VAEs with structured image covariance applied to compressed sensing MRI.

Area of Science:

• Medical Imaging
• Computational Science
• Machine Learning

Background:

• Inverse problems in medical imaging require effective regularization.
• Learned regularization offers data-driven priors but often needs paired training data.
• Unsupervised methods allow flexibility with changing forward problem parameters.

Purpose of the Study:

• Investigate generative models as priors for inverse problems.
• Develop a learned regularization method that is flexible and data-driven.
• Retain control and insight of variational regularization methods.

Main Methods:

• Utilize variational autoencoders for image generation and uncertainty estimation.
• Incorporate covariance matrices to model image-dependent uncertainty.
• Evaluate generative regularizers on sub-sampled MRI data from the fastMRI dataset.

Main Results:

• Proposed generative regularizers are competitive with state-of-the-art methods.
• The method demonstrates consistent performance across varying sampling patterns and noise levels.
• Unsupervised learning approach allows adaptation to changes in the forward problem.

Conclusions:

• Learned generative regularization provides a viable and flexible approach for inverse problems in MRI.
• Unsupervised generative priors can effectively penalize reconstructions outside the learned image manifold.
• The method shows promise for improving MRI reconstruction quality and robustness.