases, datasets include data collected from 20 signal receivers. In some cases, the generative model is a deep learning-based generative model configured to leverage a dataset of prior images or raw data. The term “deep learning” is employed herein in its conventional sense to refer to machine learning algorithms using multiple layers for feature extraction. In some such cases, the deep learning-based generative model comprises an artificial neural network. In some instances, the neural Atty. Docket: UCSF-745WO network comprises a convolutional neural network (CNN). In some such instances, the deep learning-based generative model comprises a U-net. Other neural networks that may be adapted for use include, e.g., fully convolutional neural networks (FCNNs) and region-based convolutional neural network (R-CNNs). In some cases, the deep learning-based generative model is a generative adversarial network (GAN). In some such cases, the generative model is a conditional network such as a conditional generative adversarial network (cGAN). In additional cases, the deep learning-based generative model comprises a diffusion model. In further cases, the deep learning-based generative model comprises a score-based generative model. It should be appreciated that any of the neural models described herein may be two-dimensional or three-dimensional convolutional neural networks that operate on two-dimensional data (e.g., data corresponding to a single image, for example, an image of a slice of a patient's anatomy) or three-dimensional data (e.g., data corresponding to multiple images, for example, a stack of images in a volume each of which corresponds to a respective slice of the patient's anatomy). In select versions, the generative model comprises a discriminator configured to judge the realism of the synthesized raw multichannel data. Any discriminator suitable for distinguishing between real data and the synthesized raw multichannel data may be employed. In some cases, the discriminator is a PatchGAN discriminator. The subject PatchGAN discriminator may be comprised of a network where the input image is mapped to an N x N array. PatchGAN discriminators are described in, e.g., Isola et al. Proceedings of the IEEE conference on computer vision and pattern recognition (pp.1125-1134). The size of the N x N array may vary as desired. For example, in some instances, N may range from 32 to 256. In some instances, the discriminator is a 70 x 70 PatchGAN. The PatchGAN discriminator is configured to restrict the network’s attention to the structure of local image patches. This encourages the discriminator to penalize the structure at the scale of patches rather than the whole image (as in a typical binary classifier) in order to effectively capture high-frequencies in the synthetic image. In a sense, PatchGAN acts as a classifier itself. The main difference is that the output of the PatchGAN is an N x N array in which each element signifies whether the corresponding patch in the image is real or fake. As will be appreciated with the benefit of the present disclosure, the methods are not limited to generative adversarial networks (GANs), but rather can employ other types of generative models. Non-limiting examples of such generative models include diffusion models, sometimes referred to as diffusion probabilistic models or score-based generative models, which entail learning from the latent structure of a dataset such that the sampling is done in the latent space. Similar to GANs, the 3 main parts of diffusion models are 1) a forward noising process 2) a learned reverse denoising process and 3) a sampling technique. Atty. Docket: UCSF-745WO These models can also be used to generate multiple plausible phase images from a single input magnitude image. The deep learning-based generative model may use one or more loss functions in producing the image phase. In certain versions, the deep learning-based generative model comprises a plurality of (e.g., two) loss functions. The loss functions may be configured to regulate the type of structures in the synthetic raw multichannel data. For example, the generative model may be trained to generate high-frequency structures in the synthetic image or control how many low-frequency structures are present in the image. The loss functions may vary as desired. Loss functions that can be adapted for use in the subject methods include, but are not limited to an L1 or L2 distance loss function, and a conditional adversarial loss function. In some cases, the generative model includes conditional adversarial loss function and a regularized L1 distance loss function. In one such case, the loss functions are represented as follows: !∗= #$% m)in m,ax -^,^.log 2^^, ^^3 + -^,45log 61 − 2^^, !^^, 9^^:; + <-^,^,4.‖^ − !^^, 9^‖>3 where x is the input magnitude image, y is the generated synthetic phase image that corresponds to x, and z is the latent vector. In the above, the expression -^,^.log 2^^, ^^3 + -^,45log61 − 2^^, !^^, 9^^:;is the conditional adversarial loss function and -^,^,4.‖^ − !^^, 9^‖>3 is the regularized L1 distance loss function. In this objective, G tries to minimize the objective while D tries to maximize it. In some embodiments, methods include generating synthetic multichannel data with respect to a plurality of signal receivers. A “signal receiver” as described herein may be any device configured to detect signals in the form of electromagnetic radiation. For example, in MRI applications, a signal receiver may include a radiofrequency (RF) coil. MR signals are often generated using a plurality of RF coils, e.g., in a parallel MRI (PMRI) setting. The spatial localization of signals from signal receivers may be relevant because areas of an entity being scanned that are closer to the signal receivers contribute more signals as compared to the distant parts. This sensitivity information of the receiver coils is used in PMRI to reduce the required number of phase encode steps for the MR image reconstruction. During image reconstruction, signal receiver sensitivity information and aliased pixel location in an undersampled image can be used to reconstruct a fully sampled image. Examples of such reconstruction methods include, e.g., sensitivity encoding (SENSE) methods. SENSE methods are described in, e.g., Pruessmann et al. Magn. Reson. Med.42, 952–962 (1999). Atty. Docket: UCSF-745WO In certain cases, methods include generating sensitivity profiles for the plurality of signal receivers. In certain cases, a sensitivity profile is comprised of a diagonal matrix. Sensitivity profiles can be generated in any suitable manner. In some cases, the sensitivity profiles are generated by a pre-scan method. In such methods, a quick scan is obtained using the signal receivers prior to the actual scan. This quick scan produces a low-resolution full FOV image for each signal receiver, which can be used to estimate the sensitivity profile for each signal receiver. Pre-scan protocols that may be adapted for use herein are described in, e.g., Schoenberg et al., Parallel Imaging in Clinical MR Applications (Springer, Berlin, 2007). In other cases, generating the sensitivity profiles comprises using eigenvector-derived maps. In such cases, sensitivity profiles may be estimated using, e.g., ground-truth raw data from the training dataset. Eigenvalue based methods involve a series of eigenvalue decompositions performed in k-space and image space to produce the sensitivity profiles for the signal receivers. Such eigenvalue-based methods are described in, e.g. Uecker et al. Reson. Med.71(3), 990–1001 (2014). An exemplary algorithm that may be employed to generate the sensitivity profiles is ESPIRiT, which is described in Uecker et al.. ESPIRiT combines SENSE and GRAPPA (generalized autocalibrating partial parallel acquisition) to inherit benefits from both techniques. ESPIRiT uses a flexible signal receiver sensitivity model, which can incorporate non-Cartesian sampling trajectories and arbitrary image priors. ESPIRiT is robust to artifacts that arise from inconsistent signal receiver sensitivity maps by using an extended signal receiver sensitivity model which employs multiple sets of signal receiver sensitivity maps. For example, objects that are larger than the prescribed field of view (FOV) can overlap and create discontinuities in sensitivity maps resulting in ghosting along the phase encoding direction. However, ESPIRiT is able to represent overlapping anatomies with multiple sets of coil sensitivity maps (as compared to only a single set of coil sensitivity maps), allowing overlapping components to be de-aliased separately from each other. In embodiments, methods include combining the sensitivity profiles with the initial magnitude image data and the phase image data. In certain cases, this involves converting the initial magnitude image data and the phase image data to real and imaginary components. In such cases, combining the sensitivity profiles with the initial magnitude image data and the phase image data comprises combining the sensitivity profiles with the real and imaginary components. For example, methods according to some embodiments include multiplying sensitivity maps generated as described above with the real and imaginary components to synthesize raw multichannel data, e.g., multi-coil synthetic k-space data. Methods according to select embodiments also include training a neural network to reconstruct images using the raw multichannel data produced via the subject methods. For Atty. Docket: UCSF-745WO example, in MRI applications, complex-valued data resulting from the methods described above can be used in place of ground truth k-space data to train deep learning based MRI reconstruction networks. Machine learning is used to create a data-driven MR reconstruction. Given a single sample pattern for under sampling, a machine-learnt network is trained to reconstruct with an optimal value for each of any number of reconstruction parameters, such as for denoising. Any suitable deep learning network may be trained using the synthesized raw multichannel data. The deep learning networks may be existing deep learning networks or those that are yet to be developed. Neural networks that may be adapted for use include, but are not limited to CNNs, FCNNs, R-CNNs, and the like, and combinations thereof. In some embodiments, reconstructing an image based on the synthesized raw multichannel data involves the use of a variational network, which is defined as an efficient trainable formulation for accelerated parallel imaging-based reconstruction. Variational networks are described in Hammernik et al. Magnetic Resonance in Medicine, 79(6):3055– 3071 (2018), the description of which is incorporated by reference herein in its entirety. In select embodiments involving variational networks, the variational network is an end-to-end variational network, which is configured to learn the forward process (determined by sensitivity profiles) in conjunction with reconstruction. In other words, the variational network employs the sensitivity profiles discussed above. End-to-end variational networks are described in Sriram et al. In Medical Image Computing and Computer Assisted Intervention– MICCAI 2020: 23rd International Conference, Lima, Peru, October 4–8, 2020, Proceedings, Part II 23 (pp. 64-73). Springer International Publishing, the description of which is incorporated by reference herein in its entirety. The neural network models described herein may be trained using any suitable neural network training algorithm(s), as aspects of the technology described herein are not limited in this respect. For example, in some embodiments, the neural network models described herein may be trained by using one or more iterative optimization techniques to estimate neural network parameters from training data. For example, in some embodiments, one or more of the following optimization techniques may be used: stochastic gradient descent (SGD), mini-batch gradient descent, momentum SGD, Nesterov accelerated gradient, Adagrad, Adadelta, RMSprop, Adaptive Moment Estimation (Adam), AdaMax, Nesterov- accelerated Adaptive Moment Estimation (Nadam), and AMSGrad. Additional reconstruction techniques, include, e.g., Total Variation (TV), Compressed Sensing (CS) or combined PI-CS approaches. These approaches are described in, for example, as disclosed in the document Lustig, Michael, David Donoho, and John M. Pauly. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine 58.6 (2007): 1182-1195. Other image reconstruction methods Atty. Docket: UCSF-745WO disclosed in the document Bilgic, Berkin, Vivek K. Goyal, and Elfar Adalsteinsson. Magnetic resonance in medicine 66.6 (2011): 1601-1615, the document Gong, Enhao, et al. Magnetic resonance in medicine 73.2 (2015): 523-535, and the document B. Bilgic, S. Cauley, L. Wald, and K. Setsompop, in Proc. Intl. Soc. Mag. Res. Med., 2018, p. 0940. Reconstruction methods that may be adapted for use include, for example, those described in U.S. Patent Nos.10,133,964; 10,393,842; 10,438,354; 10,573,031; 10,692,250; 10,712,416; 10,859,657; 10,896,352; 10,970,887; 10,989,779; 11,181,598; 11,125,845; 11,170,543; 11,300,645; 11,307,278; 11,315,221; 11,307,278; and 11,324,418, the disclosures of which are incorporated by reference herein in their entirety. In some embodiments, image reconstruction may take into account one or more characteristics of MRI system that collects patient data that the neural network is being trained to process once the neural network is deployed. Examples of such characteristics include, but are not limited to, size of the field of view of the MRI system, sampling patterns to be used by the MRI system during imaging (examples of various sampling patterns are provided herein), number of RF coils in the MRI system configured to detect MR data, geometry and sensitivity of RF coils in the MRI system, pulse correlation among signals received by the RF coils of the MRI system, RF interference (external and internal) that the MRI system is expected to experience during operation, RF noise (e.g., from the MR signal receive chain) that the MRI system is expected to experience during operation, pulse sequences to be used during imaging, and field strength of the MRI system. In some of the embodiments in which multiple RF coils are used to collect MR data in parallel (parallel imaging), the data may be transformed as though it were observed by a smaller number of virtual RF coils, with the data “observed” by the virtual RF coils being derived from the data actually observed by the physical RF coils part of the MRI system. For example, in some embodiments, if the MRI system collects data using 16 RF coils, the collected data may be transformed using a linear transformation A as though it were observed by 8 virtual RF coils. As a specific non-limiting example, suppose each of the 16 RF coils were to collect 100 measurements, then measurements may be organized in a 16×100 matrix M of data. In turn, the linear transformation A may be a 8×16 matrix, such that when it is applied to the data (by computing the matrix product AM), the resulting data for the virtual coils is an 8×100 matrix of data in which at each of 100 time points, eight data points corresponding to eight