
Unsupervised Deep Basis Pursuit: Learning Inverse Problems without Groundtruth Data

Jonathan I. Tamir and Stella X. Yu and Michael Lustig

Neural Information Processing Systems Workshop on Solving Inverse Problems with Deep Networks, Vancouver, Canada, 2019

Paper

Poster

Abstract

Basis pursuit is a compressed sensing optimization in which the L1norm is minimized subject to model error constraints. Here we use a deep neural network prior instead of l1regularization. Using known noise statistics, we jointly learn the prior and reconstruct images without access to groundtruth 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 groundtruth) methods. We hypothesize this technique could be used to learn reconstruction when groundtruth data are unavailable, such as in highresolution dynamic MRI.

Keywords

Unsupervised learning, inverse problems, modelbased deep learning, computational imaging, magnetic resonance imaging
