Plug-and-Play Half-Quadratic Splitting for Ptychography

TL;DR

The paper addresses the ill-posed, noise-sensitive phase retrieval problem in ptychography, where a forward measurement model and overlap constraints govern reconstruction. It introduces a half-quadratic splitting (HQS) framework to plug in data-driven priors via plug-and-play (PnP) denoisers for complex-valued images. The method yields explicit data-fidelity updates for Fourier-based measurements and extends to multi-probe ptychography with multiple auxiliary variables and a spatially varying denoising step. Experiments on natural images and a brain phantom show improved amplitude and phase reconstructions over classical PIE methods, especially at lower overlaps and higher noise. The work suggests potential reductions in acquisition time and lays groundwork for jointly reconstructing the object and the probe in future work.

Abstract

Ptychography is a coherent diffraction imaging method that uses phase retrieval techniques to reconstruct complex-valued images. It achieves this by sequentially illuminating overlapping regions of a sample with a coherent beam and recording the diffraction pattern. Although this addresses traditional imaging system challenges, it is computationally intensive and highly sensitive to noise, especially with reduced illumination overlap. Data-driven regularisation techniques have been applied in phase retrieval to improve reconstruction quality. In particular, plug-and-play (PnP) offers flexibility by integrating data-driven denoisers as implicit priors. In this work, we propose a half-quadratic splitting framework for using PnP and other data-driven priors for ptychography. We evaluate our method both on natural images and real test objects to validate its effectiveness for ptychographic image reconstruction.

Figures (3)

• Figure 1: The measurement model for ptychography. We first extract a patch from the image. We take the element-wise product of the extracted patch with the probe. Finally, we obtain the magnitude of the Fourier transform. This process is repeated for all probe positions in the image. The blue squares in the left image show two consecutive overlapping regions.
• Figure 2: Reconstructions for the $7\times 7$ probe setting with $\alpha=20.0$. We only show the center of the image where PSNR is calculated.
• Figure 3: Reconstruction of the phase of the brain phantom. The ground truth is given as the converged ePIE Maiden2009AnIP solution from oversampled measured data.

Theorems & Definitions (1)

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