virtual RF coils are to be used for further processing instead of 16 data points corresponding to 16 physical RF coils. In addition to MRI applications, the present invention can be applied to other phase-based Fourier imaging modalities. For example, in some cases, the methods can be applied to synthetic aperture radar (SAR). SAR uses signal receivers comprised of radar antennas to Atty. Docket: UCSF-745WO create one-, two-, or three-dimensional images. As such, in some cases, the initial magnitude image data received in the subject methods is SAR data. Methods can include producing phase image data from the SAR data using a generative model, generating sensitivity profiles for the radar antennas, combining the sensitivity profiles with the SAR data and the phase image data to synthesize raw multichannel SAR data, and reconstructing a SAR image using the raw multichannel SAR data (e.g., by training a machine learning model on the raw multichannel SAR data). In additional embodiments, the methods can be applied to ultrasound imaging and focused ultrasound. Ultrasound uses signal receivers comprised of mechanical transducer probes that serve as antennas to create one-, two-, or three- dimensional images. As such, in some cases, the initial magnitude image data received in the subject methods is ultrasound data. Methods can include producing phase image data from ultrasound data using a generative model, generating sensitivity profiles for the ultrasound probes, combining the sensitivity profiles with the ultrsound data and phase image data to synthesize raw multichannel multi-view ultrasound data, and reconstructing a ultrasound image using the raw multichannel ultrasound data either by training a machine learning model on the raw multichannel ultrasound data or through conventional imaging techniques such as backprojection, filtered back-projection, algebraic reconstruction techniques, iterative reconstruction techniques, or reconstruction techniques involving regularization such as those based on wavelet sparsity. In additional embodiments, the methods can be applied to time-resolved optical microscopy, described in, e.g., Suhling, et al. Photochemical & Photobiological Sciences, 4(1), 13-22. As such, in some cases, the initial magnitude image data received in the subject methods is time-resolved optical microscopy data. Methods can include producing phase image data from time-resolved optical microscopy data using a generative model, generating sensitivity profiles for the time- resolved optical microscopy photodetectors, combining the sensitivity profiles with the time- resolved optical microscopy data and the phase image data to synthesize raw time-resolved optical microscopy data, and reconstructing a time-resolved optical microscopy image using the raw multichannel time-resolved optical microscopy data. In additional cases, the initial magnitude image data is hyperspectral imaging data. Hyperspectral imaging is a technique involving the collection and processing of signals from across the electromagnetic spectrum, and is described in, e.g., Chang, C. I. (2003). Hyperspectral imaging: techniques for spectral detection and classification (Vol. 1). Springer Science & Business Media. In some embodiments, the initial magnitude data received in the subject methods is hyperspectral imaging data. Methods can include producing phase image data from the hyperspectral imaging data using a generative model, generating sensitivity profiles for hyperspectral imaging detectors, combining the sensitivity profiles with the hyperspectral imaging data and Atty. Docket: UCSF-745WO the phase image data to synthesize raw hyperspectral imaging data, and reconstructing a hyperspectral image using the raw hyperspectral imaging data. In select instances, methods include using the raw data for self-driving car navigation. FIG. 1 presents a flowchart for practicing a method of the invention according to certain embodiments. In step 101, initial magnitude data is received. As discussed above, the initial magnitude data may be from multiple sources, e.g., datasets. Subsequently, phase image data is produced from the initial magnitude image data using a generative model in step 102. In step 103, sensitivity profiles are generated based on the initial magnitude image data and the phase image data. In step 104, the sensitivity profiles are combined with the initial magnitude image data and the phase image data to synthesize raw multichannel data. Step 105 includes reconstructing an image using the raw multichannel data, which can include training a machine learning reconstruction algorithm using the raw multichannel data. The methods described herein may be implemented as instructions run as software on one or more computer systems, and the implementation is within the capability of those skilled in the art of computer image processing. In particular, the computer functions for manipulations of data described herein can be developed by a programmer skilled in the art of data and image processing. The functions can be implemented in a number and variety of programming languages including, in some cases, mixed implementations (i.e., relying on separate portions written in more than one computing language suitably configured to communicate with one another). For example, the functions, as well as any required scripting functions, can be programmed in C, C++, Java, JavaScript, VisualBasic, Tcl / Tk, Python, Perl, Net languages such as C#, and other equivalent languages. Certain mathematical functions for image processing can be written in scientific programming languages, and are preferably implemented in a form that takes advantage of a GPU. The capability of the technology is not limited by or dependent on the underlying programming language used for implementation or control of access to the basic functions. Alternatively, the functionality can be implemented from higher level functions such as toolkits that rely on previously developed functions for manipulating image data. The methods described herein may be performed on any suitable subject. In other words, the images manipulated by the subject methods may be obtained from any organismal or non-organismal subject. In certain embodiments the subject is a “mammal” or “mammalian”, where these terms are used broadly to describe organisms which are within the class Mammalia, including the orders carnivore (e.g., dogs and cats), Rodentia (e.g., mice, guinea pigs, and rats), and primates (e.g., humans, chimpanzees, and monkeys). In some instances, the subjects are humans. The methods may be applied to human subjects of both genders and at any stage of development (i.e., neonates, infant, juvenile, adolescent, Atty. Docket: UCSF-745WO adult), where in certain embodiments the human subject is a juvenile, adolescent or adult. While the present invention may be applied to human subject, it is to be understood that the methods may also be carried-out on samples from other animal subjects (that is, in “non- human subjects”) such as, but not limited to, birds, mice, rats, dogs, cats, livestock and horses. COMPUTER-READABLE MEDIA AND SYSTEMS Aspects of the present disclosure further include systems and non-transitory computer-readable media. In certain aspects, provided are one or more computer-readable media comprising instructions stored thereon, which when executed by one or more processors, cause the one or more processors to perform the subject methods. According to some embodiments, the operations performed comprise receiving initial magnitude image data and producing phase image data from the initial magnitude image data using a generative model to synthesize the raw multichannel data. In some cases, the computer readable media and systems are configured to reconstruct an image based on the synthesized raw multichannel data. While such is not required, some embodiments of the systems include one or more signal receivers, such as radiofrequency coil receivers. In some such embodiments, systems include an MRI machine configured to collect magnitude image data and / or data that may be used to train the subject machine learning models. Embodiments of the systems additionally include one or more input / output devices, such as a screen display for displaying reconstructed images. FIG.2 illustrates an example processor-based system 200 with which embodiments of the present disclosure can be implemented. Specifically, FIG. 2 illustrates system architecture wherein the components of the system are in electrical communication with each other. System architecture can include a processing unit (CPU or processor) 204. Processor 204 can include any general purpose processor and a hardware module or software module, as well as a special-purpose processor where software instructions are incorporated into the actual processor design. Processor 204 may essentially be a completely self-contained computing system, containing multiple cores or processors, a bus, memory controller, cache, etc. A multi-core processor may be symmetric or asymmetric. To enable user interaction with the computing system architecture, system 200 can include one or more input devices such as a microphone for speech, a touch-sensitive screen for gesture or graphical input, keyboard, mouse, motion input, speech and so forth. In the example of FIG.2, a keyboard 207 and mouse 208 are included. System 200 can also include Atty. Docket: UCSF-745WO an output device configured to display information such as images to a user. In the example of FIG.2, a computer monitor display 206 is included. While such is not required, some embodiments of the disclosed systems include one or more signal receivers configured to generate an image. In such embodiments, the processor 204 is in electrical communication with the signal receivers in such a manner that received signals are electronically transmitted to the processor 204. A machine learning algorithm trained using the subject methods can be employed by processor 204 to reconstruct an image based on data received from the signal receivers. In the embodiment of FIG.2, processor 204 is in electrical communication with the RF coils in MRI machine 201 and is configured to reconstruct an MRI image based on signals received from the RF coils. Embodiments within the scope of the present disclosure may also include tangible and / or non-transitory computer-readable storage media or devices for carrying or having computer-executable instructions or data structures stored thereon. Such tangible computer- readable storage devices can be any available device that can be accessed by a general purpose or special purpose computer, including the functional design of any special purpose processor as described above. By way of example, and not limitation, such tangible computer-readable devices can include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other device which can be used to carry or store desired program code in the form of computer-executable instructions, data structures, or processor chip design. When information or instructions are provided via a network or another communications connection (either hardwired, wireless, or combination thereof) to a computer, the computer properly views the connection as a computer-readable medium. Thus, any such connection is properly termed a computer- readable medium. Combinations of the above should also be included within the scope of the computer-readable storage devices. Computer-executable instructions include, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. Computer-executable instructions also include program modules that are executed by computers in stand-alone or network environments. Generally, program modules include routines, programs, components, data structures, objects, and the functions inherent in the design of special- purpose processors, etc. that perform tasks or implement abstract data types. Computer- executable instructions, associated data structures, and program modules represent examples of the program code means for executing steps of the methods disclosed herein. The particular sequence of such executable instructions or associated data structures Atty. Docket: UCSF-745WO represents examples of corresponding acts for implementing the functions described in such steps. Other embodiments of the disclosure may be practiced in network computing environments with many types of computer system configurations, including personal computers, hand-held devices, multi-processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, and the like. Embodiments may also be practiced in distributed computing environments where tasks are performed by local and remote processing devices that are linked (either by hardwired links, wireless links, or by a combination thereof) through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices. Various implementations of the technology herein can be contemplated, particularly as performed on one or more computing apparatuses (machines that can be programmed to perform arithmetic) of varying complexity, including, without limitation, workstations, PC’s, laptops, notebooks, tablets, netbooks, and other mobile computing devices, including cell- phones, mobile phones, wearable devices, and personal digital assistants. The methods herein may further be susceptible to performance on quantum computers. The computing devices can have suitably configured processors, including, without limitation, graphics processors and math coprocessors, for running software that carries out the methods herein. In addition, certain computing functions are typically distributed across more than one computer so that, for example, one computer accepts input and instructions, and a second or additional computers receive the instructions via a network connection and carry out the processing at a remote location, and optionally communicate results or output back to the first computer. The image analyses created by the technology herein, as well as the images themselves, can be displayed in tangible form, such as on one or more computer displays, such as a monitor, laptop display, or the screen of a tablet, notebook, netbook, or cellular phone or wearable device. The image analyses can further be printed to paper form, stored as electronic files in a format for saving on a computer-readable medium or for transferring or sharing between computers, or projected onto a screen of an auditorium such as during a presentation. The following examples are offered by way of illustration and not by way of limitation. EXPERIMENTAL Example 1 Atty. Docket: UCSF-745WO No methods thus far have attempted to synthesize MRI phase maps that include all the phase information. To address this, a method was created for synthesizing realistic MRI data that is complex-valued and multichannel from magnitude-only images. The solution leveraged recent advances in deep generative modeling [23, 24] to generate synthetic MRI phase images from input MRI magnitude images. Corresponding coil sensitivity maps derived from the test dataset were then used to generate synthetic multi-channel data. The resulting synthetic multicoil raw MRI data was then evaluated for its ability to be used in image reconstruction tasks by training a variational network

