Methods, systems, and computer readable media for accelerating magnetic resonance imaging using artificial intelligence

Abstract

A method for reconstructing magnetic resonance (MR) images includes receiving k-space data acquired with a non-Cartesian scanning trajectory. The method further includes transforming the k-space data into an initial image. The method further includes supplying the initial image to a diffusion model and generating a reconstructed image.

Description

[0001] METHODS, SYSTEMS, AND COMPUTER READABLE MEDIA FOR ACCELERATING MAGNETIC RESONANCE IMAGING USING ARTIFICIAL INTELLIGENCE

[0002] GOVERNMENT INTEREST

[0003] This invention was made with government support under AR076392 awarded by the National Institutes of Health. The government has certain rights in the invention.

[0004] PRIORITY CLAIM

[0005] This application claims the priority benefit of U.S. Provisional Patent Application Serial No. 63 / 633,681 , filed April 12, 2024, the disclosure of which is incorporated herein by reference in its entirety.

[0006] TECHNICAL FIELD

[0007] This specification relates generally to methods, systems, and computer readable media for accelerating magnetic resonance imaging using artificial intelligence.

[0008] BACKGROUND

[0009] During magnetic resonance imaging (MRI) acquisition, image formation occurs in k-space, a mathematical domain representing the spatial frequency spectrum of the object being scanned. K-space data is gathered through a process of signal encoding using gradient pulses. These pulses manipulate the motion of excited protons within the object, introducing spatial dependence into the received signal. The signal is then digitized and stored in k-space in a predetermined order based on the specific pulse sequence employed. K-space typically resembles a complex-valued matrix, with each element encoding signal intensity at a unique combination of spatial frequencies. Once data acquisition is complete, an inverse Fourier transform is applied to the k-space data, converting it back into the spatial domain and generating the final image. SUMMARY

[0010] This document describes methods and systems for reconstructing spiral MRI using a diffusion model. Combining multicoil imaging, spiral scanning, and under sampling enables dramatically faster imaging speeds. In some examples, the technology can be used for real-time 3D imaging.

[0011] The subject matter described herein includes a method for reconstructing magnetic resonance (MR) images, the method includes receiving k-space data acquired with a non-Cartesian scanning trajectory. The method further includes transforming the k-space data into an initial image. The method further includes supplying the initial image to a diffusion model and generating a reconstructed image.

[0012] According to another aspect of the subject matter described herein, the method for reconstructing MR images includes generating a latent noise vector sampled from a known noise distribution.

[0013] According to another aspect of the subject matter described herein, the method for reconstructing MR images includes producing an image reconstruction prior by estimating a source image using a Fourier transform.

[0014] According to another aspect of the subject matter described herein, estimating the source image comprises using one of: a non-uniform fast Fourier transform (NUFFT), including a density-corrected-NUFFT, an iterative NUFFT with conjugate gradients, or an iterative NUFFT with total variation regularization.

[0015] According to another aspect of the subject matter described herein, the method for reconstructing MR images includes performing model- facilitated denoising using a pretrained generative model and frequency guidance calculation and correction.

[0016] According to another aspect of the subject matter described herein, the method for reconstructing MR images includes repeating the model- facilitated denoising and frequency guidance calculation and correction until an end condition is reached.

[0017] According to another aspect of the subject matter described herein, performing frequency guidance calculation and correction includes calculating a non-Cartesian-sampled frequency space of a latent image, calculating a frequency gradient and an image space gradient, and performing correction using noisy interpolation between the latent image and the image space gradient of the latent image.

[0018] According to another aspect of the subject matter described herein, the k-space data comprises a plurality of samples sampled below a Nyquist frequency for the k-space data, and the method for producing MR images is performed with a reduced image acquisition time compared to Nyquist sampling.

[0019] According to another aspect of the subject matter described herein, a system for reconstructing MR images is provided. The system includes at least one processor. The system further includes an MR image reconstructor implemented on the at least one processor and configured to perform operations. The operations include receiving k-space data acquired with a non-Cartesian scanning trajectory. The operations further include transforming the k-space data into an initial image. The operations further include supplying the initial image to a diffusion model and generating a reconstructed image.

[0020] According to another aspect of the subject matter described herein, the operations comprise generating a latent noise vector sampled from a known noise distribution.

[0021] According to another aspect of the subject matter described herein, the operations comprise producing an image reconstruction prior by estimating a source image using a Fourier transform.

