# Circular Phase Representation and Geometry-Aware Optimization for Ptychographic Image Reconstruction

arXiv: https://arxiv.org/abs/2604.26664 · HTML: https://mlsanity.com/paper/2604.26664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 29 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Spherical Regression: Learning Viewpoints, Surface Normals and 3D Rotations on n-Spheres](https://mlsanity.com/paper/1904.05404/) (2019)
- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [Real-time coherent diffraction inversion using deep generative networks](https://mlsanity.com/paper/1806.03992/) (2018)
- [Deep learning at the edge enables real-time streaming ptychographic imaging](https://mlsanity.com/paper/2209.09408/) (2022)
- [Robust Phase Unwrapping via Deep Image Prior for Quantitative Phase Imaging](https://mlsanity.com/paper/2009.11554/) (2020)
- [PtychoFormer: A Transformer-based Model for Ptychographic Phase Retrieval](https://mlsanity.com/paper/2410.17377/) (2024)
- [A Physics-Inspired Deep Learning Framework with Polar Coordinate Attention for Ptychographic Imaging](https://mlsanity.com/paper/2412.06806/) (2024)
- [Deep Iterative Phase Retrieval for Ptychography](https://mlsanity.com/paper/2202.10573/) (2022)
- [Low-light phase retrieval with implicit generative priors](https://mlsanity.com/paper/2402.17745/) (2024)

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

- [Zero-Shot Cross-Material Ptychographic Phase Reconstruction Using Deep Learning](https://mlsanity.com/paper/2609.13969/) (2026)

## Abstract (arXiv)

Traditional iterative reconstruction methods are accurate but computationally expensive, limiting their use in high-throughput and real-time ptychography. Recent deep learning approaches improve speed, but often predict phase as a Euclidean scalar despite its 2π periodicity, which can introduce wrapping artifacts, discontinuities at ±π, and a mismatch between the loss and the underlying signal geometry. We present a deep learning framework for ptychographic reconstruction that models phase on the unit circle using cosine and sine components. Phase error is optimized with a differentiable geodesic loss, which avoids branch-cut discontinuities and provides bounded gradients. The network further incorporates saturation-aware dual-gain input scaling, parallel encoder branches, and three decoders for amplitude, cosine, and sine prediction, together with a composite loss that promotes circular consistency and structural fidelity. Experiments on synthetic and experimental datasets show consistent improvements in both amplitude and phase reconstruction over existing deep learning methods. Frequency-domain analysis further shows better preservation of mid- and high-frequency phase content. The proposed method also provides substantial speedup over iterative solvers while maintaining physically consistent reconstructions.