  Basis pursuit is a compressed sensing optimization in which the l1-norm is
minimized subject to model error constraints. Here we use a deep neural network
prior instead of l1-regularization. Using known noise statistics, we jointly
learn the prior and reconstruct images without access to ground-truth data.
During training, we use alternating minimization across an unrolled iterative
network and jointly solve for the neural network weights and training set image
reconstructions. At inference, we fix the weights and pass the measurements
through the network. We compare reconstruction performance between unsupervised
and supervised (i.e. with ground-truth) methods. We hypothesize this technique
could be used to learn reconstruction when ground-truth data are unavailable,
such as in high-resolution dynamic MRI.
