# Convex Augmentation for Total Variation Based Phase Retrieval

arXiv: https://arxiv.org/abs/2205.00834 · HTML: https://mlsanity.com/paper/2205.00834/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 63 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 8 of 8)

- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems](https://mlsanity.com/paper/1505.05114/) (2015)
- [Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow](https://mlsanity.com/paper/1605.08285/) (2016)
- [Phase Retrieval from Coded Diffraction Patterns](https://mlsanity.com/paper/1310.3240/) (2013)
- [Sparse Phase Retrieval: Convex Algorithms and Limitations](https://mlsanity.com/paper/1303.4128/) (2013)
- [Reshaped Wirtinger Flow and Incremental Algorithm for Solving Quadratic System of Equations](https://mlsanity.com/paper/1605.07719/) (2016)
- [Phase Retrieval from 1D Fourier Measurements: Convexity, Uniqueness, and Algorithms](https://mlsanity.com/paper/1603.05215/) (2016)
- [A Convergent 3-Block Semi-Proximal ADMM for Convex Minimization Problems with One Strongly Convex Block](https://mlsanity.com/paper/1410.7933/) (2014)

## Abstract (arXiv)

Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a convex augmentation approach for phase retrieval based on total variation regularization. In contrast to popular convex relaxation models like PhaseLift, our model can be efficiently solved by a modified semi-proximal alternating direction method of multipliers (sPADMM). The modified sPADMM is more general and flexible than the standard one, and its convergence is also established in this paper. Extensive numerical experiments are conducted to showcase the effectiveness of the proposed method.