Systems and methods for enforcing data consistency in data reconstruction

Abstract

The present disclosure provides a computing apparatus comprising a processor and computer-readable storage media storing instructions that, when executed, direct the apparatus to: receive input data for a data reconstruction task; process the input data using a neural network model comprising a first set of neural network layers configured to perform data reconstruction and a second set of neural network layers configured to enforce data consistency, wherein both sets of layers are utilized during training and inference; generate intermediate reconstructed data using the first set of layers; generate data-consistent reconstructed data by modifying the intermediate reconstructed data using the second set of layers to enforce consistency with the input data; and output the data-consistent reconstructed data as a final output of the neural network model. The system and techniques provided herein enable improved data reconstruction while maintaining consistency with input data.

Description

SYSTEMS AND METHODS FOR ENFORCING DATA CONSISTENCY IN DATA RECONSTRUCTIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 650,258, titled SYSTEMS AND METHODS FOR ENFORCING DATA CONSISTENCY IN DATA RECONSTRUCTION, filed on May 21, 2024, which is hereby incorporated by reference in its entirety.TECHNICAL FIELD

[0002] Aspects of the disclosure are related to the field of data reconstruction and machine learning systems, in particular to technology for enforcing data consistency during neural network-based reconstruction of incomplete or corrupted datasets.BACKGROUND

[0003] In the modem era, neural networks and machine learning models are becoming increasingly relied upon tools for solving a wide range of complex computational tasks, including classification, prediction, and data transformation. One critical application area is data reconstruction, where machine learning techniques are used to restore, estimate, or complete data that may be missing, noisy, or degraded. Traditional reconstraction techniques, such as interpolation or analytic transformations (e.g., inverse discrete Fourier transform), often depend on idealized assumptions like uniform sampling or linearity, which may not hold in real-world data acquisition environments. In contrast, machine learning-based methods can model non-linear relationships and high-dimensional dependencies directly from empirical data, making them more robust in practical scenarios.

[0004] Deep learning methods for data reconstruction are utilized to recover or reconstruct data from noisy, corrupted, or incomplete datasets. These techniques leverage the capabilities of deep learning models to learn complex patterns and dependencies in the data, making them particularly effective for tasks involving the reconstruction of missing data, such as image reconstruction and signal processing. For example, neural networks can be trained to reconstruct images from incomplete datasets, addressing gaps or errors in the original data. This approach is particularly useful in applications where traditional methods, like the inversediscrete Fourier transformation, rely on assumptions such as the Nyquist-Shannon sampling theorem that are often not valid in real-world scenarios.SUMMARY

[0005] Systems and methods for enforcing data consistency during data reconstruction are provided herein. In particular, an enforcement engine is disclosed that ensures reconstructed data retains any known values present in the input data throughout the reconstruction process. In one aspect, the enforcement engine may receive input data for a data reconstruction task, such as under-sampled or partially corrupted data from a sensing device. Responsive to receiving the input data, the enforcement engine may process the data using a neural network model comprising multiple sets of layers. The model includes a first set of neural network layers configured to perform data reconstruction by estimating or inferring missing values, and a second set of neural network layers configured to enforce data consistency by correcting the reconstructed output to match the known input values. Both the reconstruction and consistency layers are used during training and inference, allowing the model to learn and apply consistency-preserving behavior at all stages.

[0006] During processing, the first set of neural network layers may generate intermediate reconstructed data from the input data. This intermediate output, while partially complete, may not fully preserve the known values due to reconstruction errors or overfitting. The second set of neural network layers may then modify the intermediate reconstructed data using a data consistency operation — such as a proximal operator or projection step — to ensure that any known values in the original input are correctly retained in the final result. In some embodiments, this consistency enforcement may occur in a transformed domain, such as the Fourier domain, by applying a Fourier transform to the intermediate output, performing consistency corrections, and then transforming the corrected output back to the spatial domain. The neural network model may then output the corrected, data-consistent reconstruction as its final output.

[0007] In certain embodiments, the neural network model may also include one or more task-specific layers designed to perform downstream tasks, such as classification, segmentation, or detection, based on the data-consistent reconstructed data. In these cases, the task-specific layers may process the consistent output to generate a task-specific result, which may be returned as the final output of the model. The system may be configured to work across domains — including but not limited to magnetic resonance imaging (MRI), image processing,text processing, or audio reconstruction — and may be trained using labeled, unlabeled, or synthetically corrupted data samples. For example, in MRI applications, the input data may include under-sampled k-space data, and the consistency layer may enforce alignment with those k-space values during both learning and inference.

[0008] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Technical Disclosure. It may be understood that this Overview is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Many aspects of the disclosure may be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. While several embodiments are described in connection with these drawings, the disclosure is not limited to the embodiments disclosed herein. On the contrary, the intent is to cover all alternatives, modifications, and equivalents.

[0010] Figure 1 is a diagram of a system for enforcing data consistency during image reconstruction, in accordance with an embodiment herein.

[0011] Figure 2 is an example flow demonstrating challenges present with conventional approaches to data reconstruction, in accordance with an embodiment herein.

[0012] Figure 3 is an example flow 300 demonstrating the impact of conventional data reconstruction approaches in the context of Fourier-domain applications, in accordance with an embodiment herein.

[0013] Figure 4 is an example environment in which an enforcement engine is leveraged to enforce data consistency during data reconstruction, in accordance with an embodiment herein.

[0014] Figure 5 is a process for providing an enforcement engine and one or more of its functions, in accordance with an embodiment herein.

[0015] Figure 6 is an example flow 600 showing a data reconstruction process similar to that described in Figure 2 but augmented with a projection layer for enforcing data consistency, according to an embodiment herein.

[0016] Figure 7 is an example system 700 including a neural network model 704 and a respective training module 744, according to an embodiment herein.

[0017] Figures 8A-C provide an example set of knee MRI images illustrating the effect of data consistency enforcement on image reconstruction quality, in accordance with an embodiment herein.

[0018] Figure 9 is an example computing device suitable for enforcing data consistency in data reconstruction, in accordance with an embodiment herein.

[0019] The images included herein are representative and provided for illustrative purposes only. Although the intention was to use images generated using actual data, such data was subject to various restrictions. As a result, the included images are illustrative representations rather than the actual reconstructed images.DETAILED DESCRIPTION

[0020] Deep learning methods, widely employed for data reconstruction, exhibit a tendency to introduce inconsistencies when handling incomplete or corrupted datasets. While these techniques harness the capabilities of deep learning models to discern intricate patterns and dependencies within data, they often inadvertently alter known values while reconstructing missing or noisy data. For instance, in the domain of image reconstruction, neural networks trained to fill in gaps or correct corruptions may inadvertently modify valid data points, leading to discrepancies between the original and reconstructed data. Despite advances in reconstruction efficiency through techniques like Fourier sampling, parallel imaging, and compressed sensing, these approaches often fall short in preserving data fidelity — particularly when integrated with deep learning methods. While deep learning has the potential to improve reconstruction speed and accuracy, conventional models frequently struggle to maintain consistency with the original input data, leading to artifacts and reduced trust in the final output.

[0021] Existing frameworks for mitigating inconsistencies in deep learning-based data reconstruction commonly involve either modifying the loss function or incorporating data consistency layers into neural network architectures. While these strategies can improve alignment with expected outputs, they often fall short of addressing the underlying causes of reconstruction errors. For instance, altering the loss function may promote greater consistency but does not necessarily ensure the accuracy or fidelity of the reconstructed data. Likewise, current implementations of data consistency layers can be computationally intensive and may still produce outputs that deviate from the true data distribution.

[0022] The presence of inconsistencies in reconstructed data can lead to technical and practical consequences, particularly in high-stakes domains where data fidelity is critical. In many cases, neural networks may "hallucinate" features — generating data artifacts that do not correspond to any real input — thereby introducing false or misleading information. For example, in medical imaging applications such as CT or MRI scans, a reconstruction algorithm that inadvertently inserts a tumor-like structure into an image where none exists could lead to an incorrect diagnosis, unnecessary treatment, or undue psychological stress for the patient. Similarly, in autonomous navigation systems, a neural network that reconstructs or enhances sensor data might incorrectly insert objects — such as hallucinating a pedestrian in the vehicle’s path or failing to reconstruct an obstacle — potentially causing unsafe driving decisions and leading to collisions or other hazardous outcomes. Such errors undermine the trustworthiness and utility of machine learning systems and highlight the need for architectures that preserve data integrity throughout the reconstruction pipeline.

[0023] The challenges associated with enforcing data consistency are further exacerbated in reconstruction scenarios involving structured sensing modalities, such as those based on Fourier-domain measurements. In such cases, the measurement operator A often represents a partial or undersampled Fourier transform, as is common in magnetic resonance imaging (MRI), synthetic aperture radar (SAR), and other frequency-domain imaging techniques. While certain post-processing approaches can enforce data consistency — such as performing a Euclidean projection onto the constraint set {x : IIAx-yll < E } these methods have notable drawbacks. Here, II II denotes a norm or some other function that maps Ax-y to a scalar value. For example, Chang el al. (“Deep Learning for Undersampled MRI Reconstruction,” Phys. Med. Biol., 63(13) : 135007, 2018) demonstrated such a projection-based correction to enforce consistency after reconstruction. Although this technique can impose data consistency, it often perturbs the reconstructed image more than necessary, leading to artifacts and loss of fidelity.

[0024] Moreover, because consistency is only enforced during post-processing within these conventional approaches, the neural network model does not learn to generate data- consistent outputs during training. This disconnect between training and inference phases reduces the model’s ability to generalize and produce reliable reconstructions. The problem becomes even more pronounced in complex acquisition scenarios, such as parallel MRI or SAR with multiple sensing channels, where the sensing models involve spatially varying or overlapping sensitivity profiles. In such cases, simple projection techniques are often infeasible or insufficient to enforce consistency. As a result, maintaining data consistency in structuredsensing systems remains an unresolved technical challenge in the design of deep learning-based reconstruction frameworks.