[0025] and comparing to a network trained on ground truth data. Findings showing comparable performance in this task suggested that this framework has the potential to address the limitations that exist in current MRI datasets used for reconstruction tasks where access to raw k-space data is required. METHODSFirst, the generation of synthetic phase images from input magnitude-only images using a conditional GAN framework is described. Then, the evaluation of the synthetic data is described. Generative Modeling Neural Network Architecture The generator was a 16-layer U-Net with skip connections and the discriminator was a 70 x 70 PatchGAN. With a PatchGAN, the convolutional discriminator decided if a 70 x 70 patch is real or fake instead of the full image. Each generative model was trained with a batch size of 1. Minibatch SGD was used with the Adam optimizer using a learning rate of 2e-4 and momentum parameters ?>= 0.5 and ?^= 0.999. More implementation details can be found in

[0024] . Synthetic Phase Generation The conditional GAN objective uses a hybrid objective consisting of 2 loss functions: a conditional adversarial loss function and a L1 distance loss function (to encourage less blurring). !∗= #$% m)in m,ax -^,^.log 2^^, ^^3 + -^,45log 61 − 2^^, !^^, 9^^:; + <-^,^,4.‖^ − !^^, 9^‖>3 Where x is the input magnitude image, y is the generated synthetic phase image, and z is the latent vector. This setup is suitable because the discriminator is conditioned on the input image x, and the raw ground-truth data could be accessed, and thus also the ground-truth Atty. Docket: UCSF-745WO phase data. The network was optimized by alternating between gradient descent steps conducted for optimizing the discriminator and the generator. Specifically, a U-Net was trained to predict the phase component from input magnitude only images. During training, this synthetic phase component was compared to the ground truth phase using a hybrid objective. This mixed loss function balances realistic looking phase images via the adversarial loss and encourages less blurring via the 1-norm. Each GAN model was trained for 50 epochs with a qualitative analysis of realistic synthetic phase maps being the main stopping criteria. During inference, the trained U-Net was used to generate synthetic phase from previously unseen magnitude images, resulting in the creation of realistic synthetic MRI phase data. Multi-coil Data Generation To generate synthetic multicoil k-space, the input magnitude and generated synthetic phase images were analytically converted to real and imaginary components. Sensitivity maps were then generated using ESPIRiT

