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We propose a novel method for compressed sensing recovery using untraineddeep generative models. Our method is based on the recently proposed Deep ImagePrior (DIP), wherein the convolutional weights of the network are optimized tomatch the observed measurements. We show that this approach can be applied tosolve any differentiable linear inverse problem, outperforming previousunlearned methods. Unlike various learned approaches based on generativemodels, our method does not require pre-training over large datasets. Wefurther introduce a novel learned regularization technique, which incorporatesprior information on the network weights. This reduces reconstruction error,especially for noisy measurements. Finally, we prove that, using the DIPoptimization approach, moderately overparameterized single-layer networks canperfectly fit any signal despite the non-convex nature of the fitting problem.This theoretical result provides justification for early stopping.

Compressed Sensing with Deep Image Prior and Learned Regularization