[0025] To address the limitations of conventional data reconstruction methods — particularly their inability to ensure consistency with input data — an enforcement engine is disclosed herein. As described in further detail below, the enforcement engine operates as an integrated component within the reconstruction pipeline to enforce consistency between the reconstructed output and the input data throughout the inference process. In contrast to traditional approaches that apply data consistency heuristically in post-processing or approximate it via modified loss functions during training, the enforcement engine applies consistency constraints directly during both training and inference. This ensures that the reconstructed outputs remain faithful to the original input data — which may include raw measurement data or transformed representations thereof — thereby preserving data integrity and reducing the likelihood of reconstruction-induced artifacts or errors.

[0026] In addition to improving reconstruction accuracy, the enforcement engine offers numerous advantages in terms of data efficiency. Unlike conventional reconstruction techniques that require large, well-curated, and fully paired datasets for training, the enforcement engine enables learning from more limited or imperfect data sources. That is, the enforcement engine supports training using unpaired, partially corrupted, or undersampled datasets, making it well-suited for real- world scenarios where comprehensive ground truth data may be unavailable. The enforcement engine may also be compatible with advanced machine learning paradigms such as self-supervised learning, zero-shot reconstruction, and Physics- Informed Neural Networks (PINNs), which further enhance its generalizability across diverse data domains.

[0027] As used herein, input data refers broadly to any data provided to the reconstruction system, which may include raw measurement data (e.g., sensor outputs such as k-space data in MRI), transformed or subsampled data, text, or other intermediate representations. This flexibility is particularly valuable in environments where access to complete measurement data is constrained or where such data is discarded post-processing, as is often the case in clinical imaging workflows.

[0028] The enforcement engine also improves computational efficiency, enabling faster and more scalable reconstruction. For example, in parallel MRI imaging, the enforcement engine is capable of reconstructing high-resolution 3D volumes (e.g., 256x256x256 voxels) in under 15 seconds using a standard GPU — a process that may otherwise take over 10 minutes when performed using traditional model-based iterative optimization methods. This substantialreduction in computational burden increases throughput and allows system resources to be reallocated to more complex reconstruction tasks. By improving processing speed without compromising accuracy or data consistency, the enforcement engine supports real-time and high- volume applications across a broad range of sensing environments.

[0029] The enforcement engine is broadly applicable to any domain in which data reconstruction is required, regardless of data type or sensing modality. However, the enforcement engine may be particularly advantageous in environments involving structured sensing applications, where measurements are acquired through known transformation-based operators. These include, for example, Fourier-domain sampling (used in MRIs and SAR), Radon transforms (used in computed tomography), non-linear transformations (e.g., used with optical imaging or text-to-number encodings), and compressed sensing techniques common in industrial inspection, geophysical exploration, and astronomical imaging. In such applications, even minor inconsistencies between the reconstructed output and the input data — such as sensor or acquisition system measurements — can lead to materially incorrect results, including false positives, diagnostic omissions, or invalid inferences for downstream tasks.

[0030] To address these challenges, the enforcement engine integrates data consistency constraints directly into the neural network’s architecture in a manner that is both technically robust and computationally efficient. Unlike optimization-based post-processing or deep unrolling techniques, which typically involve repeated iterative solvers and / or require high computational cost, the enforcement engine is a lightweight architectural module. This design eliminates the need for hand-tuned regularization parameters or external correction steps, enabling the generation of consistent and accurate reconstructions in real-time and / or in resource-constrained environments .

[0031] An illustrative, though non-limiting, example of the enforcement engine’s utility is in medical image reconstruction using MRI. In this setting, the enforcement engine enables deep learning models to reconstruct high-quality images from undersampled or noisy k-space data while preserving anatomical features. For instance, the enforcement engine can suppress noise or fill in missing data without hallucinating non-existent structures or omitting subtle yet diagnostically important features — such as tumor margins or cortical boundaries — a commonly observed outcome in conventional approaches. By maintaining strict consistency with the original MRI input data, the enforcement engine reduces the likelihood of reconstruction- induced diagnostic errors and minimizes the need for rescans — conserving clinical resources and reducing patient burden.

[0032] Accordingly, the enforcement engine offers a number of distinct technical advantages over conventional data reconstruction methods. First and foremost, the enforcement engine enforces strict consistency between reconstructed outputs and input data — including measurement data — during both training and inference, rather than relying on approximate consistency through loss functions or post-processing corrections. This direct integration of consistency constraints into the neural network architecture reduces the likelihood of introducing hallucinated features or omitting details, thereby improving the reliability and fidelity of reconstructed data.

[0033] Second, the enforcement engine achieves this consistency without imposing increased computational overhead. The lightweight design of the enforcement engine eliminates the need for iterative solvers, deep unrolling, or hand-tuned regularization, enabling fast, scalable, and real-time performance even in high-resolution or multi-channel reconstruction tasks. Third, the engine supports training with minimal or imperfect datasets, including unpaired, partially corrupted, or undersampled input data, and is compatible with modern training paradigms such as supervised learning, self-supervised learning, and physics- informed modeling. This flexibility reduces data requirements, expands applicability across diverse sensing domains, and enhances the generalization capabilities of reconstruction models. Collectively, these advantages make the enforcement engine a technically robust and versatile solution for high-accuracy, low-latency, and data-efficient reconstruction across a wide range of applications.

[0034] Turning now to the Figures, example techniques and systems for enforcing data consistency during data reconstruction are provided. While the following illustrated embodiments focus on MRI imaging for ease of explanation, it should be appreciated that the systems and methods described herein are equally applicable to data reconstruction generally. For example, the systems and techniques described herein may be used for data reconstruction within decompression (e.g., audio, image, or video decompression), image or video inpainting (where a portion of an image or a video is created), audio recovery (where a portion of degraded audio is created), image recovery (where a portion of a degraded image is recovered), video recovery (where a portion of degraded video is created), language prediction (where a missing portion of text is created), other medical imaging devices (such as positron emission tomography [PET], single photon emission computed tomography [SPECT], electrical impedance tomography [EIT]), and with other Fourier sensing techniques (including radio astronomy, computed tomography, optical coherence tomography, optical projectiontomography, microscopy, radar, synthetic aperture radar, radiometry, and other interferometry).

[0035] Referring now to Figure 1, a diagram of a system 100 for enforcing data consistency during data reconstruction is shown, according to an embodiment herein. The system 100 includes an application service 101 hosted on one or more server computers 103, a sensing device 102, a data reconstruction module 104, an enforcement engine 106, and a client device 110. In some embodiments, components of the system 100 may be associated with organizations engaged in acquiring, processing, and analyzing measurement data for diagnostic, industrial, or scientific purposes. The illustrated components are exemplary and non-limiting — fewer, additional, or alternative elements may be present in various implementations. Moreover, the functional blocks shown may be distributed across physical hardware systems or implemented in software, virtualized environments, or cloud infrastructure.

[0036] The application service 101, hosted on server computers 103, serves as the centralized processing and control environment for the reconstruction pipeline. As such, the application service 101 may manage data communication between the sensing device 102, the data reconstruction module 104, the enforcement engine 106, and the client device 110. In some embodiments, the application service 101 also provides access to stored measurement data or prior reconstructions and may include modules for scheduling, task allocation, or user interaction management. The server computers 103 may include one or more physical or virtual computing systems comprising processors and non-transitory machine-readable storage configured to execute the reconstruction and enforcement logic described herein. System 900 provided in Figure 9 is broadly representative of various components provided in Figure 1, including the server computers 103 and the client device 110.

[0037] The sensing device 102 may include one or more physical systems configured to acquire measurement data from a subject or environment. In one embodiment, the sensing device 102 may be an MRI scanner configured to capture k- space data using RF, gradient, and sensing coils. In other embodiments, the sensing device may be a CT scanner, radar system, seismic array, or other domain- specific sensor. The measurement data acquired by the sensing device 102 serves as the input to the data reconstruction pipeline, where fidelity to this input is preserved via the enforcement engine 106, as described in greater detail below.

[0038] The data reconstruction module 104 may include hardware or software components that perform the core task of reconstructing output data (e.g., images, signals, or volumes) from the raw or undersampled measurement data acquired by the sensing device 102. In the contextof MRI, this may involve reconstructing images from k-space data. The data reconstruction module 104 is hosted as part of the application service 101 and interfaces directly with both the sensing device 102 and the enforcement engine 106. As will be described in greater detail below, the data reconstruction module 104 may include one or more neural network models and as such may apply deep learning-based or hybrid model-based reconstruction algorithms to convert measurement data received from the sensing device 102 into a reconstructed output, such as images or structured signal representations.

[0039] As noted above, the sensing device 102 may include one or more systems configured to acquire measurement data from a subject, object, or environment using structured sensing techniques. Such sensing devices may implement domain-specific transformations (e.g., Fourier, Radon, wavelet, or compressed sensing) during data acquisition. In one embodiment, the sensing device 102 is an MRI scanner comprising gradient coils, radiofrequency (RF) coils, and associated control electronics, configured to acquire k-space data representing the spatial frequency domain of an anatomical volume. In other embodiments, the sensing device 102 may be a CT scanner, ultrasound transducer array, positron emission tomography (PET) system, synthetic aperture radar (SAR) platform, radio telescope, spectrometer, or seismic sensor array. In other embodiments, the sensing device may be a text input system. The sensing device 102 may include integrated computing components for device control, preprocessing, or secure transmission of measurement data to a remote computing environment such as the application service 101.

[0040] The client device 1 10 may include one or more computing systems configured to interact with the application service 101 to review, analyze, or manage data reconstructed by the data reconstruction module 104. The client device 110 may be implemented as a desktop computer, tablet, mobile device, thin client terminal, or any other system capable of interfacing with remote server infrastructure, such as the application service 101. As such, the client device 1 10 may include components such as a display, processor, memory, and user interface elements for visualization, annotation, or control. The client device 110 communicates with the application service 101 via a secure communication channel and may access data through an interface 108 — such as a web-based dashboard, diagnostic viewer, or domain-specific software application. Depending on the use case, the client device 110 may be used by clinicians, engineers, researchers, or technicians to support downstream decision-making, diagnostics, or further processing workflows.