[0026] on corresponding ground-truth raw data from the test dataset and the resulting sensitivity maps were combined with the real and imaginary components to generate multi-coil synthetic k-space data. This resulting complex-valued data could be used in place of ground truth k-space data to train deep learning based MRI reconstruction networks. Dataset Multi-coil k-space data taken from the fastMRI dataset was used as training data for the conditional GAN learning model. The dataset consisted of raw (real and imaginary component) k-space with both magnitude and phase information of brain scans at 1.5 and 3T. The images were acquired with a fast spin echo (FSE) pulse sequence with an echo train length (ETL) of 4. The dataset consists of T1-weighted, T2-weighted, and FLAIR contrast images with 16-coil and 20-coil images. FIG.3A-3B depicts the proposed synthetic raw data generation (FIG.3A) and image reconstruction (FIG.3B) pipeline. The generative model takes magnitude images as an input seed and produces plausible synthetic phase images as output, which are trained to match ground truth phase images from the dataset. Synthetic complex-valued data is obtained by combining the input (ground truth) magnitude image and synthetic phase image to yield real and imaginary components. Estimated sensitivity maps calculated with ESPIRiT from the training dataset are then applied to synthetic complex-valued multi-coil data to compute multi- coil k-space encoded with synthetic phase information. The synthetic raw data are evaluated by training a Variational Network using undersampled k-space data. Atty. Docket: UCSF-745WO Experiments Generative Two generative models were trained: a 16-coil model and a 20-coil model trained on 22,691 and 18,519 magnitude-only brain images respectively. During training, the U-net generator generated a synthetic phase image and the discriminator compared the generated image to the corresponding ground truth phase image (obtained from fastMRI) in a convolutional patch-wise manner. At inference time, magnitude-only images from the test set were run through the forward pass of the trained generative models to generate 6,541 synthetic phase images for the 16-coil model and 5,845 synthetic phase images for the 20- coil model. Evaluation: Physics-based Image Reconstruction To evaluate the utility of complex-valued multi-coil k-space data synthesized from the generative model, the quality of reconstructed MR images from reconstruction networks trained on ground-truth and synthetic data was compared. Multiple equispaced undersampling masks of acceleration factors R = {4, 6, 8, 10} with a center fraction of 0.04 were applied to k-space data to be used for training. Two Variational Networks

[0025] were then trained for 10 epochs with the 16-coil and 20-coil datasets. Each model was trained on synthetic and ground truth multicoil k-space with a 80 / 10 / 10 training / validation / test split. It was decided to use the variational network for evaluation because of its reliance on undersampled multicoil k-space and coil sensitivity maps as inputs into the unrolled network. Each trained image reconstruction model was then run on the same ground-truth test set and the quality of reconstructed magnitude images was evaluated (FIG. 3B) using standard quantitative image reconstruction metrics: PSNR, NMSE, SSIM