[0022] According to another aspect of the subject matter described herein, the operations comprise performing model-facilitated denoising using a pretrained generative model and frequency guidance calculation and correction.

[0023] According to another aspect of the subject matter described herein, the operations comprise repeating the model-facilitated denoising and frequency guidance calculation and correction until an end condition is reached.

[0024] According to another aspect of the subject matter described herein, a non-transitory computer readable medium storing executable instructions that when executed by at least one processor of a computer control the computer to perform operations is provided. The operations include receiving k-space magnetic resonance imaging (MRI) data acquired with a non-Cartesian scanning trajectory. The operations further include transforming the k-space MRI data into an initial image. The operations further include supplying the initial image to a diffusion model and generating a reconstructed image.

[0025] The subject matter described herein may be implemented in hardware, software, firmware, or any combination thereof. As such, the terms “function” or “node” as used herein refer to hardware, which may also include software and / or firmware components, for implementing the feature(s) being described. In some exemplary implementations, the subject matter described herein may be implemented using a computer readable medium having stored thereon computer executable instructions that when executed by the processor of a computer control the computer to perform steps. Exemplary computer readable media suitable for implementing the subject matter described herein include non-transitory computer readable media, such as disk memory devices, chip memory devices, programmable logic devices, and application specific integrated circuits. In addition, a computer readable medium that implements the subject matter described herein may be located on a single device or computing platform or may be distributed across multiple devices or computing platforms.

[0026] BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a block diagram of an example system 100 for MRI imaging;

[0028] Figure 2A shows example trajectories and Figure 2B shows the corresponding readout gradients inxand ky

[0029] Figure 3 illustrates a process for obtaining the frequency-corrected image;

[0030] Figure 4 shows representative reconstruction results for a single 2D 16 coil image;

[0031] Figure 5 is a graph of alpha versus interleaves; Figure 6A illustrates the effect of sampling trajectory optimization, model reconstruction without frequency guidance, and model reconstruction with frequency guidance; and

[0032] Figure 6B illustrates snapshots of the image latent xfand the gradient signal Vxftaken during a diffusion sampling process.

[0033] DETAILED DESCRIPTION

[0034] MRI acceleration is achieved through a combination of scanning efficiently and reducing acquired k-space data. Successful techniques for faster scanning include radial and spiral imaging methods, which exploit the unequal distribution of image signal across k-space by densely sampling lower frequencies. Undersampling k-space - sampling below the Nyquist limit - saves time but introduces ambiguities during reconstruction, manifesting as artifacts. To resolve these ambiguities, algorithms rely on inherent data redundancy and learned or assumed image priors.

[0035] Deep learning methods have pushed acceleration factors past what was previously achievable with parallel imaging and compressed sensing. Many deep learning approaches focus on Cartesian-sampled MRI, potentially missing out on acceleration gains achieved by using nonCartesian trajectories. This document describes a diffusion model-based method for trajectory-agnostic reconstruction of under sampled multicoil spiral MRI.

[0036] This technology addresses the lack of diffusion model-based deep learning approaches for image reconstruction from data collected along nonCartesian (including but not limited to radial and spiral) sampling trajectories, including the related tasks of scan acceleration, motion correction, and artifact correction.

[0037] Potential applications of this technology are numerous. The most notable is significant scan time acceleration, on the order of 10s to 100s of times faster than conventional and commonly used sequences, and multiple times faster than comparable proposed deep learning methods. This is achieved due to multiplicative speedups attained through multicoil imaging, efficient scanning trajectories and sequences, and intelligent image reconstruction.

[0038] Faster scans can improve patient comfort and compliance, enable scanning protocols that are currently infeasible due to long scan times, reduce artifacts due to patient motion, and enable real time high-resolution 3D imaging protocols.

[0039] Figure 1 is a block diagram of an example system 100 for MRI imaging. The system 100 includes an MRI scanner 102 configured for scanning a patient 104. The system 100 includes a computer system 106 configured for receiving data from the MRI scanner 102 and producing magnetic resonance (MR) images. The computer system 106 includes one or more processors 108 and memory 110 storing instructions for the processors 108. The computer system 106 includes an MR image reconstructor 112 configured for reconstructing MR images from under sampled MRI data to accelerate MR imaging. The system 100 includes a display 114 configured to display MR images, for example, to a medical professional 116.