[0041] As noted above, in some embodiments, the sensing device 102 may capture or transmit only a subset of measurement data to the data reconstruction module 104. This mayoccur in scenarios where it is desirable to reduce acquisition time, limit data transmission bandwidth, or constrain storage requirements — such as in MRI, communication transmission, astronomical imaging, or other sensing applications. In these cases, the measurement data provided to the data reconstruction module 104 may be incomplete, sparsely sampled, or partially corrupted. To ensure that the reconstructed data remains faithful to the originally acquired measurements, the system 100 may include an enforcement engine 106. As described in greater detail with respect to Figures 4-7, the enforcement engine 106 may be operably coupled with, or integrated into, the data reconstruction module 104 and is configured to enforce consistency between the known measurement data provided by the sensing device 102 and the reconstructed output generated by the data reconstruction module 104. The enforcement engine 106 may operate as part of the neural network architecture or data reconstruction pipeline, and preserves the measured values while selectively reconstructing or inferring missing or undersampled data, thereby improving the reliability and accuracy of the final output.

[0042] Once the reconstructed data is generated by the data reconstruction module 104, it may be transmitted to the client device 110 for visualization or further analysis. In one example, the client device 110 may be operated by a physician, technician, or other medical professional who accesses the application service 101 to review a reconstructed image 112 captured by an MRI system. The image 112 may be presented via the user interface 108 of the client device 110, enabling interaction with the reconstructed data in a clinical setting. In many domains that rely on data reconstruction — such as medical imaging, industrial inspection, or remote sensing — the accuracy of the reconstruction directly impacts the reliability, interpretability, and utility of the resulting data. Continuing with the MRI example, accurate reconstruction of the MRimage 112 ensures that anatomical structures or pathological features are faithfully preserved, allowing the physician or technician to make informed diagnostic and treatment decisions based on consistent and trustworthy imaging output.

[0043] Referring now to Figure 2, an example flow 200 demonstrating challenges present with conventional approaches to data reconstruction is illustrated, according to various embodiments herein. Input data 214 may comprise measurement data captured by a sensing device, such as sensing device 102. This input data 214 is provided to a neural network model 204 that forms part of the data reconstruction module 104. Upon receiving the input data 214, the neural network model 204 may perform preprocessing, such as tokenizing or embedding the input data 216. The tokenized input data may be converted into an input vector 217 containing multiple known values 218A-218E that correspond to data points directly measuredby sensing device 102, as well as one or more missing values 220A-220B that represent unmeasured or undersampled data points.

[0044] In order to generate a complete dataset, the neural network model 204 processes the input vector 217 and attempts to reconstruct the missing values 220A-220B via one or more neural network layers 221. To do so, the neural network model 204 leverages the observed context — i.e., the known values 218A-218E — to infer and generate predicted values for the missing data points. However, under conventional approaches, the neural network model 204 may not distinguish between known and missing data during inference. As a result, while generating reconstructed values 222A-222B for the missing values 220A-220B, the neural network model 204 may also inadvertently alter one or more of the known values 218A-E. For instance, as illustrated, the neural network model 204 generates a reconstructed vector 219 containing a reconstructed value 222C that replaces a known value, such as value 218D. This undesired replacement typically arises because the neural network model 204, trained on prior datasets, attempts to generate globally consistent outputs based on statistical patterns observed during training — without enforcing strict alignment with the specific known inputs provided at inference time.

[0045] While the example in Figure 2 depicts only seven data points for illustrative clarity, practical applications often involve datasets with hundreds, thousands, or millions of data points, such as high-resolution medical images, multi-channel sensor arrays, large amounts of text, or dense signal measurements. In such cases, even small deviations — such as the replacement of a known value 218D with a reconstructed value 222C — can degrade the reliability and fidelity of the reconstructed output. This behavior may lead to the introduction of artifacts, hallucinated structures, or the suppression of diagnostically or scientifically relevant features, ultimately reducing the trustworthiness of the reconstruction. Accordingly, these challenges highlight the need for architectures that enforce data consistency and preserve known input values throughout the reconstruction process.

[0046] The challenges described above — such as the replacement of known values with reconstructed values — can be further exacerbated in applications that involve domain transformations as part of the reconstruction process. One prominent example is reconstruction from frequency-domain data using Fourier transforms, as is common in MRI, SAR, and other structured sensing domains. In these scenarios, raw measurement data is acquired in a transformed domain (e.g., k-space in MRI) and must be reconstructed into a spatial or temporal domain representation through an inverse transformation. Example transformed domains include the Fourier domain, the wavelet domain, the Radon domain, or other domains specificto a given sensor modality or acquisition technique. When only a subset of the transformed data is sampled — either due to acquisition constraints or for efficiency — neural network models tasked with reconstruction face the dual challenge of interpolating missing frequency-domain values while preserving consistency with those that are known. Conventional models often fail to enforce such consistency, leading to hallucinated structures or the loss of diagnostically or scientifically important features in the final output.

[0047] Referring now to Figure 3, an example flow 300 is illustrated to show the impact of conventional data reconstruction approaches in the context of Fourier-domain applications, according to various embodiments herein. As shown, an accurate MRI image 324 is generated using a complete set of measurement data and depicts a cross-sectional view of a human brain, including multiple visible tumors 325. To simulate an accelerated MRI scan, the measurement data corresponding to MRI image 324 is subjected to a Fourier transform 326A, which converts the spatial-domain image into frequency-domain data (commonly referred to as k-space data in MRI applications) and to sampling 328 to limit the total number of data points retained. Such sampling is common in practice to reduce acquisition time and memory usage. For example, reconstructing a high-resolution 3D MRI volume (e.g., 256x256x256 voxels) using a full k- space dataset may take 10 to 20 minutes per scan. To improve throughput, a subset of k-space data may be acquired or retained, resulting in incomplete input data 314.

[0048] The sampled input data 314, containing only a subset of the frequency-domain measurements required to satisfy the Nyquist-Shannon sampling theorem, is provided to a neural network model 304 — part of a conventional data reconstruction pipeline. The neural network model 304 processes the input data 314 to interpolate or predict values for the missing frequency components, resulting in reconstructed frequency-domain data. The reconstructed data is then passed through an inverse Fourier transform 326B to convert the frequency-domain predictions back into a spatial-domain representation, resulting in a reconstructed image 312. The goal of this reconstruction process is to approximate the original MRI image 324 as accurately as possible using only the partial measurements available.

[0049] However, as illustrated in Figure 3, the reconstructed image 312 generated by the neural network model 304 fails to preserve features that were present in the original MRI image 324 — most notably, the tumors 325. This omission is a direct consequence of the limitations of conventional neural network-based reconstruction models, which often do not enforce strict data consistency with the input measurements. In particular, the neural network model 304 may replace or overwrite known values from the input data 314 with newly generated values that more closely resemble patterns observed in its training data. While this may reduce thereconstruction loss globally, it introduces an increased risk of "hallucination" — where known, true values are substituted with plausible but incorrect predictions. In this example, such behavior leads to the tumors 325 being omitted from the reconstructed image 312, potentially resulting in false negatives during diagnosis. This highlights the importance of enforcing data consistency, especially in Fourier-based reconstruction applications like MRI, where even minor inconsistencies can lead to negative consequences.

[0050] To address at least these shortcomings of conventional approaches to data reconstruction, an enforcement engine 406 is provided herein. Referring now to Figure 4, an example environment 400 in which an enforcement engine 406 is leveraged to enforce data consistency during data reconstruction is illustrated, according to an embodiment herein. For ease of explanation, Figure 4 is described with reference to Figure 5, which illustrates a process 500 for providing an enforcement engine and one or more of its functions, according to an embodiment herein. While Figure 5 is described in relation to Figure 4, it should be appreciated that the process 500 is equally applicable to the remaining figures and components therein.

[0051] To initiate the process 500, the enforcement engine 406 may receive input data 414 for data reconstruction (505). For example, as shown, a sensing device 402 may provide measurement data 407 to the enforcement engine 406, which may be the same as or functionally similar to the enforcement engine 106 described above (510). The measurement data 407 may represent a sampling of data points measured directly by the sensing device 402 and may correspond to spatial, temporal, or frequency-domain measurements or signals depending on the application (e.g., MRI, radar, or sensor arrays). In some embodiments, the measurement data 407 includes only a subset of the full measurement domain due to constraints such as acquisition time, bandwidth, or storage limitations. In other implementations, the enforcement engine 406 may receive the measurement data 407 not directly from the sensing device 402, but instead from an external data source such as a local or cloud-based database, or archival system. This may be the case in scenarios where raw measurement data is stored for deferred processing or batch reconstruction workflows. Regardless of the source, the measurement data 407 serves as input data for the enforcement engine 406, which enforces consistency between these known data points and the output of a data reconstruction process.

[0052] Responsive to receiving the measurement data 407, the enforcement engine 406 may apply one or more preprocessing operations to convert the measurement data into a format suitable for downstream processing. In some implementations, the enforcement engine 406 may include a preprocessor 416 that performs such preprocessing, resulting in a transformed or structured version of the input, referred to as input data 414. The specific preprocessingtechnique applied may vary based on the sensing modality and data type. For example, in the case of MRI or other frequency-domain sensing applications, the preprocessor 416 may apply a Fourier transform to convert the spatial-domain measurement data 407 into frequencydomain representations (e.g., k-space), or vice versa, depending on the reconstruction pipeline. In other applications, such as natural language processing or categorical data analysis, the preprocessor 416 may apply tokenization or embedding operations to convert raw input into discrete, vectorized representations.

[0053] It should be appreciated that in some embodiments, the enforcement engine 406 may receive preprocessed input data 414 directly, such as from a data management service, and proceed to process the input data 414 as described below. In other embodiments, the enforcement engine 406 may receive raw or partially processed measurement data 407 and internally apply preprocessing operations via the preprocessor 416 to generate the input data 414 for further processing.

[0054] Once the input data 414 is generated and / or received, the enforcement engine 406 may process the input data 414 using a neural network model 404 (515). The neural network model 404 may be implemented as a machine learning model, such as a deep learning architecture trained, as described below, to perform both data reconstruction and consistency enforcement. In some embodiments, the neural network model 404 may include an encoderdecoder structure, which encodes the input data 414 into a latent representation and then decodes it into a reconstructed output. Alternatively, or additionally, the neural network model 404 may be implemented using a U-Net architecture, which is well-suited for structured data reconstruction due to its symmetric encoding-decoding paths and skip connections that preserve high-resolution features. These architectural choices enable the neural network model 404 to infer or interpolate missing or corrupted values in the input data 414 while maintaining alignment with known measurement values.

