# Self-supervised learning for phase retrieval

arXiv: https://arxiv.org/abs/2509.26203 · HTML: https://mlsanity.com/paper/2509.26203/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Builds on (most cited first, 9 of 9)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Sensing Theorems for Unsupervised Learning in Linear Inverse Problems](https://mlsanity.com/paper/2203.12513/) (2022)
- [PhaseMax: Convex Phase Retrieval via Basis Pursuit](https://mlsanity.com/paper/1610.07531/) (2016)
- [Experimental robustness of Fourier Ptychography phase retrieval algorithms](https://mlsanity.com/paper/1511.02986/) (2015)
- [Learning to Reconstruct Signals From Binary Measurements](https://mlsanity.com/paper/2303.08691/) (2023)
- [Equivariance-based self-supervised learning for audio signal recovery from clipped measurements](https://mlsanity.com/paper/2409.15283/) (2024)

## Abstract (arXiv)

In recent years, deep neural networks have emerged as a solution for inverse imaging problems. These networks are generally trained using pairs of images: one degraded and the other of high quality, the latter being called 'ground truth'. However, in medical and scientific imaging, the lack of fully sampled data limits supervised learning. Recent advances have made it possible to reconstruct images from measurement data alone, eliminating the need for references. However, these methods remain limited to linear problems, excluding non-linear problems such as phase retrieval. We propose a self-supervised method that overcomes this limitation in the case of phase retrieval by using the natural invariance of images to translations.