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

## TL;DR

This paper introduces a novel 'learning to synthesize' approach for robust phase retrieval that separately learns to handle low and high spatial frequency bands, resulting in high-resolution, artifact-free reconstructions even under low photon counts.

## Contribution

The paper proposes a new method that learns to synthesize different frequency bands separately, improving phase retrieval quality and robustness in noisy, low-photon scenarios.

## Key findings

- Achieves high-resolution, artifact-free phase reconstructions.
- Demonstrates robustness to high noise and low photon flux.
- Applicable to other inverse problems with uneven frequency treatment.

## Abstract

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.