# Recovery of Structured Signals From Corrupted Non-Linear Measurements

## TL;DR

This paper proposes an extended Lasso method to recover structured signals from a limited number of corrupted non-linear measurements, providing theoretical conditions for successful reconstruction of both signal and corruption.

## Contribution

Introduction of an extended Lasso approach for disentangling signals and corruption in non-linear measurement models with theoretical recovery guarantees.

## Key findings

- Successful recovery conditions established
- Extended Lasso effectively separates signal and corruption
- Applicable to various structured signal models

## Abstract

This paper studies the problem of recovering a structured signal from a relatively small number of corrupted non-linear measurements. Assuming that signal and corruption are contained in some structure-promoted set, we suggest an extended Lasso to disentangle signal and corruption. We also provide conditions under which this recovery procedure can successfully reconstruct both signal and corruption.