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

Researchers from academia (Carson Yu Liu, Jun Cheng, Chien-Chun Chen, Steve F. Shu) propose a deep learning framework for ptychographic image reconstruction that tackles a fundamental limitation of existing methods: phase wrapping. Traditional iterative reconstruction offers high accuracy but is computationally expensive, limiting high-throughput and real-time applications. Recent deep learning approaches improve speed but typically predict phase as a Euclidean scalar, ignoring its inherent 2π periodicity. This introduces wrapping artifacts, discontinuities at ±π, and a mismatch between the loss function and the underlying signal geometry.

The new framework models phase on the unit circle using cosine and sine components, optimizing phase error with a differentiable geodesic loss that avoids branch-cut discontinuities and provides bounded gradients. The network architecture includes saturation-aware dual-gain input scaling, parallel encoder branches, and three decoders for amplitude, cosine, and sine prediction, with a composite loss promoting 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 reveals better preservation of mid- and high-frequency phase content. The method provides substantial speedup over iterative solvers while maintaining physically consistent reconstructions, making it viable for high-throughput and real-time ptychography applications.