Compressed Sensing MRI Reconstruction Regularized by VAEs with Structured Image Covariance
It addresses MRI reconstruction for medical imaging by providing a flexible, unsupervised regularization method that adapts to changes in sampling and noise, though it is incremental as it builds on existing VAE and regularization frameworks.
The paper tackles MRI reconstruction from sub-sampled measurements by using variational autoencoders (VAEs) with structured covariance as learned priors, achieving competitive results with state-of-the-art methods on the fastMRI dataset.
Objective: This paper investigates how generative models, trained on ground-truth images, can be used \changes{as} priors for inverse problems, penalizing reconstructions far from images the generator can produce. The aim is that learned regularization will provide complex data-driven priors to inverse problems while still retaining the control and insight of a variational regularization method. Moreover, unsupervised learning, without paired training data, allows the learned regularizer to remain flexible to changes in the forward problem such as noise level, sampling pattern or coil sensitivities in MRI. Approach: We utilize variational autoencoders (VAEs) that generate not only an image but also a covariance uncertainty matrix for each image. The covariance can model changing uncertainty dependencies caused by structure in the image, such as edges or objects, and provides a new distance metric from the manifold of learned images. Main results: We evaluate these novel generative regularizers on retrospectively sub-sampled real-valued MRI measurements from the fastMRI dataset. We compare our proposed learned regularization against other unlearned regularization approaches and unsupervised and supervised deep learning methods. Significance: Our results show that the proposed method is competitive with other state-of-the-art methods and behaves consistently with changing sampling patterns and noise levels.