[0040] In operation, MR image reconstructor 112 can perform the following actions for reconstructing MR images from under sampled MRI data:

[0041] 1. Begin with k-space MRI data acquired with a non-Cartesian scanning trajectory.

[0042] 2. Generate a latent noise vector sampled from a known noise distribution.

[0043] 3. Produce an image reconstruction prior by estimating the source image using the non-uniform fast Fourier transform (NUFFT) or equivalent methods such as density-corrected-NUFFT, iterative NUFFT with conjugate gradients, or iterative NUFFT with total variation regularization.

[0044] 4. Given the latent noise vector and the image reconstruction prior, perform repeated steps of:

[0045] - Model-facilitated denoising using a pretrained generative model.

[0046] - Frequency guidance calculation and correction consisting of: - Calculate the non-Cartesian-sampled frequency space of the latent image using iterative forward NUFFT or equivalent methods.

[0047] - Calculate a frequency gradient equal to the difference between the raw frequency data and the latent frequency space.

[0048] - Calculate the corresponding image space gradient using iterative inverse NUFFT or equivalent methods.

[0049] - Perform correction using noisy interpolation between the latent image and the image space gradient of the latent image.

[0050] - Repeat until completion after a predetermined number of steps.

[0051] 5. For multicoil data, perform final coil combination of the estimated individual coil channels using a method, such as root-sum-of-squares.

[0052] Figures 2 - 6 illustrate example systems for MR image reconstruction with reference to experimental systems used for testing.

[0053] Canonical score-based models consider the mapping between a known distribution of independently and identically distributed samples of gaussian noise and an observed, but unknown distribution of data p(x). These distributions bookend a Langevin diffusion process described by the following stochastic differential equation representing the trajectory of a sample from our data distribution into a sample from our noise distribution: dx = f x, t)dt + g(t)dw. (1 )

[0054] Here, functions and #(•) are the drift and diffusion coefficients of x(f) respectively, and w is a standard Wiener process, or Brownian motion. In order to generate a novel sample from our data distribution, we can generate a random noise vector and attempt to solve the reverse-time SDE, but this is generally intractable. However, we can approximate this process by estimating the noise-conditioned score function, Vxlogpt(x), which computes the likelihood of a sample x existing between the noise and image distributions. With this, the reverse-time SDE becomes: dx = [ (%, t) - g(t .ogpt(x) dt + g(t)dw (2)

[0055] The score function can be trained using a score matching with Langevin dynamics algorithm.

[0056] The example systems used methods conducted retrospectively using human subject data made available in open access. We use an example dataset (the NYU FastMRI dataset) having 6970 fully sampled 2D brain scans on hardware ranging from 4 to 24 coils. For training and testing, we consider axial T2 weighted turbo spin echo sequences characterized by the following sequence parameters: scan time=140 s, TR=6 s, TE=1 13 ms, slices=30, slice thickness=5 mm, field of view=22 cm, matrix size=320x320. Effective scan time for a 2D slice at 2562resolution is 140sZ320 * 256X30 « 3.7s. As this data is initially acquired using Cartesian sequences, we simulated spiral acquisition by retrospectively interpolating in k-space to attain complex-valued measurements along generated spiral trajectories.

[0057] We consider spiral trajectories of the form

[0058] Here, p denotes sampling density, T is a function of time, is angular position, ) = 2rrn is frequency, with n the number of turns in k-space, X is a scaling factor equal to matrix size / (2*FOV), where FOV is field of view, and a is a bias term for oversampling the center of kspace relative to the edges. Solving this parametric equation under the constraints of capped gradient slew rate and capped gradient amplitude yields gradients gx(t) and gy(ty) as well as a spiral trajectory in thex, y-plane (Figures 2A and 2B). In doing so, we can tune sampling parameters to control for factors such as read out duration and dwell time, while varying the number of interleaves and ratio of low-to-high frequency oversampling.

[0059] Figure 2A shows example trajectories, and Figure 2B shows the corresponding readout gradients inxand ky. All trajectories shown cover the frequency space of a 256x256 image and have a readout duration of 10.0 ms.

[0060] MRI undersampled acquisition amounts to measuring an unknown signal x through some imperfect sampling function A: y = Ax + e. Here, y is the measured multicoil k-space data, and A is the non-uniform fourier transform, e is measurement noise and exists in the same domain as the y; in MRI, noise is gaussian-distributed across the real and imaginary components of y for each coil. Reconstruction is an ill-posed inverse problem of recovering an image signal x from a set of incomplete k-space measurements y. As x and / exist in different domains, xis hidden behind a sampling operator A.

