Title: Compressed Sensing with Deep Image Prior and Learned Regularization,
Abstract: 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.