[0055] As shown, the neural network model 404 includes multiple sets of neural network layers, including a first set of neural network layers 430, a second set of neural network layers 432, and a set of task-specific layers 434. Each set of layers 430-434 performs a distinct function in the overall data reconstruction pipeline. As will be described in greater detail below, the input data 414 is processed by these sets of layers to generate a completed and data- consistent output. Specifically, the neural network model 404 may analyze the known values present in the input data 414 and infer or interpolate reconstructed values for one or more missing or unobserved data points. The resulting output may include both the original known values and the predicted values, combined in a manner that maintains consistency with theinput measurement data 407. This layered architecture enables the neural network model 404 to support both general-purpose reconstruction and task-specific optimization while enforcing constraints that preserve the integrity of the original input data 414.

[0056] As will be expanded on in greater detail below with respect to Figure 7, the enforcement engine 406 may include a training module 444. The training module 444 may utilize a training dataset 446 to train the neural network model 404 to perform accurate and consistent data reconstruction. In particular, the training module 444 may be configured to train the neural network model 404 to generate data-consistent reconstructed data — ensuring that known values originally present in the measurement data 407 are preserved in the final output. This may involve optimizing the neural network model 404 to minimize reconstruction loss while simultaneously enforcing data consistency constraints, such as through the application of a proximal operator or projection mechanism within the model architecture. Through this training process, the neural network model 404 learns to distinguish between observed and unobserved portions of the input and to reconstruct missing data points without overwriting or altering verified measurements, thereby improving the reliability and fidelity of the final output.

[0057] Responsive to receiving the input data 414, the neural network model 404 may process the input data 414 using the first set of neural network layers 430 to generate intermediate reconstructed data 436 (520). The first set of neural network layers 430 may include transformer layers, convolutional layers, or other reconstruction-specific architectures trained to infer missing or corrupted values of the input data based on learned patterns. The first set of neural network layers 430 may be trained using a training dataset 446 that includes paired examples of incomplete inputs and their corresponding fully observed or high-fidelity outputs. During inference, the first set of neural network layers 430 applies this learned knowledge to reconstruct the missing or undersampled values of the input data 414. The resulting intermediate reconstructed data 436 may include predicted values for data points that were absent from the original input while preserving or approximating the structure and distribution of the training dataset 446.

[0058] The intermediate reconstructed data 436, however, may not yet be fully consistent with the known values originally present in the input data 414. This can occur because the first set of neural network layers 430 — while capable of reconstructing missing values — may also inadvertently modify or overwrite values or datapoints that should remain fixed. This issue becomes particularly pronounced in reconstruction tasks involving transformed domains, suchas Fourier or wavelet transforms, where reconstruction occurs in a domain different from the input measurement space.

[0059] To mitigate this, the intermediate reconstructed data 436 is provided to the second set of neural network layers 432, which, as described herein, enforce data consistency within the intermediate reconstructed data 436. Responsive to receiving the intermediate reconstructed data 436, the second set of neural network layers 432 generates data-consistent reconstructed data 438 (525). In some implementations, the output of the second set of neural network layers output is the data consistent representation that is closest to the intermediate reconstructed data 436. In some implementations, the neural network layers 432, which is also referred to herein as a projection layer, may function as a proximal operator of the indicator function for the set of data consistent representations to enforce adherence to the known values in the input data 414 (530), correcting deviations introduced by the first set of neural network layers 430.

[0060] The proximal operator functions as a mathematical correction mechanism that forces the final output — the data-consistent reconstructed data 438 — to conform to known constraints, particularly the known values in the original measurement data 407. The projection layer provides an additional layer to ensure that the known values in the input data 414 are preserved to within a noise bound. The proximal operator overwrites or re-aligns the reconstructed values within the intermediate reconstructed data 436 with the original known values of the input data 414, effectively suppressing hallucinations and anchoring the data- consistent reconstructed data 438 to the measured data 407 (535).

[0061] Moreover, in scenarios where the sensing operator A satisfies the Restricted Isometry Property or the Restricted Isometry Property in Levels, the hallucinated values Xh in the null space of A are both small in magnitude and spatially diffuse. In the case of hard data consistency, where the output is within the set {x:Ax=b}, the proximal operator ensures that only reconstructed values are adjusted — while leaving the known values untouched — thereby producing the data-consistent reconstructed data 438 that faithfully reflects the original input and avoids artifacts that could lead to diagnostic or decision-making errors. In the case of soft data consistency, where the output is within the set {x: IIAx-bll < e}.

[0062] Several forms of proximal operators may be used depending on the reconstruction objective and the domain of the input data 414. One common class includes projection proximal operators, which perform a projection of the intermediate output onto a constrained set defined by the known data. For instance, in Fourier-domain reconstruction tasks such as MRI, the proximal operator may enforce that the Fourier coefficients of the reconstructed data match theoriginal coefficients at known frequency indices. Mathematically, this may be expressed as P(x) = flp (x) where Fir (•) is the Euclidean projection onto set F, and F = { lF y (fanOwn) = b] denotes the set of all outputs whose values at the sampled frequency locations fanown match the measured values b. This approach ensures that the data-consistent reconstructed data 438 remains grounded in the known values of the input data 414.

[0063] In an example embodiment, the proximal operator used as the projection layer of the second set of neural network layers 432 may be defined in terms of a constraint on the reconstruction’s consistency with the input data 414. For instance, for a general matrix A, the goal is to ensure that the reconstruction x satisfies the constraint IIAx-blh < s, where b represents the known measurements. The constraint defines the set of acceptable, or data- consistent, solutions. To enforce this constraint using the proximal operator, an indicator function is defined as:I (II Ax- b||2 < 8),

[0064] where the indicator function returns 0 if the constraint is satisfied (i.e., when x is data-consistent), and infinity otherwise. The indicator function acts as a filter only allowing solutions that lie inside the set defined by the constraint and penalizes all others with an infinite cost.

[0065] Then, the proximal operator of a function f finds the closest point (in Euclidean distance) that minimizes a given function (x), the proximal operator becomes:

[0066] which, in simple terms, finds the point x that both (1) makes the function / small and (2) stays as close as possible to the input v (e.g., the intermediate reconstructed data 436). When the function Jis the indicator function described above, the proximal operator becomes:

[0067] which corresponds to the Euclidean projection of v onto the set of data-consistent reconstructed data 438. In the context of deep learning, v corresponds to the intermediate reconstructed data 436 (e.g., output from the first set of neural network layers 430), and the projection step (e.g., the second set of neural network layers 432) modifies this output minimally to ensure it satisfies the data consistency constraints provided by the proximal operator. As a result, the projection layer outputs the closest possible data-consistent reconstructed data 438 to the intermediate reconstructed data 436, thereby preserving theknown values in the output of the projection layer. The projection layer corrects the interpolation to ensure that it aligns with the known values — effectively removing any hallucinated or inconsistent values while preserving what is already accurate.

[0068] In some embodiments, the neural network model 404 includes one or more taskspecific layers 434. These task-specific layers 434 may be configured to perform downstream processing based on the data-consistent reconstructed data 438. Depending on the application, the task-specific layers 434 may include convolutional layers, fully connected layers, attention modules, or other domain-specific architectures designed to support tasks such as classification, segmentation, regression, or anomaly detection. For example, in a medical imaging context, the task-specific layers 434 may identify anatomical structures or detect pathological features within a reconstructed image. In other contexts, such as industrial inspection or remote sensing, the task-specific layers may be configured to extract features or make predictive assessments from the reconstructed data. As such, the data-consistent reconstructed data 438 may be fed into the task-specific layers 434 to execute any designated tasks assigned to the neural network model 404. From the task-specific layers 434, a taskspecific output is generated based on the processed input (540).

[0069] It should be appreciated that while the second set of neural network layers 432 are illustrated as subsequent to the first set of neural network layers 430, in some embodiments, one or more copies of the second set of neural network layers 432 are included in the first set of neural network layers 430. For example, with an unrolled network commonly used to reconstruct MR images, the second set of neural network layers 432 may be included in each roll of the unrolled network. Other arrangements of the neural network layers 430 and 432 are contemplated herein depending on the architectural design of the neural network model 404.

[0070] Once the neural network model 404 processes the input data 414 through the one or more sets of neural network layers 430-434, as described above, it may output the data- consistent reconstructed data 438 as the final output 442 (545). In some embodiments, particularly where the neural network model 404 is configured to perform an additional downstream task, the task-specific output generated by the task-specific layers 434 may instead serve as the final output 442 from the neural network model 404 (550). The determination of whether task-specific output or the data-consistent reconstructed data 438 serves as the final output 442 may depend on the reconstruction pipeline and the intended use case. In some embodiments, both the data-consistent reconstructed data 438 and the task-specific output(s) of the task specific layers are the final output 442 from the neural network model 404.

[0071] Depending on the application, the enforcement engine 406 may further apply one or more post-processing steps to the selected final output 442 (not shown). For instance, in applications involving domain transformations, such as MRI reconstruction or signal processing, the final output 442 may be transformed back into its original measurement domain. This may involve applying a forward transformation — such as a revised Fourier transform — to map the spatial-domain data points present in the final output 442 back into the frequency domain (e.g., k-space) or another transformed representation. These post-processing operations enable compatibility with downstream systems or facilitate comparison with raw sensor outputs, completing the data reconstruction and enforcement workflow.

[0072] As shown, in some cases, the final output 442 from the neural network model 404 may be further processed by an image generator 440. For example, in scenarios where the measurement data 407 originates from an MRI system and the final output 442 comprises reconstructed spatial-domain data (e.g., voxel intensity values), the image generator 440 may convert this data into a visual representation suitable for human interpretation. In such cases, the image generator 440 may generate a reconstructed image 412 from the data-consistent output, which accurately reflects the anatomical structures or signal features captured by the original measurement data 407. Once generated, the reconstructed image 412 may be transmitted to a client device 410, which may be the same or similar to the client device 110 described above. The client device 410 may include a display or user interface, such as the user interface 108, for visualization, review, or diagnostic interpretation by a clinician, technician, or analyst.

