# 3D-2D Neural Nets for Phase Retrieval in Noisy Interferometric Imaging

arXiv: https://arxiv.org/abs/2402.06063 · HTML: https://mlsanity.com/paper/2402.06063/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 39 references that are in the map.
- First posted on arXiv 8 Feb 2024.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Phase recovery and holographic image reconstruction using deep learning in neural networks](https://mlsanity.com/paper/1705.04286/) (2017)
- [Low Photon Count Phase Retrieval Using Deep Learning](https://mlsanity.com/paper/1806.10029/) (2018)
- [Learning to Synthesize: Robust Phase Retrieval at Low Photon counts](https://mlsanity.com/paper/1907.11713/) (2019)
- [Unsupervised Hyperspectral Stimulated Raman Microscopy Image Enhancement: Denoising and Segmentation via One-Shot Deep Learning](https://mlsanity.com/paper/2104.08338/) (2021)

## Abstract (arXiv)

In recent years, neural networks have been used to solve phase retrieval problems in imaging with superior accuracy and speed than traditional techniques, especially in the presence of noise. However, in the context of interferometric imaging, phase noise has been largely unaddressed by existing neural network architectures. Such noise arises naturally in an interferometer due to mechanical instabilities or atmospheric turbulence, limiting measurement acquisition times and posing a challenge in scenarios with limited light intensity, such as remote sensing. Here, we introduce a 3D-2D Phase Retrieval U-Net (PRUNe) that takes noisy and randomly phase-shifted interferograms as inputs, and outputs a single 2D phase image. A 3D downsampling convolutional encoder captures correlations within and between frames to produce a 2D latent space, which is upsampled by a 2D decoder into a phase image. We test our model against a state-of-the-art singular value decomposition algorithm and find PRUNe reconstructions consistently show more accurate and smooth reconstructions, with a x2.5 - 4 lower mean squared error at multiple signal-to-noise ratios for interferograms with low (< 1 photon/pixel) and high (~100 photons/pixel) signal intensity. Our model presents a faster and more accurate approach to perform phase retrieval in extremely low light intensity interferometry in presence of phase noise, and will find application in other multi-frame noisy imaging techniques.