[0027] . PSNR, NMSE, and SSIM values are presented below in Tables 1-6. It was decided to use the Variational Network for evaluation because of its reliance on undersampled multi-coil k-space and coil sensitivity maps as inputs into the unrolled network. All models (generative and reconstruction) were implemented in PyTorch and trained on NVIDIA (Santa Clara, CA) Titan RTX and Quadro 8000 RTX GPUs. RESULTS FIG.4A-4B shows sample comparisons between synthetic and ground truth phase images. The synthetic phase images showed several expected features, including low spatial-frequency components, a noisy background, and tissue phase contrast, for example, between the ventricles and adjacent brain tissue. It was not expected for the synthetic phase Atty. Docket: UCSF-745WO to exactly match the ground truth phase because the MRI phase is not deterministic and can vary based on B0homogeneity and RF coil induced phase shifts. In some cases, there were blocking artifacts, possibly resulting from the patchGAN discriminator. FIG. 5A-5B and FIG.6A-6B show representative images reconstructed with variational network models trained with undersampled k-space from ground truth or synthetic data. FIG. 5A-5B show sample image comparisons at 4x (FIG. 5A) and 8x (FIG. 5B) acceleration factors for the 20-coil dataset, while FIG. 6A-6B show sample image comparisons at 4x (FIG.6A) and 8x (FIG.6B) acceleration factors for the 16-coil dataset. For R = {4, 8} acceleration factors, the reconstructed images trained on synthetic data contain slightly more error structures compared to the images trained on ground-truth data. However, visually, there are no obvious artifacts in the reconstructed images in either method. For the R = 8 acceleration factor, more errors in high resolution features were observed, possibly due to the lack of high frequency details in the synthetic phase images used to train the reconstruction network. FIG. 7A-7B compares variational network reconstruction performance metrics of PSNR, NMSE, and SSIM on models trained on ground truth and synthetic data at different acceleration factors. Data from the 16-coil dataset is shown in FIG.7A while data from the 20-coil dataset is shown in FIG.7B. At up to 10x acceleration factors, synthetically trained models showed comparable performance to ground-truth trained models. From the plots, it is seen that variational networks trained on undersampled synthetic data performed comparably to the same model trained on ground truth undersampled k-space at R = {4, 6} as measured by PSNR, NMSE and SSIM. At R = {8, 10} acceleration factors, the performance of networks trained on synthetic data dipped, especially the SSIM curve, but remained relatively comparable to that of the networks trained on ground truth data. Additionally, the networks trained on synthetic data outperformed networks trained on sinusoidal phase data in all quantitative metrics for the 20-coil dataset. For the 16-coil dataset, similar results were observed for the PSNR and NMSE measurements, while the performance in the SSIM metric was comparable to the sinusoidal phase trained network. The data shown in FIG.7A-7B is also presented in Tables 1-6, below: Table 1: PSNR values for VarNet trained on different types of phase at various acceleration factors for the 16-coil dataset. Bold values indicate the best performing type of phase (not including ground truth) Phase Type R=4 R=6 R=8 R=10 Atty. Docket: UCSF-745WO Sinusoidal Phase 23.652 23.229 22.99 22.590 Random Phase 23.938 22.255 22.028 22.581 ion factors for the 20-coil dataset. Bold values indicate the best performing type of phase (not including ground truth) Phase Type R=4 R=6 R=8 R=10 Ground Truth 32.605 30.0454 28.367 27.747 ion factors for the 16-coil dataset. Bold values indicate the best performing type of phase (not including ground truth) Phase Type R=4 R=6 R=8 R=10 Table 4: NMSE values for VarNet trained on different types of phase at various acceleration factors for the 20-coil dataset. Bold values indicate the best performing type of phase (not including ground truth) Phase Type R=4 R=6 R=8 R=10 Atty. Docket: UCSF-745WO Table 5: SSIM values for VarNet trained on different types of phase at various acceleration factors for the 16-coil dataset. Bold values indicate the best performing type of phase (not including ground truth) Phase Type R=4 R=6 R=8 R=10 Ground Truth 0.8425 0.816 0.773 0.767 ion factors for the 20-coil dataset. Bold values indicate the best performing type of phase (not including ground truth) Phase Type R=4 R=6 R=8 R=10 G d T th 08189 0790 0731 0722 Overall, the results showed that the proposed method (i) generates realistic looking MR phase maps, (ii) outperforms current methods used to generate synthetic phase data for training reconstruction models and (iii) image reconstruction networks trained on synthetic multi-coil data perform comparably to the same networks trained on real data. The findings suggested that this framework has the potential to address the limitations that exist in current MRI datasets used for reconstruction tasks where access to raw k-space data is required. DISCUSSION This work proposed a framework to generate synthetic complex multicoil MRI data from magnitude-only MR images and evaluated its utility by training a physics-based image reconstruction model. There exists a massive number of magnitude-only images as this is what is typically stored in clinical imaging databases (e.g. PACS), which do not usually contain phase and multicoil information or k-space data. The demonstrated framework aimed to allow for use of these large imaging databases for developing data-driven methods that require MRI raw data. It was chosen to evaluate using a variational network image reconstruction model as a proof of concept to demonstrate the effectiveness of the method. Atty. Docket: UCSF-745WO It was believed that a more significant opportunity for such a synthetic data pipeline is to train multi-task networks [5] including both image reconstruction and another downstream task such as image segmentation or classification that have been shown to allow for shorter scans. In these methods, the synthetic data pipeline can take advantage of existing clinical images and annotations for the downstream tasks, enabling creation of customized datasets for machine learning that includes image reconstruction tasks. Other approaches that generate synthetic MRI data for the purposes of training data typically build off natural image datasets [21, 22]. For example, the authors in

[0021] used image processing and simulated signal voids in MR masks to generate synthetic data. In

[0022] , the authors used a natural image dataset and modulate the training images with a ”sinusoidal phase at random frequency”. They further showed that training with this synthetic data showed ”substantially higher” level of aliasing artifacts compared to using MRI data suggesting that training image content defined the structure of reconstructed aliasing artifacts. In contrast, the approach described herein used only MRI-based datasets which results in more realistic and relevant phase maps. Furthermore, the authors of

[0022] observed that deviations in SNR, acquisition type, and aliasing patterns between training and test time can result in widely varying image reconstruction quality. The proposed generative modeling approach showed more realistic image phase maps that include both the low-frequency features, which these prior methods aimed to incorporate, as well as contrast based on the underlying tissues and anatomy (FIG.4A-4B). The quantitative results (FIG.7A-7B; Tables 1-6) suggest that encoding this tissue phase information (not just low-frequency or sinusoidal phase information) into training data for deep learning models adds more useful information for the network to learn higher quality image reconstructions. In addition to generating synthetic phase maps, a major aim of this work was to generate multi-coil data to increase the clinical relevancy of the technique. This work also took advantage of the well-established coil sensitivity map algorithm ESPIRiT

[0026] to estimate coil sensitivities instead of trying to learn them directly. This approach requires running ESPIRiT on prior ground truth data from fastMRI and, thus, a paired dataset with magnitude and ground truth phase information is still required for this part of the method for image generation. In previous experiments, multi-coil data was generated by adding a two-channel real and imaginary component to the output of the conditional GAN. This would result in generated synthetic real and imaginary images for N coils from a single magnitude-only image input. While this approach produced reasonable phase maps and comparable reconstructions for generative models trained on data acquired with a small number of coils (e.g., N = 4), the phase maps resulting from generative models trained on N = {16, 20} Atty. Docket: UCSF-745WO number of coils suffered from large amounts of structure hallucination and blocking artifacts. It was hypothesized that, during training, gradients across multiple individual coil images are ill-behaved and, thus, GAN models trying to generate a large number of coil images have difficulty converging. The advantage of the proposed technique is that it is coil-agnostic; it can be applied to MR images acquired with any number of coils with the generative model learning a one- to-one mapping from magnitude to phase. This results in more stable training and gradient flow, especially for GANs. It is important to note that it is not expected for the synthetic phase maps to be necessarily consistent with the ground truth phase maps. This is because MR phase is not deterministic, and can vary due to tissue composition, scan parameters such as TE, magnetic field homogeneity, and the RF coil configuration and loading. This inconsistency would be problematic for performing any quantification on the synthetic maps themselves. However, consistency with ground truth phase for individual datasets is not required when the synthetic data are used for training, but rather the synthetic phase should be consistent with population-level phase patterns. Nevertheless, enforcing a physics-based consistency between the input magnitude image and output phase image by adding a regularized term in k-space to the training objective could be a useful follow-up experiment to this work. Such a change could result in even more representative phase maps. However, GAN stability during training with this new objective remains an open question and would have to be answered empirically. In lieu of this, a score-based generative model could be used for this technique due to their improved training stability compared to GANs Another limitation of this study was the homogeneous makeup of fast spin-echo (FSE) acquired images in fastMRI used to train the generative model. The exclusion of gradient- recalled echo acquired data in the training dataset made the trained generative models and downstream reconstruction models susceptible to distribution shift errors when run at inference time on images not acquired with FSE acquisitions. Follow up experiments could include fine tuning existing trained generative models with MR images acquired with GRE sequences. Additionally, quantifying the uncertainty in distributions not seen at inference time as proposed in

[0028] could give insight into how the generative model is synthesizing phase images on a pixel-wise basis. Finally, evaluation of generative models is still an open debate. While this study used an MRI-centric approach to evaluate the utility of synthetic phase and multi-coil k-space using unrolled image reconstruction, more traditional methods such as the Inception Score

[0029] or FID score

[0030] could be used to characterize the distribution of the generated synthetic phase data. Incorporating a customized implementation based on medical imaging datasets such as

[0031] instead of existing methods based on features trained on natural images could be Atty. Docket: UCSF-745WO more fruitful in characterizing synthetic phase and directing generative model training to datasets customized for downstream tasks. CONCLUSION This work presented a new method for synthesizing realistic MRI data that is complex- valued and multichannel from magnitude-only images, which were evaluated by comparing the reconstruction performance of Variational Networks trained on ground-truth k-space and synthetic k-space. The results suggested that this approach for generating synthetic phase and multicoil data is adequate for training MRI reconstruction models at typical acceleration factors (up to 10x), shown by the Variational Networks results. Taken together, results suggested that image-to-image translation generative adversarial networks are able to generate MRI phase images that are both realistic looking and can also provide good performance when used for training an image reconstruction task. This allows for the possibility of using large and diverse clinical imaging databases when developing deep learning methods that include image reconstruction tasks.

