Compressed Sensing with Deep Image Prior and Learned Regularization

We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match the observed measurements. We show that this approach can be applied to solve any differentiable inverse problem. We also introduce a novel learned regularization technique which incorporates a small amount of prior information, further reducing the number of measurements required for a given reconstruction error. Our algorithm requires approximately 4-6x fewer measurements than classical Lasso methods. Unlike previous approaches based on generative models, our method does not require the model to be pre-trained. As such, we can apply our method to various medical imaging datasets for which data acquisition is expensive and no known generative models exist.