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

TL;DR

This paper introduces a geometry-aware deep learning framework for ptychographic image reconstruction that models phase on the unit circle, improving accuracy, consistency, and speed over existing methods.

Contribution

It proposes a novel phase modeling approach using cosine and sine components with a geodesic loss, enhancing reconstruction quality and computational efficiency.

Findings

Improved phase and amplitude reconstruction accuracy.

Better preservation of high-frequency phase content.

Significant speedup over traditional iterative methods.

Abstract

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 $2\pi$ periodicity, which can introduce wrapping artifacts, discontinuities at $\pm\pi$, 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.