# The phase unwrapping of under-sampled interferograms using radial basis function neural networks

arXiv: https://arxiv.org/abs/2210.10541 · HTML: https://mlsanity.com/paper/2210.10541/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 88 references that are in the map.
- First posted on arXiv 19 Oct 2022.

## Builds on (most cited first, 7 of 7)

- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [Layer-Parallel Training of Deep Residual Neural Networks](https://mlsanity.com/paper/1812.04352/) (2018)
- [Temporal phase unwrapping using deep learning](https://mlsanity.com/paper/1903.09836/) (2019)
- [Surrogate Optimization of Deep Neural Networks for Groundwater Predictions](https://mlsanity.com/paper/1908.10947/) (2019)
- [Robust Phase Unwrapping via Deep Image Prior for Quantitative Phase Imaging](https://mlsanity.com/paper/2009.11554/) (2020)
- [A Joint Convolutional and Spatial Quad-Directional LSTM Network for Phase Unwrapping](https://mlsanity.com/paper/2010.13268/) (2020)
- ["Parallel Training Considered Harmful?": Comparing series-parallel and parallel feedforward network training](https://mlsanity.com/paper/1706.07119/) (2017)

## Built on by (most cited first, 1 of 1)

- [Towards Real-Time Inference of Thin Liquid Film Thickness Profiles from Interference Patterns Using Vision Transformers](https://mlsanity.com/paper/2510.25157/) (2025)

## Abstract (arXiv)

Interferometry can measure the shape or the material density of a system that could not be measured otherwise by recording the difference between the phase change of a signal and a reference phase. This difference is always between -π and π while it is the absolute phase that is required to get a true measurement. There is a long history of methods designed to recover accurately this phase from the phase "wrapped" inside ]-π,π]. However, noise and under-sampling limit the effectiveness of most techniques and require highly sophisticated algorithms that can process imperfect measurements. Ultimately, analysing successfully an interferogram amounts to pattern recognition, a task where radial basis function neural networks truly excel at. The proposed neural network is designed to unwrap the phase from two-dimensional interferograms, where aliasing, stemming from under-resolved regions, and noise levels are significant. The neural network can be trained in parallel and in three stages, using gradient-based supervised learning. Parallelism allows to handle relatively large data sets, but requires a supplemental step to synchronized the fully unwrapped phase across the different networks.