[0061] Solving this problem necessitates prior knowledge. In our case, we learn an underlying conditional distribution of images and seek to reconstruct samples from this distribution consistent with the measurements. Information is supplied in two forms: first, we learn a conditional score function V ogpt(xt|-1y0), where yo is the measurement in frequency space and i4-1is an approximate inverse of A, in our case the inverse nufft solved iteratively using conjugate gradients. We find that adding this supervision during training helps to constrain the model when faced with a large number of input image channels and the periodic ambiguity inherent when operating on complex numbers.

[0062] Second, we use frequency space gradients to weakly guide the sampling process. At each time step during sampling, we compute the forward nufft of an uncorrected and take a difference between that and the measurements yo. To minimize this difference, the approximate gradient in image space is calculated by solving a modified approximate inverse nufft Af1, which corrects for low frequency biases and applies time stepdependent noising determined by the noise schedule <j(t), which is necessary for sampling with langevin diffusion.

[0063] We choose a linear noise schedule and observe that the underlying ordinary differential equation describing transit from latent to image is locally linear, so summation of xt-xand Vxt_i to obtain a frequency-corrected image is akin to gradient descent.

[0064] Figure 3 illustrates a process for obtaining the frequency-corrected image. Given measurements yo, reconstruction follows a modified diffusion sampling process. At each timestep, a noisy latent xfis concatenated with a prior po and passed to the denoising model to obtain x^. To enforce consistency with yo, we compute a frequency gradient Vyt_i and solve for the image gradient using a modified iterative inverse nufft. A weighted sum of Xf.i and Vxt_i yields the corrected image xt-. This is repeated until t = 0.

[0065] In practice, due to the non-invertibility of the nufft, imperfections in the approximate inverse nufft bleed into the final image reconstruction, introducing artifacts and reducing quality. To avoid this, we anneal the guidance signal following an empirically chosen linear schedule y(f) = / 3(1 -f), ensuring strong guidance at the outset of sampling and minimal artifacts at the end of sampling. A consequence of this choice is that we do not strongly enforce that Axo = yo at time 0.

[0066] Results from experiments are described below for the purpose of illustration and not limitation.

[0067] Model reconstruction performance was evaluated on a held-out test dataset. Test trajectories have a fixed readout duration of 0.02 seconds, in which time the measurements needed to reconstruct a 256x256 pixel, 22x22 cm22D image are acquired. Reconstructed image quality was scored using structural similarity (SSIM).

[0068] Figure 4 shows representative reconstruction results for a single 2D 16 coil image. Retrospective k-space data was sampled with an optimized 23 interleave sequence with a total readout duration of 0.02 s. Rows 1 and 2 show the RSS-reconstructed images and log-scaled k-space magnitudes for the ground truth, inverse nufft, and proposed model reconstructions. Below are the individual coil magnitude and phase images for the fully sampled image, the inverse nufft reconstructions, and the model predictions.

[0069] To investigate the effect choosing different scanning trajectories has on the quality of reconstructed images, we also performed a grid hyperparameter search of spiral trajectories with a fixed readout duration of 0.02 seconds and varying a and interleaves. Specifically, we varied the number of interleaves from 1 to 125 and alpha from 1 to 4 (see Figure 5). Based on structural similarity of the model-reconstructed images, we found multiple trajectories that yield improved image quality. In comparison, the naive Archimedean spiral, corresponding to 1 interleave and a = 1 , performs very poorly. Figure 6A illustrates the effect of sampling trajectory optimization, model reconstruction without frequency guidance, and model reconstruction with frequency guidance. For the non-optimized trajectory, we used a single interleave Archimedean spiral with a readout duration of 0.02 s. The optimized trajectory uses a 23 interleave, a = 1.23 sequence with an identical readout duration. Figure 6B illustrates snapshots of the image latent xfand the gradient signal Vxftaken during a diffusion sampling process.

[0070] Surprisingly, the common ’naive’ trajectory, a single interleave Archimedean spiral, corresponding to a = 1 , performs very poorly when sampled below the Nyquist limit. Trajectories which perform better tended to lie along two logarithmic curves roughly characterized by a = 1 .33log(0.39 interleaves) and a = 0.87log(0.54 interleaves).

