Compressed Sensing with Deep Image Prior and Learned Regularization

TL;DR

This paper introduces a new compressed sensing recovery method using untrained deep generative models based on Deep Image Prior, enhanced with learned regularization, achieving improved results without large dataset pre-training.

Contribution

The paper presents a novel untrained deep generative approach for compressed sensing, incorporating learned regularization and theoretical insights into network fitting behavior.

Findings

Outperforms previous unlearned methods in compressed sensing tasks

Introduces a learned regularization technique that reduces reconstruction error

Provides theoretical proof that overparameterized single-layer networks can fit any signal

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 can perfectly fit any signal despite the non-convex nature of the fitting problem. This theoretical result provides justification for early stopping.