[0073] It should be appreciated that while the image generator 440 is illustrated as part of the enforcement engine 406, in some embodiments, the image generator 440 — or any other post-processing component responsible for formatting, analyzing, visualizing, or re-encoding the final output 442 — may be implemented separately. For example, these post-processing operations may be performed by an external system, module, or service outside of the enforcement engine 406, such as a PACS (Picture Archiving and Communication System), cloud-based visualization platform, or custom rendering pipeline. The modularity of this architecture allows for flexible integration of the enforcement engine 406 within broader medical imaging or signal processing workflows.

[0074] Referring now to Figure 6, an example flow 600 is illustrated showing a data reconstruction process similar to that described in Figure 2 but augmented with a projection layer for enforcing data consistency, according to various embodiments. As shown, input data 614 — which may be the same as or similar to input data 414 — may be provided to a neuralnetwork model 604, which may likewise be the same as or similar to the neural network model 404. In the illustrated example, the input data 614 is preprocessed into an input vector 617 that contains a mixture of known values 618A-618E and missing values 620A-620B. The input vector 617 is processed by a first set of neural network layers 630 to generate an intermediate vector 619. Similar to conventional reconstruction processes, the intermediate vector 619 includes reconstructed values 622A-622C. While reconstructed values 622A and 622B appropriately fill in for missing values 620A and 620B, respectively, the reconstructed value 622C incorrectly replaces a known value — specifically, known value 618D. This behavior illustrates a common issue in conventional neural networks where known input values may be inadvertently overwritten during the reconstruction process.

[0075] To ensure that the neural network model 604 preserves the known values 61 SA- 618E in the input vector 617, the intermediate vector 619 — similar in function to intermediate reconstructed data 436 — is subsequently processed by one or more projection layers 632. As described above, the projection layers 632 may include a proximal operator configured to enforce data consistency by selectively correcting reconstructed outputs. In particular, the proximal operator identifies locations where reconstructed values in the intermediate vector 619 correspond to known values in the input and reverts those values back to their original, measured form. For example, the reconstructed value 622C, which replaced known value 618D, is reverted to the correct known by the projection. The output of this process is an output vector 623 — functionally similar to data-consistent reconstructed data 438 — which preserves the integrity of the known measurements while retaining inferred values only for previously missing positions. By applying the projection layer 632 in this manner, the model enforces strict data consistency with the input data 614, ensuring that hallucinated or spurious modifications to known values are eliminated from the final reconstruction.

[0076] While Figure 6 illustrates a numerical example in the context of a neural network reconstructing a masked or undersampled input vector, similar inconsistencies arise across a wide range of domains and data modalities. For instance, in natural language processing, a masked language model (MLM) may accurately reconstruct a masked token but inadvertently alter adjacent unmasked tokens. Similarly, in image compression and decompression pipelines — such as those involving discrete cosine or wavelet transforms (e.g., JPEG or JPEG2000) — a neural network model trained to reconstruct compressed images may introduce hallucinated or smoothed-over values that overwrite known coefficients. The same challenge applies to other structured signals, such as spectrograms in audio reconstruction or corruptedgrayscale images. In each of these cases, a neural network model’s learned reconstruction may satisfy global objectives but still violate local consistency with known values.

[0077] To address this cross-domain challenge, the architecture shown in Figure 6 — particularly the use of projection layers 632 implementing a proximal operator — can be generalized to enforce data consistency across all such tasks. By comparing the reconstructed output with the known values present in the original input (whether a numeric vector, compressed image, or partially corrupted spectrogram), the projection layer can correct overwritten values and restore those that should remain fixed. As such, the neural network model comprising the reconstruction layers 630 and the projection layers 632 can be trained end-to-end to produce an output that not only completes missing information, but also respects and retains all observed data. This ensures that reconstructed outputs are both semantically meaningful and mathematically consistent with the original measurements, thereby reducing the risk of hallucination or loss of information across different applications.

[0078] Referring now to Figure 7, an example system 700 including a neural network model 704 and a respective training module 744 is illustrated, according to various embodiments herein. The system 700 includes a neural network model 704 and an associated training module 744 which may be configured to enable dual-objective training for both data reconstruction and task-specific learning. As shown, the neural network model 704 includes a layered architecture including an input layer 748, transformer layers 730, a projection layer 732, one or more task-specific layers 734, and an output layer 750. As expanded on below, the neural network model 704 may be trained using the training module 744 to ensure data consistency across a variety of input data types and applications.

[0079] When input data is submitted to the neural network model 704, the input layer 748 receives the input data for initial processing. The input data may include structured, semistructured, or unstructured data, such as textual sequences, signal measurements, sensor outputs, image pixels, or frequency-domain data (e.g., k-space data in MRI applications). Depending on the data modality, the input layer 748 may include or be preceded by one or more preprocessing components, such as a tokenizer (for text), a feature encoder (for structured fields), or a normalization module (for continuous signals or image data). For textual input, the tokenizer may segment input strings into tokens, subword units, or embeddings, and map them to discrete identifiers or vectors. The input layer 748 may further embed or project the processed inputs into a format suitable for downstream transformer layers, such as fixed-size dense vectors with associated position encodings. These representations are then passed todeeper layers in the neural network model 704 for further contextualization and task-specific processing.

[0080] After the input data is processed by the input layer 748, the resulting embedded or encoded representations are provided to the transformer layers 730. The transformer layers 730 may include a sequence of attention-based blocks configured to model both short-range and long-range dependencies within the input data. Each block may include multi-head selfattention mechanisms, position-wise feedforward networks, layer normalization, and residual connections. Tn some implementations, the transformer layers 730 may he configured to interpolate or predict missing values or data points that are absent from the input data. For example, in scenarios involving masked or undersampled inputs — such as masked language modeling, image inpainting, or sparse signal reconstruction — the transformer layers 730 may infer the missing content based on contextual information from observed portions of the input. The output of the transformer layers 730 includes contextualized feature representations that preserve both local and global relationships, enabling the model to support reconstruction, classification, or other downstream tasks.

[0081] The output generated by the transformer layers 730 comprises a set of contextualized feature representations that capture the relationships between both observed and inferred portions of the input data. In reconstruction tasks, these representations may reflect interpolated or predicted values intended to fill in missing or corrupted portions of the original input. This intermediate reconstructed data reflects a semantically and structurally coherent estimate of the input data, but may not yet be constrained to strictly match known or measured input values (e.g., known tokens in text, or acquired k-space data in MRI). Accordingly, the intermediate reconstructed data is passed to the projection layer 732 for further refinement and consistency enforcement.

[0082] The projection layer 732 receives the intermediate reconstructed data from the transformer layers 730 and applies transformations to map it into a latent space suitable for downstream objectives. In some implementations, the projection layer 732 is further configured to enforce data consistency by aligning portions of the intermediate reconstructed data with known or uncorrupted input values. For example, in partially masked or undersampled data scenarios, the projection layer 732 may selectively retain original input values in locations where they are available, while preserving interpolated values elsewhere. This operation may be implemented as a learned or fixed projection, a residual correction, or an operator that conditionally replaces or fuses values based on confidence or mask information. The result is a data-consistent reconstructed representation that integrates both model-inferred predictionsand verified input measurements. The output of the projection layer 732 thus forms a unified, task-agnostic representation that reflects both learned structure and strict consistency with known data. In some embodiments, output may then be supplied in parallel to the training module 744 for loss computation, and to the task-specific layer(s) 734 for downstream task optimization.

[0083] The task-specific layer(s) 734 receive the data-consistent reconstructed data output from the projection layer 732 and apply further transformations tailored to a designated downstream task. These layers are designed to specialize the general -purpose, consistency- enforced representations for application-specific objectives. Depending on the nature of the target task, the task-specific layer(s) 734 may include one or more neural network components, such as fully connected layers, convolutional blocks (e.g., for spatial feature extraction), recurrent units (e.g., for sequence modeling), capsule blocks (e.g., for context), or additional transformer blocks (e.g., for hierarchical reasoning). In some embodiments, attention mechanisms may also be incorporated to dynamically weight salient features within the data- consistent input. The task-specific layer(s) 734 adapt the shared latent representation to a form optimized for task performance — for example, distinguishing between classes in a classification task, identifying spatial boundaries in a segmentation task, or reconstructing temporally aligned signals in a time-series forecasting or imaging context.

[0084] The output layer 750 receives the task-specific output generated by the task-specific layer(s) 734 and produces the final output of the neural network model 704. This layer is responsible for converting the refined task-adapted features into a format appropriate for the downstream application. The structure and activation function of the output layer 750 may vary based on the task type: for example, the output layer 750 may be implemented as a softmax layer for multi-class classification, a sigmoid activation for binary classification, a linear layer for regression tasks, or a reconstruction layer configured to generate structured outputs such as images, sequences, or multidimensional sensor signals. In some implementations, the output layer 750 may constitute an entire neural network with many layers. In some implementations, the output layer 750 may also support probabilistic outputs, uncertainty quantification, or domain-specific constraints, depending on the task objective. The output produced by the output layer 750 may be used directly during inference, or may be compared against labeled ground truth during training to compute a task-specific loss 758 used to guide model updates, as described below.

[0085] As noted above, the training module 744 enables supervised and self-supervised training of the neural network model 704. The training module 744 may include two distinctbranches: a masked language modeling (MLM) head 752 and a task-specific head 756. The MLM head 752 may receive feature representations from the projection layer 732 and predicts masked tokens or missing elements in the input data. The MLM head 752 supports selfsupervised learning by encouraging the neural network model 704 to learn semantic and structural relationships in the input data. A corresponding MLM loss 754 may then be computed by comparing the MLM head’s 752 predictions to the original unmasked input tokens, and the MLM loss 754 is minimized to improve contextual prediction performance.

[0086] The task-specific head 756 receives features from the task-specific layer(s) 734 and generates predictions for the downstream task. These predictions may be class labels, bounding boxes, next word predictions, structured outputs, or other task-relevant formats. The taskspecific head 756 computes a task-specific loss 758 based on ground-truth labels or known output targets for the given task. The task-specific loss 758 may be minimized to improve performance on the target task.

