# Phaseless compressive sensing using partial support information

## TL;DR

This paper investigates conditions for accurately recovering real signals from phaseless measurements using weighted  minimization, especially when partial support info is available, and introduces new theoretical guarantees.

## Contribution

It provides a strong restricted isometry property condition and a weighted null space property for successful phaseless signal recovery with partial support information.

## Key findings

- Established a strong restricted isometry property condition.
- Derived the weighted null space property as a necessary and sufficient condition.
- Numerical experiments validate the theoretical results.

## Abstract

We study the recovery conditions of weighted $\ell_1$ minimization for real-valued signal reconstruction from phaseless compressive sensing measurements when partial support information is available. A strong restricted isometry property condition is provided to ensure the stable recovery. Moreover, we present the weighted null space property as the sufficient and necessary condition for the success of $k$-sparse phaseless recovery via weighted $\ell_1$ minimization. Numerical experiments are conducted to illustrate our results.