Robust Resilient Signal Reconstruction under Adversarial Attacks

TL;DR

This paper introduces a novel robust signal reconstruction method that combines deep learning and estimation theory to effectively identify and mitigate sparse adversarial attacks, validated through water system simulations.

Contribution

It proposes a new constrained optimization framework with a pruning algorithm for attack support estimation, enhancing robustness against malicious corruptions.

Findings

Improved attack support localization accuracy.

Established conditions for successful signal reconstruction.

Validated effectiveness through water distribution system simulation.

Abstract

We consider the problem of signal reconstruction for a system under sparse signal corruption by a malicious agent. The reconstruction problem follows the standard error coding problem that has been studied extensively in the literature. We include a new challenge of robust estimation of the attack support. The problem is then cast as a constrained optimization problem merging promising techniques in the area of deep learning and estimation theory. A pruning algorithm is developed to reduce the ``false positive" uncertainty of data-driven attack localization results, thereby improving the probability of correct signal reconstruction. Sufficient conditions for the correct reconstruction and the associated reconstruction error bounds are obtained for both exact and inexact attack support estimation. Moreover, a simulation of a water distribution system is presented to validate the proposed techniques.