# Single-shot Phase Retrieval from a Fractional Fourier Transform Perspective

arXiv: https://arxiv.org/abs/2311.10950 · HTML: https://mlsanity.com/paper/2311.10950/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 64 references that are in the map.
- First posted on arXiv 18 Nov 2023.

## Builds on (most cited first, 13 of 13)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Uformer: A General U-Shaped Transformer for Image Restoration](https://mlsanity.com/paper/2106.03106/) (2021)
- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Phase Retrieval from Coded Diffraction Patterns](https://mlsanity.com/paper/1310.3240/) (2013)
- [TFPnP: Tuning-free Plug-and-Play Proximal Algorithm with Applications to Inverse Imaging Problems](https://mlsanity.com/paper/2012.05703/) (2020)
- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [DeepPhaseCut: Deep Relaxation in Phase for Unsupervised Fourier Phase Retrieval](https://mlsanity.com/paper/2011.10475/) (2020)
- [SiSPRNet: End-to-End Learning for Single-Shot Phase Retrieval](https://mlsanity.com/paper/2205.11434/) (2022)
- [Dynamic Proximal Unrolling Network for Compressive Imaging](https://mlsanity.com/paper/2107.11007/) (2021)
- [STFT Phase Retrieval: Uniqueness Guarantees and Recovery Algorithms](https://mlsanity.com/paper/1508.02820/) (2015)
- [Snapshot Ptychography on Array cameras](https://mlsanity.com/paper/2111.03517/) (2021)

## Abstract (arXiv)

The realm of classical phase retrieval concerns itself with the arduous task of recovering a signal from its Fourier magnitude measurements, which are fraught with inherent ambiguities. A single-exposure intensity measurement is commonly deemed insufficient for the reconstruction of the primal signal, given that the absent phase component is imperative for the inverse transformation. In this work, we present a novel single-shot phase retrieval paradigm from a fractional Fourier transform (FrFT) perspective, which involves integrating the FrFT-based physical measurement model within a self-supervised reconstruction scheme. Specifically, the proposed FrFT-based measurement model addresses the aliasing artifacts problem in the numerical calculation of Fresnel diffraction, featuring adaptability to both short-distance and long-distance propagation scenarios. Moreover, the intensity measurement in the FrFT domain proves highly effective in alleviating the ambiguities of phase retrieval and relaxing the previous conditions on oversampled or multiple measurements in the Fourier domain. Furthermore, the proposed self-supervised reconstruction approach harnesses the fast discrete algorithm of FrFT alongside untrained neural network priors, thereby attaining preeminent results. Through numerical simulations, we demonstrate that both amplitude and phase objects can be effectively retrieved from a single-shot intensity measurement using the proposed approach and provide a promising technique for support-free coherent diffraction imaging.