VAEs with structured image covariance applied to compressed sensing MRI

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 \changes{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.

Improved Magnetic Resonance Image Reconstruction using Compressed Sensing and Adaptive Multi Extreme Particle Swarm Optimization Algorithm

“…However, the L0-norm used in the above expression, counting the number of non-zero elements, is non-convex and computationally challenging to work with. Therefore, the L1-norm is often used as a convex surrogate for sparsity, leading to a more tractable optimization problem [2].…”

“…Magnetic resonance imaging (MRI), a non-ionizing radiation medical imaging technology [1] is widely utilized in medical procedures. However, the extensive data collection required for one image as necessitated by the Nyquist criterion [2], makes the process time-consuming, constrained by technical and physiological limitations [3] since more samples are needed for optimal resolution. To expedite data acquisition without compromising quality, data compression is a viable solution.…”