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 on the network weights. Compared to previous unlearned methods for compressed sensing, our algorithm requires fewer measurements in most cases. Unlike previous learned approaches based on generative models, our method does not require pre-training over large datasets. As such, we can apply our method to various medical imaging datasets for which data acquisition is expensive and generative models are difficult to train.