[0087] In some implementations, the MLM loss 754 and the task-specific loss 758 may be combined into a total loss function. The total loss may be computed as a weighted sum of the individual losses 764 and 766 and used to jointly optimize the neural network model 704 during training. The system 700 may then apply backpropagation or other parameter update procedures 760 to update the weights and parameters of the neural network model 704 based on gradients computed from one of the MLM loss 754, the task-specific loss 758, and / or the total loss. The updates propagate from the output layer 750 back through the task-specific layer(s) 734, the projection layer 732, the transformer layers 730, and ultimately to the input layer 748, enabling end-to-end training of the full architecture.

[0088] By incorporating both self-supervised and supervised learning signals, the system 700 enables the neural network model 704 to learn general-purpose representations that are both semantically rich and optimized for task-specific outcomes. A key component of this architecture is the inclusion of the projection layer 732 during the training process, which enforces data consistency by ensuring that known values present in the input data — such as unmasked tokens or measured signal points — are preserved throughout the reconstruction process. This prevents the neural network model 704 from hallucinating or erroneously replacing verified input values with inferred or reconstructed values during training. As a result, the neural network model 704 learns to distinguish between known and unknown data points, enabling it to make precise predictions only where needed while retaining the integrity of the original input. This consistency-aware training approach improves generalization, reduces the risk of overfitting or overcorrection, and minimizes the reliance on large, labeled datasets.Additionally, the dual-headed architecture supports modular deployment across a variety of machine learning applications by allowing both pretraining via masked prediction and fine- tuning for task-specific objectives.

[0089] Referring now to Figures 8A-8C, a representative set of knee MRI images 800A-800C is shown, illustrating the effect of data consistency enforcement on image reconstruction quality, according to various embodiments. The images 800A-800C included herein are illustrative representations of reconstructed images. Although the initial intent was to use images generated using actual data, licensing restrictions on the underlying dataset prevented this. Consequently, images 800A-800C are designed to visually represent the intended reconstructed images, without directly utilizing the restricted data.

[0090] Figure 8A illustrates the image 800A, which represents a fully sampled reconstruction generated using the complete dataset acquired by an MRI device. The image 800A serves as a ground truth reference, depicting the knee anatomy without artifacts or omissions.

[0091] Figure 8B illustrates the image 800B, which shows a reconstructed image generated using only 25% of the original data, processed via a conventional neural network model that does not enforce data consistency. As shown, this approach results in a hallucinated artifact 862 — an erroneous structure not present in the original anatomy — likely introduced due to the model overfitting to prior training distributions or failing to preserve known values from the measurement data. The artifact 862 exemplifies the limitations of conventional undersampled reconstruction techniques.

[0092] Figure 8C illustrates the image 800C, which is generated using the same 25% under-sampled data but reconstructed using the enforcement engine described herein. In this embodiment, a neural network model incorporates a projection layer or proximal operator that enforces consistency between the reconstructed output and the known values in the original measurement data. As depicted, the reconstructed image 800C eliminates the hallucinated artifact 862 and more closely matches the fully sampled reference in Figure 8A. This demonstrates that the techniques disclosed herein effectively suppress hallucinated features and enhance reconstruction fidelity, even when trained on out-of-distribution data, by preserving the integrity of the known measurements and enforcing structural consistency throughout the reconstruction process.

[0093] Referring to Figure 9, Figure 9 illustrates a computing apparatus 991 that may be used for providing an enforcement engine and related functions, as described herein. That is, the enforcement engine may be executed by a computing device, such as the client device110 or 410, or by an application service, such as the application service 101 for enforcing data consistency during data reconstruction. For example, a neural network model associated with the application service 101 may be executed on a server computer 103, which may be or include the computing apparatus 991 . As illustrated, the computing apparatus 991 includes a processing system 992 that includes a microprocessor and other circuitry that retrieves and executes software 995 from storage system 993. The processing system 992 may be implemented within a single processing device but may also be distributed across multiple processing devices or sub-systems that cooperate in executing program instructions. Examples of the processing system 992 include general purpose central processing units, graphical processing units, application specific processors, and logic devices, as well as any other type of processing device, combinations, or variations thereof.

[0094] The storage system 993 may comprise any computer-readable storage media or medium readable by processing system 992 and capable of storing software 995. The storage system 993 may include volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information, such as computer readable instructions, data structures, program modules, or other data. Examples of storage media include random access memory, read only memory, magnetic disks, optical disks, flash memory, virtual memory and non-virtual memory, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other suitable storage media. In no case is the computer readable storage media a propagated signal.

[0095] In addition to computer readable storage media, in some implementations the storage system 993 may also include computer readable communication media over which at least some of the software 995 may be communicated internally or externally. The storage system 993 may be implemented as a single storage device but may also be implemented across multiple storage devices or sub-systems co-located or distributed relative to each other. The storage system 993 may comprise additional elements, such as a controller capable of communicating with the processing system 992 or possibly other systems.

[0096] The software 995 (including enforcement engine 996) may be implemented in program instructions and among other functions may, when executed by the processing system 992, direct the processing system 992 to operate as described with respect to the various operational scenarios, sequences, and processes illustrated herein. For example, the software 995 may include program instructions for implementing an enforcement engine, and related functions, for enforcing data consistency during data reconstruction such as process 500 of Figure 5, as described herein.

[0097] As used herein, the term “engine” refers to a computer-related entity, including but not limited to a component, module, or system. An engine may be implemented as software running on a general-purpose processor, hardware, firmware, or any combination thereof. For example, an engine can take the form of a process executing on a hardware processor, a hardware-based processor itself, an object, an executable, a thread of execution, a program, or even an entire computing device.

[0098] In particular, the program instructions may include various components or modules that cooperate or otherwise interact to carry out the various processes and operational scenarios described herein. The various components or modules may be embodied in compiled or interpreted instructions, or in some other variation or combination of instructions. The various components or modules may be executed in a synchronous or asynchronous manner, serially or in parallel, in a single threaded environment or multi-threaded, or in accordance with any other suitable execution paradigm, variation, or combination thereof. The software 995 may include additional processes, programs, or components, such as operating system software, virtualization software, or other application software. The software 995 may also comprise firmware or some other form of machine-readable processing instructions executable by the processing system 992.

[0099] In general, the software 995 may, when loaded into the processing system 992 and executed, transform a suitable apparatus, system, or device (of which computing apparatus 991 is representative) overall from a general-purpose computing system into a special-purpose computing system customized to generate features, functionality, and user experiences provided by the enforcement engine. Indeed, encoding the software 995 on the storage system 993 may transform the physical structure of the storage system 993. The specific transformation of the physical structure may depend on various factors in different implementations of this description. Examples of such factors may include, but are not limited to, the technology used to implement the storage media of the storage system 993 and whether the computer- storage media are characterized as primary or secondary storage, as well as other factors.

[0100] For example, if the computer readable storage media are implemented as semiconductor-based memory, the software 995 may transform the physical state of the semiconductor memory when the program instructions are encoded therein, such as by transforming the state of transistors, capacitors, or other discrete circuit elements constituting the semiconductor memory. A similar transformation may occur with respect to magnetic or optical media. Other transformations of physical media are possible without departing from thescope of the present description, with the foregoing examples provided only to facilitate the present discussion.

[0101] Communication interface system 997 may include communication connections and devices that allow for communication with other computing systems (not shown) over communication networks (not shown). Examples of connections and devices that together allow for inter-system communication may include network interface cards, antennas, power amplifiers, RF circuitry, transceivers, and other communication circuitry. The connections and devices may communicate over communication media to exchange communications with other computing systems or networks of systems, such as metal, glass, air, or any other suitable communication media. The aforementioned media, connections, and devices are well known and need not be discussed at length here.

[0102] Communication between the computing apparatus 991 and other computing systems (not shown), may occur over a communication network or networks and in accordance with various communication protocols, combinations of protocols, or variations thereof. Examples include intranets, internets, the Internet, local area networks, wide area networks, wireless networks, wired networks, virtual networks, software defined networks, data center buses and backplanes, or any other type of network, combination of network, or variation thereof. The aforementioned communication networks and protocols are well known and need not be discussed at length here.

[0103] While some examples of methods and systems herein are described in terms of software executing on various machines, the methods and systems may also be implemented as specifically-configured hardware, such as field-programmable gate array (FPGA) specifically to execute the various methods according to this disclosure. For example, examples can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in a combination thereof. In one example, a device may include a processor or processors. The processor comprises a computer-readable medium, such as a random access memory (RAM) coupled to the processor. The processor executes computer-executable program instructions stored in memory, such as executing one or more computer programs. Such processors may comprise a microprocessor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), field programmable gate arrays (FPGAs), and state machines. Such processors may further comprise programmable electronic devices such as PLCs, programmable interrupt controllers (PICs), programmable logic devices (PLDs), programmable read-only memories (PROMs), electronically programmable read-only memories (EPROMs or EEPROMs), or other similar devices.

[0104] Such processors may comprise, or may be in communication with, media, for example one or more non-transitory computer-readable media, which may store processorexecutable instructions that, when executed by the processor, can cause the processor to perform methods according to this disclosure as carried out, or assisted, by a processor. Examples of may include, but are not limited to, an electronic, optical, magnetic, or other storage device capable of providing a processor, such as the processor in a web server, with processor-executable instructions. Other examples of non-transitory computer-readable media include, but are not limited to, a floppy disk, CD-ROM, magnetic disk, memory chip, ROM, RAM, ASIC, configured processor, all optical media, all magnetic tape or other magnetic media, or any other medium from which a computer processor can read. The processor, and the processing, described may be in one or more structures, and may be dispersed through one or more structures. The processor may comprise code to carry out methods (or parts of methods) according to this disclosure.

[0105] Examples are described herein in the context of systems and methods for enforcing data consistency in data reconstruction. Those of ordinary skill in the art will realize that the foregoing description is illustrative only and is not intended to be in any way limiting. Reference is made in detail to implementations of examples as illustrated in the accompanying drawings. The same reference indicators will be used throughout the drawings and the following description to refer to the same or like items.

