Compressed Sensing with Deep Image Prior and Learned Regularization
This method addresses compressed sensing problems for signal processing applications without requiring large pre-training datasets, though it builds incrementally on existing Deep Image Prior work.
The paper tackles compressed sensing recovery by using untrained deep generative models with Deep Image Prior and a learned regularization technique, achieving lower reconstruction error especially for noisy measurements and proving that overparameterized networks can perfectly fit signals.
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 linear inverse problem, outperforming previous unlearned methods. Unlike various learned approaches based on generative models, our method does not require pre-training over large datasets. We further introduce a novel learned regularization technique, which incorporates prior information on the network weights. This reduces reconstruction error, especially for noisy measurements. Finally, we prove that, using the DIP optimization approach, moderately overparameterized single-layer networks can perfectly fit any signal despite the non-convex nature of the fitting problem. This theoretical result provides justification for early stopping.