Robust Compressed Sensing MRI with Deep Generative Priors

Jalal, Ajil; Arvinte, Marius; Daras, Giannis; Price, Eric; Dimakis, Alexandros G.; Tamir, Jonathan I.

doi:10.48550/arxiv.2108.01368

Cited by 6 publications

(13 citation statements)

References 52 publications

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“…An unsupervised alternative is to approximate the conditional score function with an unconditionallytrained score model s θ ˚px t , tq « ∇ xt log p t px t q and the measurement distribution ppy | xq. Many existing works (Song et al, 2021;Kawar et al, 2021;Kadkhodaie & Simoncelli, 2020;Jalal et al, 2021) have implemented this idea in different ways. However, the methods in Kawar et al (2021) and Kadkhodaie & Simoncelli (2020) both require computing the singular value decomposition (SVD) of A P R mˆn , which can be difficult for many measurement processes in medical imaging.…”

Section: Solving Inverse Problems With Score-based Generative Modelsmentioning

confidence: 99%

“…However, the methods in Kawar et al (2021) and Kadkhodaie & Simoncelli (2020) both require computing the singular value decomposition (SVD) of A P R mˆn , which can be difficult for many measurement processes in medical imaging. The method proposed in Jalal et al (2021) is only designed for a specific sampling method called annealed Langevin dynamics (ALD, Song & Ermon, 2019), which proves to be inferior to more advanced sampling algorithms such as Predictor-Corrector methods (Song et al, 2021).…”

Section: Solving Inverse Problems With Score-based Generative Modelsmentioning

confidence: 99%

“…For example, we can convert the sampler in Algorithm 1 to an inverse problem solver in Algorithm 2 by adding/modifying just three lines of pseudo-code. Unlike the concurrent work Jalal et al (2021), our method is not limited to annealed…”

Section: Incorporating a Given Observation Into An Unconditional Samp...mentioning

confidence: 99%

“…We compare with several existing methods that apply score-based generative models to inverse problem solving. Specifically, we consider the "Langevin" approach proposed in Jalal et al (2021), and the "Score SDE" method in Song et al (2021), where the former is limited to annealed Langevin dynamics (ALD) sampling, and the latter was based on a crude approximation to the conditional score function ∇ xt log p t px t | yq in Eq. ( 4), and was proposed as a theoretical possibility in Appendix I.4 of Song et al (2021) without experiments.…”

Section: Standard Techniques In Medical Imagingmentioning

confidence: 99%

“…Comparing against existing score-based methods We compare our method against Langevin (Jalal et al, 2021) and Score SDE (Song et al, 2021) for undersampled MRI reconstruction on BraTS. Two variants of our approach are considered, which respectively use annealed Langevin dynamics (ALD) and the Predictor-Corrector (PC) sampler for score-based generative models as the backend.…”

Section: Standard Techniques In Medical Imagingmentioning

confidence: 99%

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Solving Inverse Problems in Medical Imaging with Score-Based Generative Models

Song¹,

Shen²,

Liu³

et al. 2021

Preprint

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Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes.

show abstract

Section: Solving Inverse Problems With Score-based Generative Modelsmentioning

confidence: 99%

Section: Solving Inverse Problems With Score-based Generative Modelsmentioning

confidence: 99%

Section: Incorporating a Given Observation Into An Unconditional Samp...mentioning

confidence: 99%

Section: Standard Techniques In Medical Imagingmentioning

confidence: 99%

Section: Standard Techniques In Medical Imagingmentioning

confidence: 99%

See 3 more Smart Citations

Solving Inverse Problems in Medical Imaging with Score-Based Generative Models

Song¹,

Shen²,

Liu³

et al. 2021

Preprint

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Bias‐reduced neural networks for parameter estimation in quantitative MRI

Mao,

Flassbeck,

Assländer

2024

Magnetic Resonance in Med

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PurposeTo develop neural network (NN)‐based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér–Rao bound.Theory and MethodsWe generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications.ResultsIn simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér–Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as nonlinear least‐squares fitting, while state‐of‐the‐art NNs show larger deviations.ConclusionThe proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

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Semantic regularization of electromagnetic inverse problems

Zhang,

Chen,

Wang

et al. 2024

Nat Commun

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Solving ill-posed inverse problems typically requires regularization based on prior knowledge. To date, only prior knowledge that is formulated mathematically (e.g., sparsity of the unknown) or implicitly learned from quantitative data can be used for regularization. Thereby, semantically formulated prior knowledge derived from human reasoning and recognition is excluded. Here, we introduce and demonstrate the concept of semantic regularization based on a pre-trained large language model to overcome this vexing limitation. We study the approach, first, numerically in a prototypical 2D inverse scattering problem, and, second, experimentally in 3D and 4D compressive microwave imaging problems based on programmable metasurfaces. We highlight that semantic regularization enables new forms of highly-sought privacy protection for applications like smart homes, touchless human-machine interaction and security screening: selected subjects in the scene can be concealed, or their actions and postures can be altered in the reconstruction by manipulating the semantic prior with suitable language-based control commands.

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Robust Compressed Sensing MRI with Deep Generative Priors

Cited by 6 publications

References 52 publications

Solving Inverse Problems in Medical Imaging with Score-Based Generative Models

Solving Inverse Problems in Medical Imaging with Score-Based Generative Models

Bias‐reduced neural networks for parameter estimation in quantitative MRI

Semantic regularization of electromagnetic inverse problems

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