Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models trained on Corrupted Data

We provide a framework for solving inverse problems with diffusion models learned from linearly corrupted data. Our method, Ambient Diffusion Posterior Sampling (A-DPS), leverages a generative model pre-trained on one type of corruption (e.g. image inpainting) to perform posterior sampling conditioned on measurements from a potentially different forward process (e.g. image blurring). We test the efficacy of our approach on standard natural image datasets (CelebA, FFHQ, and AFHQ) and we show that A-DPS can sometimes outperform models trained on clean data for several image restoration tasks in both speed and performance. We further extend the Ambient Diffusion framework to train MRI models with access only to Fourier subsampled multi-coil MRI measurements at various acceleration factors (R=2, 4, 6, 8). We again observe that models trained on highly subsampled data are better priors for solving inverse problems in the high acceleration regime than models trained on fully sampled data. We open-source our code and the trained Ambient Diffusion MRI models: https://github.com/utcsilab/ambient-diffusion-mri .

Optimizing Sampling Patterns for Compressed Sensing MRI with Diffusion Generative Models

Diffusion-based generative models have been used as powerful priors for magnetic resonance imaging (MRI) reconstruction. We present a learning method to optimize sub-sampling patterns for compressed sensing multi-coil MRI that leverages pre-trained diffusion generative models. Crucially, during training we use a single-step reconstruction based on the posterior mean estimate given by the diffusion model and the MRI measurement process. Experiments across varying anatomies, acceleration factors, and pattern types show that sampling operators learned with our method lead to competitive, and in the case of 2D patterns, improved reconstructions compared to baseline patterns. Our method requires as few as five training images to learn effective sampling patterns.

Conditional Score-Based Reconstructions for Multi-contrast MRI

Magnetic resonance imaging (MRI) exam protocols consist of multiple contrast-weighted images of the same anatomy to emphasize different tissue properties. Due to the long acquisition times required to collect fully sampled k-space measurements, it is common to only collect a fraction of k-space for some, or all, of the scans and subsequently solve an inverse problem for each contrast to recover the desired image from sub-sampled measurements. Recently, there has been a push to further accelerate MRI exams using data-driven priors, and generative models in particular, to regularize the ill-posed inverse problem of image reconstruction. These methods have shown promising improvements over classical methods. However, many of the approaches neglect the multi-contrast nature of clinical MRI exams and treat each scan as an independent reconstruction. In this work we show that by learning a joint Bayesian prior over multi-contrast data with a score-based generative model we are able to leverage the underlying structure between multi-contrast images and thus improve image reconstruction fidelity over generative models that only reconstruct images of a single contrast.

Accelerated Motion Correction for MRI using Score-Based Generative Models

Magnetic Resonance Imaging (MRI) is a powerful medical imaging modality, but unfortunately suffers from long scan times which, aside from increasing operational costs, can lead to image artifacts due to patient motion. Motion during the acquisition leads to inconsistencies in measured data that manifest as blurring and ghosting if unaccounted for in the image reconstruction process. Various deep learning based reconstruction techniques have been proposed which decrease scan time by reducing the number of measurements needed for a high fidelity reconstructed image. Additionally, deep learning has been used to correct motion using end-to-end techniques. This, however, increases susceptibility to distribution shifts at test time (sampling pattern, motion level). In this work we propose a framework for jointly reconstructing highly sub-sampled MRI data while estimating patient motion using score-based generative models. Our method does not make specific assumptions on the sampling trajectory or motion pattern at training time and thus can be flexibly applied to various types of measurement models and patient motion. We demonstrate our framework on retrospectively accelerated 2D brain MRI corrupted by rigid motion.

FSE Compensated Motion Correction for MRI Using Data Driven Methods

Magnetic Resonance Imaging (MRI) is a widely used medical imaging modality boasting great soft tissue contrast without ionizing radiation, but unfortunately suffers from long acquisition times. Long scan times can lead to motion artifacts, for example due to bulk patient motion such as head movement and periodic motion produced by the heart or lungs. Motion artifacts can degrade image quality and in some cases render the scans nondiagnostic. To combat this problem, prospective and retrospective motion correction techniques have been introduced. More recently, data driven methods using deep neural networks have been proposed. As a large number of publicly available MRI datasets are based on Fast Spin Echo (FSE) sequences, methods that use them for training should incorporate the correct FSE acquisition dynamics. Unfortunately, when simulating training data, many approaches fail to generate accurate motion-corrupt images by neglecting the effects of the temporal ordering of the k-space lines as well as neglecting the signal decay throughout the FSE echo train. In this work, we highlight this consequence and demonstrate a training method which correctly simulates the data acquisition process of FSE sequences with higher fidelity by including sample ordering and signal decay dynamics. Through numerical experiments, we show that accounting for the FSE acquisition leads to better motion correction performance during inference.