# Corrupted Sensing with Sub-Gaussian Measurements

## TL;DR

This paper addresses the challenge of recovering structured signals from corrupted sub-Gaussian measurements, proposing methods with theoretical guarantees under various prior knowledge scenarios.

## Contribution

It introduces three reconstruction procedures for signals with different prior knowledge, supported by an extended matrix deviation inequality for isotropic sub-Gaussian matrices.

## Key findings

- Stable recovery conditions established for structured signals with corruption.
- Extended matrix deviation inequality developed for isotropic sub-Gaussian matrices.
- Theoretical analysis applicable to various prior knowledge settings.

## Abstract

This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of prior knowledge are available. In each case, we provide conditions for stable signal recovery from structured corruption with added unstructured noise. The key ingredient in our analysis is an extended matrix deviation inequality for isotropic sub-Gaussian matrices.