[0002] Atty. Docket: UCSF-745WO REFERENCES [1] Florian Knoll, Tullie Murrell, Anuroop Sriram, Nafissa Yakubova, Jure Zbontar, Michael Rabbat, Aaron Defazio, Matthew J. Muckley, Daniel K. Sodickson, C. Lawrence Zitnick, and Michael P. Recht. Advancing machine learning for MR image reconstruction with an open competition: Overview of the 2019 fastMRI challenge. Magnetic Resonance in Medicine, 84(6):3054–3070, June 2020. [2] Efrat Shimron, Jonathan I. Tamir, Ke Wang, and Michael Lustig. Implicit data crimes: Machine learning bias arising from misuse of public data. Proceedings of the National Academy of Sciences, 119(13), March 2022. [3] Kerstin Hammernik, Thomas K¨ustner, Burhaneddin Yaman, Zhengnan Huang, Daniel Rueckert, Florian Knoll, and Mehmet Akcakaya. Physics-driven deep learning for computational magnetic resonance imaging, 2022. [4] Matthew J. Muckley, Bruno Riemenschneider, Alireza Radmanesh, Sunwoo Kim, Geunu Jeong, Jingyu Ko, Yohan Jun, Hyungseob Shin, Dosik Hwang, Mahmoud Mostapha, Simon Arberet, Dominik Nickel, Zaccharie Ramzi, Philippe Ciuciu, Jean-Luc Starck, Jonas Teuwen, Dimitrios Karkalousos, Chaoping Zhang, Anuroop Sriram, Zhengnan Huang, Nafissa Yakubova, Yvonne W. Lui, and Florian Knoll. Results of the 2020 fastMRI challenge for machine learning MR image reconstruction. IEEE Transactions on Medical Imaging, 40(9):2306–2317, September 2021. [5] Francesco Caliva’, Rutwik Shah, Upasana Upadhyay Bharadwaj, Sharmila Majumdar, Peder Larson, and Valentina Pedoia. Breaking speed limits with simultaneous ultra-fast {mri} reconstruction and tissue segmentation. In Medical Imaging with Deep Learning, 2020. [6] Holger Eggers and Peter B¨ornert. Chemical shift encoding-based water-fat separation methods. Journal of Magnetic Resonance Imaging, 40(2):251–268, January 2014. [7] Xiang He and Dmitriy A. Yablonskiy. Biophysical mechanisms of phase contrast in gradient echo MRI. Proceedings of the National Academy of Sciences, 106(32):13558–13563, August 2009. [8] Michael Markl, Frandics P. Chan, Marcus T. Alley, Kris L. Wedding, Mary T. Draney, Chris J. Elkins, David W. Parker, Ryan Wicker, Charles A. Taylor, Robert J. Herfkens, and Norbert J. Pelc. Timeresolved three-dimensional phase-contrast MRI. Journal of Magnetic Resonance Imaging, 17(4):499–506, March 2003. Atty. Docket: UCSF-745WO [9] Baiyan Zhuang, Arlene Sirajuddin, Shihua Zhao, and Minjie Lu. The role of 4d flow MRI for clinical applications in cardiovascular disease: current status and future perspectives. Quantitative Imaging in Medicine and Surgery, 11(9):4193–4210, September 2021.

[0010] Jeff H. Duyn, Peter van Gelderen, Tie-Qiang Li, Jacco A. de Zwart, Alan P. Koretsky, and Masaki Fukunaga. High-field MRI of brain cortical substructure based on signal phase. Proceedings of the National Academy of Sciences, 104(28):11796–11801, July 2007.

[0011] Elizabeth Cole, Joseph Cheng, John Pauly, and Shreyas Vasanawala. Analysis of deep complex-valued convolutional neural networks for MRI reconstruction and phase-focused applications. Magnetic Resonance in Medicine, 86(2):1093–1109, March 2021.

[0012] Joshua Bassey, Lijun Qian, and Xianfang Li. A survey of complex-valued neural networks, 2021.

[0013] Sooyeon Ji, Dongjin Yang, Jongho Lee, Seung Hong Choi, Hyeonjin Kim, and Koung Mi Kang. Synthetic scpMRI / scp : Technologies and applications in neuroradiology. Journal of Magnetic Resonance Imaging, 55(4):1013–1025, November 2020.

[0014] Vikas Gulani, Peter Schmitt, Mark A. Griswold, Andrew G. Webb, and Peter M. Jakob. Towards a single-sequence neurologic magnetic resonance imaging examination: Multiple- contrast images from an IR TrueFISP experiment. Investigative Radiology, 39(12):767–774, December 2004.

[0015] J.B.M. Warntjes, O. Dahlqvist Leinhard, J. West, and P. Lundberg. Rapid magnetic resonance quantification on the brain: Optimization for clinical usage. Magnetic Resonance in Medicine, 60(2):320–329, August 2008.

[0016] Yongsheng Chen, Saifeng Liu, Yu Wang, Yan Kang, and E. Mark Haacke. STrategically acquired gradient echo (STAGE) imaging, part i: Creating enhanced t1 contrast and standardized susceptibility weighted imaging and quantitative susceptibility mapping. Magnetic Resonance Imaging, 46:130–139, February 2018.

[0017] Yu Wang, Yongsheng Chen, Dongmei Wu, Ying Wang, Sean K. Sethi, Guang Yang, Haibin Xie, Shuang Xia, and E. Mark Haacke. STrategically acquired gradient echo (STAGE) imaging, part II: Correcting for RF inhomogeneities in estimating t1 and proton density. Magnetic Resonance Imaging, 46:140–150, February 2018. Atty. Docket: UCSF-745WO

[0018] E. Mark Haacke, Yongsheng Chen, David Utriainen, BoWu, YuWang, Shuang Xia, Naying He, Chunyan Zhang, Xiao Wang, M. Marcella Lagana, Yu Luo, Ali Fatemi, Saifeng Liu, Sara Gharabaghi, Dongmei Wu, Sean K. Sethi, Feng Huang, Taotao Sun, Feifei Qu, Brijesh K. Yadav, Xiaoyue Ma, Yan Bai, Meiyun Wang, Jingliang Cheng, and Fuhua Yan. STrategically acquired gradient echo (STAGE) imaging, part III: Technical advances and clinical applications of a rapid multi-contrast multi-parametric brain imaging method. Magnetic Resonance Imaging, 65:15–26, January 2020.

[0019] Martina F. Callaghan, Siawoosh Mohammadi, and Nikolaus Weiskopf. Synthetic quantitative MRI through relaxometry modelling. NMR in Biomedicine, 29(12):1729–1738, October 2016.

[0020] I Blystad, JBM Warntjes, O Smedby, A-M Landtblom, P Lundberg, and E-M Larsson. Synthetic mri of the brain in a clinical setting. Acta Radiologica, 53(10):1158–1163, December 2012.

[0021] Michael Loecher, Luigi E. Perotti, and Daniel B. Ennis. Using synthetic data generation to train a cardiac motion tag tracking neural network. Medical Image Analysis, 74:102223, December 2021.