[0071] Finally, we conduct an ablation study to disentangle the effects of optimal sampling trajectory without model reconstruction, model reconstruction without frequency guidance, and model reconstruction with frequency guidance (Figures 6A and 6B). We find that all three contribute to noticeable increases in image quality, both visual, and quantitative based on SSIM. The combination of choosing an optimal trajectory, performing model reconstruction with conditioning, and using annealed frequency guidance results in large improvements in image quality, up to and exceeding a 0.15 boost in SSIM.

[0072] These examples demonstrate reconstructing spiral MRI using a diffusion model. Combining multicoil imaging, spiral scanning, and undersampling enables dramatically faster imaging speeds. Applications of this work are widespread; in addition to the numerous typical benefits associated with faster scanning, including better patient compliance and fewer motion artifacts, these methods have the potential to reach the extremely high acceleration factors necessary to achieve high resolution real-time 3D imaging.

[0073] The disclosure of each of the following references is incorporated herein by reference in its entirety. References

[0074] [1] Mark J Blum, Michael Braun, and Dov Rosenfeld, “Fast magnetic resonance imaging using spiral trajectories,” in Medical Imaging. SPIE, 1987, vol. 767, pp. 40-46.

[0075] [2] Stefanie Winkelmann, Tobias Schaeffter, Thomas Koehler, Holger Eggers, and Olaf Doessel, “An optimal radial profile order based on the golden ratio for time-resolved mri,” IEEE transactions on medical imaging, vol. 26, no. 1 , pp. 68-76, 2006.

[0076] [3] Daniel K Sodickson and Warren J Manning, “Simultaneous acquisition of spatial harmonics (smash): fast imaging with radiofrequency coil arrays,” Magnetic resonance in medicine, vol. 38, no. 4, pp. 591-603, 1997.

[0077] [4] Michael Lustig, David Donoho, and John M Pauly, “Sparse mri: The application of compressed sensing for rapid mr imaging,” Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, vol. 58, no. 6, pp. 1182-1195, 2007.

[0078] [5] Julio A Oscanoa, Matthew J Middione, Cagan Alkan, Mahmut Yurt, Michael Loecher, Shreyas S Vasanawala, and Daniel B Ennis, “Deep learning-based reconstruction for cardiac mri: A review,” Bioengineering, vol. 10, no. 3, pp. 334, 2023.

[0079] [6] Yang Song, Liyue Shen, Lei Xing, and Stefano Ermon, “Solving inverse problems in medical imaging with score-based generative models,” arXiv preprint arXiv:2111 .08005, 2021 .

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[0081] [8] Zhuo-Xu Cui, Chentao Cao, Jing Cheng, Sen Jia, Hairong Zheng, Dong Liang, and Yanjie Zhu, “Spirit-diffusion: Self-consistency driven diffusion model for accelerated mri,” arXiv preprint arXiv:2304.05060, 2023.

[0082] [9] Asad Aali, Marius Arvinte, Sidharth Kumar, and Jonathan I Tamir, “Solving inverse problems with score-based generative priors learned from noisy data,” arXiv preprint arXiv:2305.01166, 2023.

[0010] Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole, “Score-based generative modeling through stochastic differential equations,” arXiv preprint arXiv:2011.13456, 2020.

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[0012] Florian Knoll, Jure Zbontar, Anuroop Sriram, Matthew J Muckley, Mary Bruno, Aaron Defazio, Marc Parente, Krzysztof J Geras, Joe Katsnelson, Hersh Chandarana, et aL, “fastmri: A publicly available raw k- space and dicom dataset of knee images for accelerated mr image reconstruction using machine learning,” Radiology: Artificial Intelligence, vol. 2, no. 1 , pp. e190007, 2020.

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[0013] Dong-hyun Kim, Elfar Adalsteinsson, and Daniel M Spielman, “Simple analytic variable density spiral de-sign,” Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, vol. 50, no. 1 , pp. 214-219, 2003.

[0086] Although specific examples and features have been described above, these examples and features are not intended to limit the scope of the present disclosure, even where only a single example is described with respect to a particular feature. Examples of features provided in the disclosure are intended to be illustrative rather than restrictive unless stated otherwise. The above description is intended to cover such alternatives, modifications, and equivalents as would be apparent to a person skilled in the art having the benefit of this disclosure.

