# Phase inpainting in time-frequency plane

## TL;DR

This paper introduces phase inpainting, a new problem of reconstructing signals from partial phase information in the time-frequency domain, and compares three algorithms for solving it.

## Contribution

It formulates the phase inpainting problem and adapts three existing algorithms, including two semidefinite programming methods, for this new task.

## Key findings

- Knowledge of certain phases improves reconstruction quality.
- Semidefinite programming algorithms outperform iterative methods.
- The proposed methods effectively recover missing phase information.

## Abstract

We propose a new problem of missing data reconstruction in the time-frequency plane. This problem called phase inpainting, consists in reconstructing a signal from time-frequency observations where all amplitudes and some phases are known while the remaining phases are missing. A mathematical formulation of this problem is given. We propose three alternatives of existing algorithms. An iterative algorithm: Griffin and Lim and two semidefinite programming optimization algorithms: PhaseLift and PhaseCut. The obtained results show that knowledge of certain phases improves the reconstruction's quality.