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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.
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Robust Compressed Sensing MRI with Deep Generative Priors
The CSGM framework (Bora-Jalal-Price-Dimakis'17) has shown that deepgenerative priors can be powerful tools for solving inverse problems.However, to date this framework has been empirically successful only oncertain datasets (for example, human faces and MNIST digits), and itis known to perform poorly on out-of-distribution samples. In thispaper, we present the first successful application of the CSGMframework on clinical MRI data. We train a generative prior on brainscans from the fastMRI dataset, and show that posterior sampling viaLangevin dynamics achieves high quality reconstructions. Furthermore,our experiments and theory show that posterior sampling is robust tochanges in the ground-truth distribution and measurement process.Our code and models are available at: \url{https://github.com/utcsilab/csgm-mri-langevin}.
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- PAR ID:
- 10336434
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- Volume:
- 34
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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