[0106] Additionally, the foregoing description of some examples has been presented only for the purpose of illustration and description and is not intended to be exhaustive or to limit the disclosure to the precise forms disclosed. Numerous modifications and adaptations thereof will be apparent to those skilled in the art without departing from the spirit and scope of the disclosure. In the interest of clarity, not all of the routine features of the examples described herein are shown and described. It will, of course, be appreciated that in the development of any such actual implementation, numerous implementation- specific decisions must be made in order to achieve the developer’s specific goals, such as compliance with application- and business-related constraints, and that these specific goals will vary from one implementation to another and from one developer to another.

[0107] Reference herein to an example or implementation means that a particular feature, structure, operation, or other characteristic described in connection with the example may be included in at least one implementation of the disclosure. The disclosure is not restricted to the particular examples or implementations described as such. The appearance of the phrases “in one example,” “in an example,” “in one implementation,” or “in an implementation,” orvariations of the same in various places in the specification does not necessarily refer to the same example or implementation. Any particular feature, structure, operation, or other characteristic described in this specification in relation to one example or implementation may be combined with other features, structures, operations, or other characteristics described in respect of any other example or implementation.

[0108] Use herein of the word “or” is intended to cover inclusive and exclusive OR conditions. In other words, A or B or C includes any or all of the following alternative combinations as appropriate for a particular usage: A alone; B alone; C alone; A and B only; A and C only; B and C only; and A and B and C.EXAMPLES

[0109] These illustrative examples are mentioned not to limit or define the scope of this disclosure, but rather to provide examples to aid understanding thereof. Illustrative examples are discussed above in the Detailed Description, which provides further description. Advantages offered by various examples may be further understood by examining this specification.

[0110] As used below, any reference to a series of examples is to be understood as a reference to each of those examples disjunctively (e.g., “Examples 1-4” is to be understood as “Examples 1, 2, 3, or 4”).

[0111] Example 1 is a computing apparatus comprising: a computer-readable storage media comprising processor-executable instructions stored thereon; and a processor coupled to the computer-readable storage media and configured to execute the processor-executable instructions that, when executed by the processor, direct the computing apparatus to at least: receive input data for a data reconstruction task; process the input data using a neural network model comprising: a first set of neural network layers configured to perform data reconstruction; and a second set of neural network layers configured to enforce data consistency, wherein the first set and the second set of neural network layers are each utilized during both training and inference of the neural network model; wherein processing the input data comprises: generating, by the first set of neural network layers, intermediate reconstructed data based on the input data; and generating, by the second set of neural network layers, data- consistent reconstructed data by modifying the intermediate reconstructed data to enforce consistency with the input data; and output the data-consistent reconstructed data as a final output of the neural network model.

[0112] Example 2 is the computing apparatus of any previous or subsequent Example, wherein: the neural network model further comprises one or more task-specific layers; and the processor-executable instructions, when executed by the processor, further direct the computing apparatus to: provide the data-consistent reconstructed data to the one or more taskspecific layers; generate, by the one or more task- specific layers, a task-specific output based on the data-consistent reconstructed data; and output the task-specific output as the final output of the neural network model.

[0113] Example 3 is the computing apparatus of any previous or subsequent Example, wherein: the second set of neural network layers comprises a proximal operator; and the processor-executable instructions to generate, by the second set of neural network layers, the data-consistent reconstructed data by modifying the intermediate reconstructed data to enforce consistency with the input data, when executed by the processor, further direct the computing apparatus to: apply the proximal operator to the intermediate reconstructed data; and generate the data-consistent reconstructed data based on application of the proximal operator.

[0114] Example 4 is the computing apparatus of any previous or subsequent Example, wherein: the second set of neural network layers is configured to perform a data consistency projection using a Fourier-domain operation; and the processor-executable instructions to generate, by the second set of neural network layers, the data-consistent reconstructed data by modifying the intermediate reconstructed data to enforce consistency with the input data, when executed by the processor, further direct the computing apparatus to: transform the intermediate reconstructed data into a frequency domain using a Fourier transform; modify the transformed data to enforce consistency with the input data in the frequency domain; and transform the modified data back into a spatial domain using an inverse Fourier transform.

[0115] Example 5 is the computing apparatus of any previous or subsequent Example, wherein: the processor-executable instructions to receive the input data for the data reconstruction task, when executed by the processor, further direct the computing apparatus to: receive the input data from a magnetic resonance imaging (MRI) sensing device, wherein the input data comprises k-space data; and the processor-executable instructions to process the input data using the neural network model, when executed by the processor, further direct the computing apparatus to: reconstruct, using the neural network model, image data from the k- space data.

[0116] Example 6 is the computing apparatus of any previous or subsequent Example, wherein: the second set of neural network layers is configured to enforce consistency with the k-space data during both training and inference; and the processor-executable instructions togenerate, by the second set of neural network layers, the data-consistent reconstructed data, when executed by the processor, further direct the computing apparatus to: compare the intermediate reconstructed data to the k-space data inputted into the neural network model; and modify the intermediate reconstructed data to reduce inconsistency with the k-space data.

[0117] Example 7 is a computer-implemented method for data reconstruction, comprising: processing, by a neural network model, input data, wherein the neural network model comprising: a first set of neural network layers configured to generate intermediate reconstructed data from the input data; and a second set of neural network layers configured to modify the intermediate reconstructed data to enforce consistency with the input data, wherein the first set and the second set of neural network layers are configured to be used during both training and inference of the neural network model; wherein processing, by the neural network model, the input data comprises: generating, by the first set of neural network layers, the intermediate reconstructed data; and generating, by the second set of neural network layers, data-consistent reconstructed data by modifying the intermediate reconstructed data based on the input data; and outputting, from the neural network model, the data-consistent reconstructed data as a final output of the neural network model.

[0118] Example 8 is the method of any previous or subsequent Example, wherein the transformed domain comprises a Fourier domain, wavelet domain, or other sensor-specific acquisition domain.

[0119] Example 9 is the method of any previous or subsequent Example, wherein the method further comprises: training the neural network model by minimizing a data consistency loss function during training, wherein the data consistency loss function quantifies a divergence between the intermediate reconstructed data and a projection of the input data in a transformed domain.

[0120] Example 10 is the method of any previous or subsequent Example, wherein: the input data comprises a first set of data points; the intermediate reconstructed data comprises a second set of data points generated by the first set of neural network layers; and wherein generating, by the second set of neural network layers, the data-consistent reconstructed data further comprises: applying, by the second set of neural network layers, one or more consistency constraints to the intermediate reconstructed data to cause the inclusion of the first set of data points and a plurality of reconstructed data points in the data-consistent reconstructed data.

[0121] Example 11 is the method of any previous or subsequent Example, wherein generating, by the second set of neural network layers, the data-consistent reconstructed datafurther comprises: transforming the intermediate reconstructed data into a frequency domain using a Fourier transform; modifying the transformed data to enforce consistency with the input data in the frequency domain; and transforming the modified data back into a spatial domain using an inverse Fourier transform.

[0122] Example 12 is the method of any previous or subsequent Example, wherein the neural network model further comprises one or more task-specific layers, and the method further comprises: providing the data-consistent reconstructed data to the one or more taskspecific layers; generating, by the one or more task-specific layers, a task-specific output based on the data-consistent reconstructed data; and outputting the task-specific output as a final output of the neural network model.

[0123] Example 13 is the method of any previous or subsequent Example, wherein the method further comprises: training the neural network model using a self-supervised learning strategy, wherein training data used as the input data comprises synthetically corrupted examples generated from unpaired or unlabeled samples.

[0124] Example 14 is the method of any previous or subsequent Example, wherein the neural network model comprises an encoder-decoder architecture or a U-Net structure configured to support both the reconstruction and consistency enforcement processes.

[0125] Example 15 is a non- transitory computer-readable medium storing instructions that, when executed by one or more processors, cause a computing system to: implement a neural network model comprising: a first set of neural network layers configured to perform data reconstruction from input data; and a second set of neural network layers configured to enforce data consistency with the input data by modifying output generated by the first set of neural network layers, wherein the first set and the second set of neural network layers are configured for use during both training and inference; process, using the neural network model, the input data by: generating intermediate reconstructed data using the first set of neural network layers; and generating data-consistent reconstructed data by modifying the intermediate reconstructed data using the second set of neural network layers to enforce consistency with the input data; and output, from the neural network model, the data-consistent reconstructed data as a final output.

[0126] Example 16 is the non-transitory computer-readable medium of any previous or subsequent Example, wherein: the second set of neural network layers comprises a proximal operator; and the instructions to the data-consistent reconstructed data by modifying the intermediate reconstructed data using the second set of neural network layers to enforce consistency with the input data cause the processor to further execute processor-executableinstructions stored in the non-transitory computer-readable medium to: apply the proximal operator to the intermediate reconstructed data; and generate the data-consistent reconstructed data based on the application of the proximal operator.

[0127] Example 17 is the non-transitory computer-readable medium of any previous or subsequent Example, wherein the instructions to the data-consistent reconstructed data by modifying the intermediate reconstructed data using the second set of neural network layers to enforce consistency with the input data cause the processor to further execute processorexecutable instructions stored in the non-transitory computer-readable medium to: transform the intermediate reconstructed data into a frequency domain using a Fourier transform; modify the transformed data to enforce consistency with the input data in the frequency domain; and transform the modified data back into a spatial domain using an inverse Fourier transform.

[0128] Example 18 is the non-transitory computer-readable medium of any previous or subsequent Example, wherein: the instructions to cause the processor to further execute processor-executable instructions stored in the non-transitory computer-readable medium to: receive input data from a magnetic resonance imaging (MRI) sensing device, wherein the input data comprises k-space data representing a frequency domain encoding of an anatomical region; the instructions to generate the intermediate reconstructed data using the first set of neural network layers cause the processor to further execute processor-executable instructions stored in the non-transitory computer-readable medium to: generate, by the first set of neural network layers, the intermediate reconstructed data from the k-space data; the instructions to generate, by the second set of neural network layers, the data-consistent reconstructed data cause the processor to further execute processor-executable instructions stored in the non- transitory computer-readable medium to: compare the intermediate reconstructed data to the k- space data; and modify the intermediate reconstructed data to reduce inconsistency with the k- space data; and the instructions to output, from the neural network model, the data-consistent reconstructed data as the final output cause the processor to further execute processorexecutable instructions stored in the non-transitory computer-readable medium to: output, from the neural network model, a reconstructed image based on the data-consistent reconstructed data as the final output from the neural network model.