[0022] Florian Knoll, Kerstin Hammernik, Erich Kobler, Thomas Pock, Michael P Recht, and Daniel K Sodickson. Assessment of the generalization of learned image reconstruction and the potential for transfer learning. Magnetic Resonance in Medicine, 81(1):116–128, May 2018.

[0023] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Z. Ghahramani, M. Welling, C. Cortes, N. Lawrence, and K.Q. Weinberger, editors, Advances in Neural Information Processing Systems, volume 27. Curran Associates, Inc., 2014.

[0024] Phillip Isola, Jun-Yan Zhu, Tinghui Zhou, and Alexei A. Efros. Image-to-image translation with conditional adversarial networks. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, July 2017.

[0025] Anuroop Sriram, Jure Zbontar, Tullie Murrell, Aaron Defazio, C. Lawrence Zitnick, Nafissa Yakubova, Florian Knoll, and Patricia Johnson. End-to-end variational networks for accelerated MRI reconstruction. In Medical Image Computing and Computer Assisted Intervention – MICCAI 2020, pages 64–73. Springer International Publishing, 2020. Atty. Docket: UCSF-745WO

[0026] Martin Uecker, Peng Lai, Mark J. Murphy, Patrick Virtue, Michael Elad, John M. Pauly, Shreyas S. Vasanawala, and Michael Lustig. ESPIRiT-an eigenvalue approach to autocalibrating parallel MRI: Where SENSE meets GRAPPA. Magnetic Resonance in Medicine, 71(3):990– 1001, May 2013.

[0027] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4):600–612, 2004.

[0028] Anastasios N Angelopoulos, Amit Pal Kohli, Stephen Bates, Michael Jordan, Jitendra Malik, Thayer Alshaabi, Srigokul Upadhyayula, and Yaniv Romano. Image-to-image regression with distributionfree uncertainty quantification and applications in imaging. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, and Sivan Sabato, editors, Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pages 717–730. PMLR, 17–23 Jul 2022.

[0029] Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, Xi Chen, and Xi Chen. Improved techniques for training gans. In D. Lee, M. Sugiyama, U. Luxburg, I. Guyon, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 29. Curran Associates, Inc., 2016.

[0030] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. In I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017.

[0031] Xueyan Mei, Zelong Liu, Philip M. Robson, Brett Marinelli, Mingqian Huang, Amish Doshi, Adam Jacobi, Chendi Cao, Katherine E. Link, Thomas Yang, Ying Wang, Hayit Greenspan, Timothy Deyer, Zahi A. Fayad, and Yang Yang. RadImageNet: An open radiologic deep learning research dataset for effective transfer learning. Radiology: Artificial Intelligence, 4(5), September 2022. Example 2 – Multi Synthetic Multi-Coil Data Generation Require: MRI Magnitude-only image ^D^^, ^^ a (single-channel) image capturing magnitude component of an MRI scan. Atty. Docket: UCSF-745WO Ensure: Synthetic multi-coil datasets in image domain ^FE,^^^, ^, G^ of k-space domain ^EF,^^^^, ^^, G^ each synthetic dataset is a matrix of complex numbers representing spatial frequency components, produced for multiple coils. 1. Train latent vector 9 with magnitude / phase BicycleGAN to model the distribution of MRI phase images 2. Randomly sample HIphase images ϕE^^, ^^ from trained latent vector 9 where ϕE^^, ^^~L MN$ O = 1 PN HIfor i = 1 to Np;these images represent possible phase variations of a given magnitude image 3. Randomly select HQcoils R^^^, ^, G^ from the RF coil library where R^~R MN$ ^ = 1 PN HQ: these coils represent different sensitivity patterns from the MRI scanner and each coil includes a set of sensitivity maps corresponding to each coil element in the final dimension, G. 4. Apply 2D Gaussian filter to coil sensitivity maps yielding RTS^^, ^, G^ = !#UVVO#W^,^(R^^^, ^, G^^: this step smooths the sensitivity maps to reduce noise and artifacts 5. Randomly rotate sensitivity maps in a given coil by 90˚ yielding rotated maps for RXY^, ^, G^ = ZNP#P^^RX^^^, ^, G, ^, 90˚^ for G = 1 PN H\where H\is the number of coil elements: this operation models variations in coil orientation 6. Create complex-valued synthetic image sampling from the synthetic phase images: ^EF^^, ^^ = ^D^^, ^^ ∗ ^^]^OϕE^^, ^^^7. incorporating one of the RF coil sensitivity profiles from the RF coil library: ^EF,^^^, ^, G^ = ^EF^^, ^^ ∗ RTS^^, ^, G^ for G = 1 PN H\8. If desired, convert images to k-space data via the Fourier Transform in the spatial dimensions: ^EF,^^^^, ^^, G^ =^^^,^^Y^EF,^^^, ^, G^} 9. Repeat for multiple combinations of synthetic phase ϕEand RF coils, R^and return all generated multi-coil datasets Accordingly, the preceding merely illustrates the principles of the present disclosure. It will be appreciated that those skilled in the art will be able to devise various arrangements which, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples and conditional language recited herein are principally intended to aid the reader in understanding the principles of the invention and the concepts contributed by the inventors to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and Atty. Docket: UCSF-745WO embodiments of the invention as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents and equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure. The scope of the present invention, therefore, is not intended to be limited to the exemplary embodiments shown and described herein.

Claims

Atty. Docket: UCSF-745WO WHAT IS CLAIMED IS:

1. A method of synthesizing raw multichannel data, the method comprising: receiving initial magnitude image data; and producing phase image data from the initial magnitude image data using a generative model to synthesize the raw multichannel data.

2. The method according to claim 1, further comprising reconstructing an image based on the synthesized raw multichannel data.

3. The method according to claim 1 or 2, further comprising generating sensitivity profiles for a plurality of signal receivers.

4. The method according to claim 3, further comprising combining the sensitivity profiles with the initial magnitude image data and the phase image data.

5. The method according to claim 3 or 4, wherein generating the sensitivity profiles comprises using eigenvector-derived maps.

6. The method according to claim 5, wherein generating the sensitivity profiles comprises an ESPIRiT process.

7. The method according to any one of claims 1 to 6, comprising a premade RF coil library which contains a set of plausible RF coil sensitivity profiles.

8. The method according to any one of claims 4 to 7, further comprising analytically converting the initial magnitude image data and the phase image data to real and imaginary components.

9. The method according to claim 8, wherein combining the sensitivity profiles with the initial magnitude image data and the phase image data comprises combining the sensitivity profiles with the real and imaginary components.

10. The method according to any one of the preceding claims, wherein the generative model is a deep learning-based generative model configured to leverage a dataset of prior images or raw data.Atty. Docket: UCSF-745WO 11. The method according to claim 10, wherein the dataset is a concurrent dataset.

12. The method according to claim 10, wherein the dataset is a historical dataset.

13. The method according to any one of claims 10 to 12, wherein the generative model comprises a discriminator configured to judge the realism of the synthesized raw multichannel data.

14. The method according to claim 13, wherein the discriminator is a PatchGAN discriminator.

15. The method according to any one of claims 10 to 14, wherein the generative model is a generative adversarial network (GAN).

16. The method according to any one of claims 10 to 14, wherein the generative model is a diffusion model 17. The method according to any one of claims 10 to 15, wherein the generative model is a conditional deep learning-based generative model.

18. The method according to any one of the preceding claims, wherein the generative model comprises an optimized loss function.

19. The method according to claim 18, wherein the generative model comprises a plurality of loss functions.

20. The method according to claim 18 or 19, wherein the generative model generates multiple plausible phase images from a single input magnitude image.

21. The method according to claim 19 or 20, wherein the generative model comprises a loss function derived by a probabilistic model.

