Compressed Sensing with Deep Image Prior and Learned Regularization
Authors: Dave Van Veen, Ajil Jalal, Mahdi Soltanolkotabi, Eric Price, Sriram Vishwanath, Alexandros G. Dimakis
Keywords: compressed sensing, sparsity, inverse problems
TL;DR: Compressed sensing methods with untrained networks and theoretical guarantees
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 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 trained can perfectly fit any signal despite the nonconvex nature of the fitting problem. This theoretical result provides justification for early stopping.