# Learning to Synthesize: Robust Phase Retrieval at Low Photon counts

arXiv: https://arxiv.org/abs/1907.11713 · HTML: https://mlsanity.com/paper/1907.11713/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2019.

## Built on by (most cited first, 16 of 16)

- [Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces](https://mlsanity.com/paper/2201.00217/) (2022)
- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [Fourier Imager Network (FIN): A deep neural network for hologram reconstruction with superior external generalization](https://mlsanity.com/paper/2204.10533/) (2022)
- [Deep Operator Learning Lessens the Curse of Dimensionality for PDEs](https://mlsanity.com/paper/2301.12227/) (2023)
- [IAE-Net: Integral Autoencoders for Discretization-Invariant Learning](https://mlsanity.com/paper/2203.05142/) (2022)
- [Self-supervised learning of hologram reconstruction using physics consistency](https://mlsanity.com/paper/2209.08288/) (2022)
- [Holographic image reconstruction with phase recovery and autofocusing using recurrent neural networks](https://mlsanity.com/paper/2102.12281/) (2021)
- [eFIN: Enhanced Fourier Imager Network for generalizable autofocusing and pixel super-resolution in holographic imaging](https://mlsanity.com/paper/2301.03162/) (2023)
- [Few-shot Transfer Learning for Holographic Image Reconstruction using a Recurrent Neural Network](https://mlsanity.com/paper/2201.11333/) (2022)
- [SiSPRNet: End-to-End Learning for Single-Shot Phase Retrieval](https://mlsanity.com/paper/2205.11434/) (2022)
- [Nonlinear functional regression by functional deep neural network with kernel embedding](https://mlsanity.com/paper/2401.02890/) (2024)
- [A Physics-Inspired Deep Learning Framework with Polar Coordinate Attention for Ptychographic Imaging](https://mlsanity.com/paper/2412.06806/) (2024)
- [Low-light phase retrieval with implicit generative priors](https://mlsanity.com/paper/2402.17745/) (2024)
- [Towards Practical Single-shot Phase Retrieval with Physics-Driven Deep Neural Network](https://mlsanity.com/paper/2208.08604/) (2022)
- [3D-2D Neural Nets for Phase Retrieval in Noisy Interferometric Imaging](https://mlsanity.com/paper/2402.06063/) (2024)
- [PtyGenography: using generative models for regularization of the phase retrieval problem](https://mlsanity.com/paper/2502.01338/) (2025)

## Abstract (arXiv)

The quality of inverse problem solutions obtained through deep learning [Barbastathis et al, 2019] is limited by the nature of the priors learned from examples presented during the training phase. In the case of quantitative phase retrieval [Sinha et al, 2017, Goy et al, 2019], in particular, spatial frequencies that are underrepresented in the training database, most often at the high band, tend to be suppressed in the reconstruction. Ad hoc solutions have been proposed, such as pre-amplifying the high spatial frequencies in the examples [Li et al, 2018]; however, while that strategy improves resolution, it also leads to high-frequency artifacts as well as low-frequency distortions in the reconstructions. Here, we present a new approach that learns separately how to handle the two frequency bands, low and high; and also learns how to synthesize these two bands into the full-band reconstructions. We show that this "learning to synthesize" (LS) method yields phase reconstructions of high spatial resolution and artifact-free; and it is also resilient to high-noise conditions, e.g. in the case of very low photon flux. In addition to the problem of quantitative phase retrieval, the LS method is applicable, in principle, to any inverse problem where the forward operator treats different frequency bands unevenly, i.e. is ill-posed.