Robustness of Deep Equilibrium Architectures to Changes in the Measurement Model

TL;DR

This paper investigates the robustness of deep equilibrium architectures in imaging inverse problems, showing that DEQ priors trained under mismatched measurement models can outperform traditional denoisers, challenging previous assumptions.

Contribution

It provides a comparative analysis of DEQ and PnP frameworks, revealing that DEQ priors can be more robust to measurement model changes than previously believed.

Findings

DEQ priors trained under mismatched models outperform denoisers

DEQ architectures demonstrate robustness to measurement model variations

Challenging the assumption that PnP is more robust than DEQ

Abstract

Deep model-based architectures (DMBAs) are widely used in imaging inverse problems to integrate physical measurement models and learned image priors. Plug-and-play priors (PnP) and deep equilibrium models (DEQ) are two DMBA frameworks that have received significant attention. The key difference between the two is that the image prior in DEQ is trained by using a specific measurement model, while that in PnP is trained as a general image denoiser. This difference is behind a common assumption that PnP is more robust to changes in the measurement models compared to DEQ. This paper investigates the robustness of DEQ priors to changes in the measurement models. Our results on two imaging inverse problems suggest that DEQ priors trained under mismatched measurement models outperform image denoisers.