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Diffusion models (DMs) are a powerful frame- work for image generation and restoration. How- ever, existing DMs are primarily trained in a su- pervised manner by using a large corpus of clean images. This poses fundamental challenges in many real-world scenarios, where acquiring noise- free data is hard or infeasible. While some meth- ods are capable of training DMs using noisy data, they are effective only when the amount of noise is very mild or when additional noise-free data is available. In addition, existing methods for training DMs from incomplete measurements re- quire access to multiple complementary acquisi- tion processes, a significant practical limitation. Here we introduce the first approach for learning DMs for image restoration using only noisy mea- surement data from a single operator. First, we show that DMs, and more broadly minimum mean squared error denoisers, exhibit a weak form of scale equivariance linking rescaling in signal am- plitude to changes in noise intensity. We then leverage this theoretical insight to develop a de- noising score-matching strategy that generalizes robustly to noise levels below the training data, thereby enabling the learning of DMs from noisy measurements. For problems involving measure- ments both noisy and incomplete, we integrate our method with equivariant imaging, a complemen- tary self-supervised learning framework that ex- ploits the inherent invariants of imaging problems. This allows training DMs for image restoration from single-operator noisy measurements. We validate the effectiveness of our approach through extensive experiments on image denoising, demo- saicing, inpainting, and MRI reconstruction along with comparisons with the state of the art. 

Purpose: Magnetic Resonance Imaging (MRI) enables non‐invasive assessment of brain abnormalities during early life development. Permanent magnet scanners operating in the neonatal intensive care unit (NICU) facilitate MRI of sick infants, but have long scan times due to lower signal‐to‐noise ratios (SNR) and limited receive coils. This work accelerates in‐NICU MRI with diffusion probabilistic generative models by developing a training pipeline accounting for these challenges. Methods: We establish a novel training dataset of clinical, 1 Tesla neonatal MR images in collaboration with Aspect Imaging and Sha'are Zedek Medical Center. We propose a pipeline to handle the low quantity and SNR of our real‐world dataset (1) modifying existing network architectures to support varying resolutions; (2) training a single model on all data with learned class embedding vectors; (3) applying self‐supervised denoising before training; and (4) reconstructing by averaging posterior samples. Retrospective under‐sampling experiments, accounting for signal decay, evaluated each item of our proposed methodology. A clinical reader study with practicing pediatric neuroradiologists evaluated our proposed images reconstructed from under‐sampled data. Results: Combining all data, denoising pre‐training, and averaging posterior samples yields quantitative improvements in reconstruction. The generative model decouples the learned prior from the measurement model and functions at two acceleration rates without re‐training. The reader study suggests that proposed images reconstructed from under‐sampled data are adequate for clinical use. Conclusion: Diffusion probabilistic generative models applied with the proposed pipeline to handle challenging real‐world datasets could reduce the scan time of in‐NICU neonatal MRI. 

We provide a framework for solving inverse problems with diffusion models learned from linearly corrupted data. Firstly, we extend the Ambient Diffusion framework to enable training directly from measurements corrupted in the Fourier domain. Subsequently, we train diffusion models for MRI with access only to Fourier sub- sampled multi-coil measurements at acceleration factors R= 2,4,6,8. Secondly, we propose Ambient Diffusion Posterior Sampling (A-DPS), a reconstruction al- gorithm that leverages generative models pre-trained on one type of corruption (e.g. image inpainting) to perform posterior sampling on measurements from a different forward process (e.g. image blurring). For MRI reconstruction in high acceleration regimes, we observe that A-DPS models trained on subsampled data are better suited to solving inverse problems than models trained on fully sampled data. We also test the efficacy of A-DPS on natural image datasets (CelebA, FFHQ, and AFHQ) and show that A-DPS can sometimes outperform models trained on clean data for several image restoration tasks in both speed and performance. 

Implicit Neural Representations (INRs) are a learning-based approach to accelerate Magnetic Resonance Imaging (MRI) acquisitions, particularly in scan-specific settings when only data from the under-sampled scan itself are available. Previous work has shown that INRs improve rapid MRI through inherent regularization imposed by neural network architectures. Typically parameterized by fully connected neural networks, INRs provide continuous image representations by mapping a physical coordinate location to its intensity. Prior approaches have applied unlearned regularization priors during INR training and were limited to 2D or low-resolution 3D acquisitions. Meanwhile, diffusion-based generative models have recently gained attention for learning powerful image priors independent of the measurement model. This work proposes INFusion, a technique that regularizes INR optimization from under-sampled MR measurements using pre-trained diffusion models to enhance reconstruction quality. In addition, a hybrid 3D approach is introduced, enabling INR application on large-scale 3D MR datasets. Experimental results show that in 2D settings, diffusion regularization improves INR training, while in 3D, it enables feasible INR training on matrix sizes of 256 × 256 × 80. 

Given the enormous output and pace of development of artificial intelligence (AI) methods in medical imaging, it can be challenging to identify the true success stories to determine the state-of-the-art of the field. This report seeks to provide the magnetic resonance imaging (MRI) community with an initial guide into the major areas in which the methods of AI are contributing to MRI in oncology. After a general introduction to artificial intelligence, we proceed to discuss the successes and current limitations of AI in MRI when used for image acquisition, reconstruction, registration, and segmentation, as well as its utility for assisting in diagnostic and prognostic settings. Within each section, we attempt to present a balanced summary by first presenting common techniques, state of readiness, current clinical needs, and barriers to practical deployment in the clinical setting. We conclude by presenting areas in which new advances must be realized to address questions regarding generalizability, quality assurance and control, and uncertainty quantification when applying MRI to cancer to maintain patient safety and practical utility. 

Abstract PurposeThe aim of this work is to develop a method to solve the ill‐posed inverse problem of accelerated image reconstruction while correcting forward model imperfections in the context of subject motion during MRI examinations. MethodsThe proposed solution uses a Bayesian framework based on deep generative diffusion models to jointly estimate a motion‐free image and rigid motion estimates from subsampled and motion‐corrupt two‐dimensional (2D) k‐space data. ResultsWe demonstrate the ability to reconstruct motion‐free images from accelerated two‐dimensional (2D) Cartesian and non‐Cartesian scans without any external reference signal. We show that our method improves over existing correction techniques on both simulated and prospectively accelerated data. ConclusionWe propose a flexible framework for retrospective motion correction of accelerated MRI based on deep generative diffusion models, with potential application to other forward model corruptions.