Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors

TL;DR

This paper provides theoretical guarantees and practical algorithms for using untrained deep neural networks as image priors in inverse imaging problems like compressive sensing and phase retrieval, demonstrating improved performance over traditional priors.

Contribution

It introduces a new framework for applying untrained neural network priors to inverse imaging, along with convergence guarantees and empirical validation.

Findings

Untrained deep network priors outperform traditional priors in image quality.

The proposed gradient descent scheme converges reliably for inverse problems.

Deep priors enable higher compression rates at similar image quality.

Abstract

Deep neural networks as image priors have been recently introduced for problems such as denoising, super-resolution and inpainting with promising performance gains over hand-crafted image priors such as sparsity and low-rank. Unlike learned generative priors they do not require any training over large datasets. However, few theoretical guarantees exist in the scope of using untrained neural network priors for inverse imaging problems. We explore new applications and theory for untrained neural network priors. Specifically, we consider the problem of solving linear inverse problems, such as compressive sensing, as well as non-linear problems, such as compressive phase retrieval. We model images to lie in the range of an untrained deep generative network with a fixed seed. We further present a projected gradient descent scheme that can be used for both compressive sensing and phase retrieval and provide rigorous theoretical guarantees for its convergence. We also show both theoretically as well as empirically that with deep network priors, one can achieve better compression rates for the same image quality compared to hand crafted priors.