Localized adversarial artifacts for compressed sensing MRI

TL;DR

This paper investigates the robustness of compressed sensing MRI reconstruction methods against localized adversarial artifacts, revealing vulnerabilities in traditional TV-regularized methods not present in DNN-based approaches.

Contribution

It introduces localized adversarial attacks for MRI reconstruction, highlighting inherent vulnerabilities in TV-minimization methods compared to DNNs.

Findings

Adversarial perturbations cause severe localized artifacts in TV-regularized MRI reconstructions.

DNN-based reconstructions are less susceptible to the proposed localized adversarial attacks.

The vulnerability to localized artifacts is inherent in methods with guaranteed exact recovery, like compressed sensing with TV or $\,l^1$-minimization.

Abstract

As interest in deep neural networks (DNNs) for image reconstruction tasks grows, their reliability has been called into question (Antun et al., 2020; Gottschling et al., 2020). However, recent work has shown that, compared to total variation (TV) minimization, when appropriately regularized, DNNs show similar robustness to adversarial noise in terms of $\ell^2$-reconstruction error (Genzel et al., 2022). We consider a different notion of robustness, using the $\ell^\infty$-norm, and argue that localized reconstruction artifacts are a more relevant defect than the $\ell^2$-error. We create adversarial perturbations to undersampled magnetic resonance imaging measurements (in the frequency domain) which induce severe localized artifacts in the TV-regularized reconstruction. Notably, the same attack method is not as effective against DNN based reconstruction. Finally, we show that this phenomenon is inherent to reconstruction methods for which exact recovery can be guaranteed, as with compressed sensing reconstructions with $\ell^1$- or TV-minimization.