Compressed Sensing MRI Reconstruction Regularized by VAEs with Structured Image Covariance

Abstract

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.

References in corpus (15)

• Auto-Encoding Variational Bayes
• Image reconstruction by domain transform manifold learning
• Variational Inference with Normalizing Flows
• On instabilities of deep learning in image reconstruction - Does AI come at a cost?
• Compressed Sensing MRI Reconstruction using a Generative Adversarial Network with a Cyclic Loss
• fastMRI: An Open Dataset and Benchmarks for Accelerated MRI
• Deep learning for undersampled MRI reconstruction
• Plug and play methods for magnetic resonance imaging (long version)
• Do GANs actually learn the distribution? An empirical study
• Stochastic Segmentation Networks: Modelling Spatially Correlated Aleatoric Uncertainty
• Modeling Sparse Deviations for Compressed Sensing using Generative Models
• Correction by Projection: Denoising Images with Generative Adversarial Networks
• Robust Image Reconstruction with Misaligned Structural Information
• Training VAEs Under Structured Residuals
• Regularising Inverse Problems with Generative Machine Learning Models

Cited by in corpus (2)

• Variational Bayes image restoration with compressive autoencoders
• Deep priors for satellite image restoration with accurate uncertainties