[0087] The scope of the present disclosure includes any feature or combination of features disclosed in this specification (either explicitly or implicitly), or any generalization of features disclosed, whether or not such features or generalizations mitigate any or all of the problems described in this specification. Accordingly, new claims may be formulated during prosecution of this application (or an application claiming priority to this application) to any such combination of features. In particular, with reference to the appended claims, features from dependent claims may be combined with those of the independent claims and features from respective independent claims may be combined in any appropriate manner and not merely in the specific combinations enumerated in the appended claims.

Claims

CLAIMSWhat is claimed is:

1. A method for reconstructing magnetic resonance (MR) images, the method comprising: receiving k-space data acquired with a non-Cartesian scanning trajectory; transforming the k-space data into an initial image; and supplying the initial image to a diffusion model and generating a reconstructed image.

2. The method of claim 1 , comprising generating a latent noise vector sampled from a known noise distribution.

3. The method of claim 2, comprising producing an image reconstruction prior by estimating a source image using a Fourier transform.

4. The method of claim 3, wherein estimating the source image comprises using one of: a non-uniform fast Fourier transform (NUFFT), including a density-corrected-NUFFT, an iterative NUFFT with conjugate gradients, or an iterative NUFFT with total variation regularization.

5. The method of claim 3, comprising performing model-facilitated denoising using a pretrained generative model and frequency guidance calculation and correction.

6. The method of claim 5, comprising repeating the model-facilitated denoising and frequency guidance calculation and correction until an end condition is reached.

7. The method of claim 5, wherein performing frequency guidance calculation and correction comprises: calculating a non-Cartesian-sampled frequency space of a latent image; calculating a frequency gradient and an image space gradient; and performing correction using noisy interpolation between the latent image and the image space gradient of the latent image.

8. The method of claim 1 , wherein the k-space data comprises a plurality of samples sampled below a Nyquist frequency for the k-spacedata, and wherein the method is performed with a reduced image acquisition time compared to Nyquist sampling.

9. A system for reconstructing magnetic resonance (MR) images, the system comprising: at least one processor; and an MR image reconstructor implemented on the at least one processor and configured to perform operations comprising: receiving k-space data acquired with a non-Cartesian scanning trajectory; transforming the k-space data into an initial image; and supplying the initial image to a diffusion model and generating a reconstructed image.

10. The system of claim 9, wherein the operations comprise generating a latent noise vector sampled from a known noise distribution.

11. The system of claim 10, wherein the operations comprise producing an image reconstruction prior by estimating a source image using a Fourier transform.

12. The system of claim 11 , wherein estimating the source image comprises using one of: a non-uniform fast Fourier transform (NUFFT), including a density-corrected-NUFFT, an iterative NUFFT with conjugate gradients, or an iterative NUFFT with total variation regularization.

13. The system of claim 11 , wherein the operations comprise performing model-facilitated denoising using a pretrained generative model and frequency guidance calculation and correction.

14. The system of claim 13, wherein the operations comprise repeating the model-facilitated denoising and frequency guidance calculation and correction until an end condition is reached.

15. The system of claim 13, wherein performing frequency guidance calculation and correction comprises: calculating a non-Cartesian-sampled frequency space of a latent image; calculating a frequency gradient and an image space gradient; andperforming correction using noisy interpolation between the latent image and the image space gradient of the latent image.

16. A non-transitory computer readable medium storing executable instructions that when executed by at least one processor of a computer control the computer to perform operations comprising: receiving k-space magnetic resonance imaging (MRI) data acquired with a non-Cartesian scanning trajectory; transforming the k-space MRI data into an initial image; and supplying the initial image to a diffusion model and generating a reconstructed image.

17. The non-transitory computer readable medium of claim 16, comprising generating a latent noise vector sampled from a known noise distribution.

18. The non-transitory computer readable medium of claim 17, comprising producing an image reconstruction prior by estimating a source image using a Fourier transform.

19. The non-transitory computer readable medium of claim 18, wherein estimating the source image comprises using one of: a non-uniform fast Fourier transform (NUFFT), including a density-corrected-NUFFT, an iterative NUFFT with conjugate gradients, or an iterative NUFFT with total variation regularization.

20. The non-transitory computer readable medium of claim 18, comprising performing model-facilitated denoising using a pretrained generative model and frequency guidance calculation and correction.

21. The non-transitory computer readable medium of claim 20, comprising repeating the model-facilitated denoising and frequency guidance calculation and correction until an end condition is reached.

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