[0129] Example 19 is the non-transitory computer-readable medium of any previous or subsequent Example, wherein: the neural network model further comprises one or more taskspecific layers; and the instructions cause the processor to further execute processor-executable instructions stored in the non-transitory computer-readable medium to: provide the data- consistent reconstructed data to the one or more task-specific layers; generate, by the one ormore task-specific layers, a task-specific output based on the data-consistent reconstructed data; and output the task-specific output as the final output of the neural network model.

[0130] Example 20 is the non-transitory computer-readable medium of any previous or subsequent Example, wherein: the instructions cause the processor to further execute processor-executable instructions stored in the non-transitory computer-readable medium to: train the neural network model using training data that comprises missing values in a frequency domain; the processor-executable instructions to generate the data-consistent reconstructed data by modifying the intermediate reconstructed data using the second set of neural network layers to enforce consistency with the input data cause the processor to further execute processor-executable instructions stored in the non-transitory computer-readable medium to: interpolate, by the first set of neural network layers, a set of missing values absent in the input data; and preserve consistency with known Fourier values present in the input data.

Claims

CLAIMS1. A computing apparatus comprising: a computer-readable storage media comprising processor-executable instructions stored thereon; and a processor coupled to the computer-readable storage media and configured to execute the processor-executable instructions that, when executed by the processor, direct the computing apparatus to at least: receive input data for a data reconstruction task; process the input data using a neural network model comprising: a first set of neural network layers configured to perform data reconstruction; and a second set of neural network layers configured to enforce data consistency, wherein the first set and the second set of neural network layers are each utilized during both training and inference of the neural network model; wherein processing the input data comprises: generating, by the first set of neural network layers, intermediate reconstructed data based on the input data; and generating, by the second set of neural network layers, data-consistent reconstructed data by modifying the intermediate reconstructed data to enforce consistency with the input data: and output the data-consistent reconstructed data as a final output of the neural network model.

2. The computing apparatus of claim 1, wherein: the neural network model further comprises one or more task- specific layers; and the processor-executable instructions, when executed by the processor, further direct the computing apparatus to: provide the data-consistent reconstructed data to the one or more task-specific layers; generate, by the one or more task-specific layers, a task-specific output based on the data-consistent reconstructed data; and output the task-specific output as the final output of the neural network model.

3. The computing apparatus of claim 1, wherein: the second set of neural network layers comprises a proximal operator; and the processor-executable instructions to generate, by the second set of neural network layers, the data-consistent reconstructed data by modifying the intermediate reconstructed data to enforce consistency with the input data, when executed by the processor, further direct the computing apparatus to: apply the proximal operator to the intermediate reconstructed data; and generate the data-consistent reconstructed data based on application of the proximal operator.

4. The computing apparatus of claim 1, wherein: the second set of neural network layers is configured to perform a data consistency projection using a Fourier-domain operation; and the processor-executable instructions to generate, by the second set of neural network layers, the data-consistent reconstructed data by modifying the intermediate reconstructed data to enforce consistency with the input data, when executed by the processor, further direct the computing apparatus to: transform the intermediate reconstructed data into a frequency domain using a Fourier transform; modify the transformed data to enforce consistency with the input data in the frequency domain; and transform the modified data back into a spatial domain using an inverse Fourier transform.

5. The computing apparatus of claim 1, wherein: the processor-executable instructions to receive the input data for the data reconstruction task, when executed by the processor, further direct the computing apparatus to: receive the input data from a magnetic resonance imaging (MRI) sensing device, wherein the input data comprises k-space data; and the processor-executable instructions to process the input data using the neural network model, when executed by the processor, further direct the computing apparatus to: reconstruct, using the neural network model, image data from the k-space data.

6. The computing apparatus of claim 5, wherein: the second set of neural network layers is configured to enforce consistency with the k- space data during both training and inference; and the processor-executable instructions to generate, by the second set of neural network layers, the data-consistent reconstructed data, when executed by the processor, further direct the computing apparatus to: compare the intermediate reconstructed data to the k-space data inputted into the neural network model ; and modify the intermediate reconstructed data to reduce inconsistency with the k- space data.

7. A computer-implemented method for data reconstruction, comprising: processing, by a neural network model, input data, wherein the neural network model comprising: a first set of neural network layers configured to generate intermediate reconstructed data from the input data; and a second set of neural network layers configured to modify the intermediate reconstructed data to enforce consistency with the input data, wherein the first set and the second set of neural network layers are configured to be used during both training and inference of the neural network model; wherein processing, by the neural network model, the input data comprises: generating, by the first set of neural network layers, the intermediate reconstructed data; and generating, by the second set of neural network layers, data-consistent reconstructed data by modifying the intermediate reconstructed data based on the input data; and outputting, from the neural network model, the data-consistent reconstructed data as a final output of the neural network model.

8. The method of claim 7, wherein the transformed domain comprises a Fourier domain, wavelet domain, or other sensor-specific acquisition domain.

9. The method of claim 8, wherein the method further comprises: training the neural network model by minimizing a data consistency loss function during training, wherein the data consistency loss function quantifies a divergence between the intermediate reconstructed data and a projection of the input data in a transformed domain.

10. The method of claim 7, wherein: the input data comprises a first set of data points; the intermediate reconstructed data comprises a second set of data points generated by the first set of neural network layers; and wherein generating, by the second set of neural network layers, the data-consistent reconstructed data further comprises: applying, by the second set of neural network layers, one or more consistency constraints to the intermediate reconstructed data to cause the inclusion of the first set of data points and a plurality of reconstructed data points in the data-consistent reconstructed data.

11. The method of claim 7, wherein generating, by the second set of neural network layers, the data-consistent reconstructed data further comprises: transforming the intermediate reconstructed data into a frequency domain using a Fourier transform; modifying the transformed data to enforce consistency with the input data in the frequency domain; and transforming the modified data back into a spatial domain using an inverse Fourier transform.

12. The method of claim 7, wherein the neural network model further comprises one or more task- specific layers, and the method further comprises: providing the data-consistent reconstructed data to the one or more task-specific layers; generating, by the one or more task-specific layers, a task-specific output based on the data-consistent reconstructed data; and outputting the task-specific output as a final output of the neural network model.

13. The method of claim 7, wherein the method further comprises: training the neural network model using a self-supervised learning strategy, wherein training data used as the input data comprises synthetically corrupted examples generated from unpaired or unlabeled samples.

14. The method of claim 7, wherein the neural network model comprises an encoder-decoder architecture or a U-Net structure configured to support both the reconstruction and consistency enforcement processes.

15. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause a computing system to: implement a neural network model comprising: a first set of neural network layers configured to perform data reconstruction from input data; and a second set of neural network layers configured to enforce data consistency with the input data by modifying output generated by the first set of neural network layers, wherein the first set and the second set of neural network layers are configured for use during both training and inference; process, using the neural network model, the input data by: generating intermediate reconstructed data using the first set of neural network layers; and generating data-consistent reconstructed data by modifying the intermediate reconstructed data using the second set of neural network layers to enforce consistency with the input data; and output, from the neural network model, the data-consistent reconstructed data as a final output.

16. The non-transitory computer-readable medium of claim 15, wherein: the second set of neural network layers comprises a proximal operator; and the instructions to the data-consistent reconstructed data by modifying the intermediate reconstructed data using the second set of neural network layers to enforce consistency with the input data cause the processor to further execute processor-executable instructions stored in the non-transitory computer-readable medium to: apply the proximal operator to the intermediate reconstructed data; andgenerate the data-consistent reconstructed data based on the application of the proximal operator.

17. The non-transitory computer-readable medium of claim 15, wherein the instructions to the data-consistent reconstructed data by modifying the intermediate reconstructed data using the second set of neural network layers to enforce consistency with the input data cause the processor to further execute processor-executable instructions stored in the non-transitory computer-readable medium to: transform the intermediate reconstructed data into a frequency domain using a Fourier transform; modify the transformed data to enforce consistency with the input data in the frequency domain; and transform the modified data back into a spatial domain using an inverse Fourier transform.

18. The non-transitory computer-readable medium of claim 15, wherein: the instructions to cause the processor to further execute processor-executable instructions stored in the non-transitory computer- readable medium to: receive input data from a magnetic resonance imaging (MRI) sensing device, wherein the input data comprises k-space data representing a frequency domain encoding of an anatomical region; the instructions to generate the intermediate reconstructed data using the first set of neural network layers cause the processor to further execute processor-executable instructions stored in the non-transitory computer-readable medium to: generate, by the first set of neural network layers, the intermediate reconstructed data from the k-space data; the instructions to generate, by the second set of neural network layers, the data- consistent reconstructed data cause the processor to further execute processor-executable instructions stored in the non-transitory computer- readable medium to: compare the intermediate reconstructed data to the k-space data; and modify the intermediate reconstructed data to reduce inconsistency with the k- space data; andthe instructions to output, from the neural network model, the data-consistent reconstructed data as the final output cause the processor to further execute processorexecutable instructions stored in the non-transitory computer-readable medium to: output, from the neural network model, a reconstructed image based on the data- consistent reconstructed data as the final output from the neural network model.

19. The non-transitory computer-readable medium of claim 15, wherein: the neural network model further comprises one or more task-specific layers; and the instructions cause the processor to further execute processor-executable instructions stored in the non-transitory computer-readable medium to: provide the data-consistent reconstructed data to the one or more task-specific layers; generate, by the one or more task-specific layers, a task-specific output based on the data-consistent reconstructed data; and output the task-specific output as the final output of the neural network model.

20. The non-transitory computer-readable medium of claim 15, wherein: the instructions cause the processor to further execute processor-executable instructions stored in the non-transitory computer-readable medium to: train the neural network model using training data that comprises missing values in a frequency domain; the processor-executable instructions to generate the data-consistent reconstructed data by modifying the intermediate reconstructed data using the second set of neural network layers to enforce consistency with the input data cause the processor to further execute processorexecutable instructions stored in the non-transitory computer-readable medium to: interpolate, by the first set of neural network layers, a set of missing values absent in the input data; and preserve consistency with known Fourier values present in the input data.

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