22. The method according to claim 3, wherein the signal receivers are radiofrequency coil receivers.Atty. Docket: UCSF-745WO 23. The method according to any one of the preceding claims, wherein the initial magnitude image data is magnetic resonance imaging (MRI) image data.

24. The method according to claim 23, wherein the raw multichannel data is k-space data.

25. The method according to any one of claims 1 to 21, wherein initial magnitude image data is synthetic aperture radar (SAR) data.

26. The method according to any one of claims 1 to 21, wherein initial magnitude image data is ultrasound data.

27. The method according to any one of claims 1 to 21, wherein the initial magnitude image data is time-resolved optical microscopy data.

28. The method according to any one of claims 1 to 21, wherein the initial magnitude image data is hyperspectral imaging data.

29. The method according to any one of claims 1 to 21, further comprising using the raw data for self-driving car navigation.

30. A non-transitory computer-readable medium comprising instructions stored thereon, which when executed by a processor, cause the processor to perform a method comprising: receiving initial magnitude image data; and producing phase image data from the initial magnitude image data using a generative model to synthesize the raw multichannel data.

31. The non-transitory computer-readable medium according to claim 30, wherein the method further comprises reconstructing an image based on the synthesized raw multichannel data.

32. The non-transitory computer-readable medium according to claim 30 or 31, wherein the method further comprises generating sensitivity profiles for a plurality of signal receivers.Atty. Docket: UCSF-745WO 33. The non-transitory computer-readable medium according to claim 32, wherein the method further comprises combining the sensitivity profiles with the initial magnitude data and the phase image data.

34. The non-transitory computer-readable medium according to claim 32 or 33, wherein generating the sensitivity profiles comprises using eigenvector maps.

35. The non-transitory computer-readable medium according to claim 34, wherein generating the sensitivity profiles comprises an ESPIRiT process.

36. The non-transitory computer-readable medium according to any one of claims 33 to 35, wherein the method further comprises analytically converting the initial magnitude image data and the phase image data to real and imaginary components.

37. The non-transitory computer-readable medium according to claim 36, wherein combining the sensitivity profiles with the initial magnitude image data and the phase image data comprises combining the sensitivity profiles with the real and imaginary components.

38. The non-transitory computer-readable medium according to any one of claims 30 to 37, wherein the generative model is a deep learning-based generative model configured to leverage a dataset of prior images or raw data.

39. The non-transitory computer-readable medium according to claim 38, wherein the dataset is a concurrent dataset.

40. The non-transitory computer-readable medium according to claim 38, wherein the dataset is a historical dataset.

41. The non-transitory computer-readable medium according to any one of claims 38 to 40, wherein the generative model comprises a discriminator configured to judge the realism of the synthesized raw multichannel data.

42. The non-transitory computer-readable medium according to claim 41, wherein the discriminator is a PatchGAN discriminator.Atty. Docket: UCSF-745WO 43. The non-transitory computer-readable medium according to any one of claims 38 to 42, wherein the generative model is a generative adversarial network (GAN).

44. The non-transitory computer-readable medium according to any one of claims 38 to 42, wherein the generative model is a diffusion model.

45. The non-transitory computer-readable medium according to any one of claims 38 to 43, wherein the generative model is a conditional deep learning-based generative model.

46. The non-transitory computer-readable medium according to any one of claims 30 to 45, wherein the generative model comprises a loss function.

47. The non-transitory computer-readable medium according to claim 46, wherein the generative model comprises a plurality of loss functions.

48. The non-transitory computer-readable medium according to claim 46 or 47, wherein the generative model comprises a loss function derived by a probabilistic model.

49. The non-transitory computer-readable medium according to any one of claims 30 to 48, wherein the initial magnitude image data is magnetic resonance imaging (MRI) data.

50. The non-transitory computer-readable medium according to claim 49, wherein the raw multichannel data is k-space data.

51. The non-transitory computer-readable medium according to any one of claims 30 to 48, wherein initial magnitude image data is synthetic aperture radar (SAR) data.

52. The non-transitory computer-readable medium according to any one of claims 30 to 48, wherein initial magnitude image data is ultrasound data.

53. The non-transitory computer-readable medium according to any one of claims 30 to 48, wherein the initial magnitude image data is time-resolved optical microscopy data.

54. The non-transitory computer-readable medium according to any one of claims 30 to 48, wherein the initial magnitude image data is hyperspectral imaging data.Atty. Docket: UCSF-745WO 55. The non-transitory computer-readable medium according to any one of claims 30 to 48, wherein the method further comprises using the raw data for self-driving car navigation.

56. A system for synthesizing raw multichannel data, the system comprising: a processor; and a non-transitory computer-readable medium comprising instructions stored thereon, which when executed by the processor, cause the processor to: receive initial magnitude image data from a plurality of signal receivers; and produce phase image data from the initial magnitude image data using a generative model.

57. The system according to claim 56, wherein the system is configured to reconstruct an image based on the synthesized raw multichannel data.

58. The system according to claim 56 or 57, wherein the processor is configured to generate sensitivity profiles for a plurality of signal receivers.

59. The system according to claim 58, wherein the processor is configured to combine the sensitivity profiles with the initial magnitude image data and the phase image data to synthesize the raw multichannel data.

60. The system according to claim 58 or 59, wherein generating the sensitivity profiles comprises using eigenvector maps.

61. The system according to claim 60, wherein generating the sensitivity profiles comprises an ESPIRiT process.

62. The system according to any one of claims 59 to 61, wherein the system is configured to convert the initial magnitude image data and the phase image data to real and imaginary components.

63. The system according to claim 62, wherein combining the sensitivity profiles with the initial magnitude image data and the phase image data comprises combining the sensitivity profiles with the real and imaginary components.Atty. Docket: UCSF-745WO 64. The system according to any one of claims 56 to 63, wherein the generative model is a deep learning-based generative model configured to leverage a dataset of prior images or raw data.

65. The system according to claim 64, wherein the dataset is a concurrent dataset.

66. The system according to claim 64, wherein the dataset is a historical dataset.

67. The system according to any one of claims 64 to 66, wherein the generative model comprises a discriminator configured to judge the realism of the synthesized raw multichannel data.

68. The system according to claim 67, wherein the discriminator is a PatchGAN discriminator.

69. The system according to any one of claims 64 to 68, wherein the generative model is a generative adversarial network (GAN).

70. The system according to any one of claims 64 to 68, wherein the generative model is a diffusion model.

71. The system according to any one of claims 64 to 69, wherein the generative model is a conditional deep learning-based generative model.

72. The system according to any one of claims 56 to 71, wherein the generative model comprises a loss function.

73. The system according to claim 72, wherein the generative model comprises a plurality of loss functions.

74. The system according to claim 73, wherein the generative model comprises a loss function derived by a probabilistic model.

75. The system according to claim 58, further comprising the plurality of signal receivers.Atty. Docket: UCSF-745WO 76. The system according to claim 75, wherein the signal receivers are radiofrequency coil receivers.

77. The system according to any one of claims 56 to 76, wherein the initial magnitude image data is magnetic resonance imaging (MRI) data.

78. The system according to claim 77, wherein the raw multichannel data is k-space data.

79. The system according to any one of claims 56 to 76, wherein initial magnitude image data is synthetic aperture radar (SAR) data.

80. The system according to any one of claims 56 to 76, wherein initial magnitude image data is ultrasound data.

81. The system according to any one of claims 56 to 76, wherein the initial magnitude image data is time-resolved optical microscopy data.

82. The system according to any one of claims 56 to 76, wherein the initial magnitude image data is hyperspectral imaging data.

83. The system according to any one of claims 56 to 76, wherein the system is comprised of a self-driving car.

84. The system according to claim 57, further comprising a display configured to portray the reconstructed image.

Images