Position-Blind Ptychography: Viability of image reconstruction via data-driven variational inference

2025-09-28

AI Summary

This work addresses position-blind ptychography—a novel blind inverse problem requiring joint recovery of the object image and probe positions under completely unknown scanning coordinates. Motivated by single-particle X-ray diffraction imaging, where highly focused beams render diffraction patterns sensitive to particle positions that are both uncontrollable and unrecorded, we propose the first data-driven variational inference framework for this task. Our approach incorporates a fractional diffusion model as a strong structural prior, enabling noise-robust joint reconstruction. Systematic evaluation on a two-dimensional simplified model demonstrates stable, high-fidelity recovery of both object images and positional parameters across diverse imaging scenarios; only marginal performance degradation occurs under extreme complexity. These results validate the feasibility and robustness of our method, establishing a new paradigm for label-free, prior-free single-particle imaging.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Probabilistic Circuits and Graphical Models
• Computer Vision: Diffusion Models for Vision

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

In this work, we present and investigate the novel blind inverse problem of position-blind ptychography, i.e., ptychographic phase retrieval without any knowledge of scan positions, which then must be recovered jointly with the image. The motivation for this problem comes from single-particle diffractive X-ray imaging, where particles in random orientations are illuminated and a set of diffraction patterns is collected. If one uses a highly focused X-ray beam, the measurements would also become sensitive to the beam positions relative to each particle and therefore ptychographic, but these positions are also unknown. We investigate the viability of image reconstruction in a simulated, simplified 2-D variant of this difficult problem, using variational inference with modern data-driven image priors in the form of score-based diffusion models. We find that, with the right illumination structure and a strong prior, one can achieve reliable and successful image reconstructions even under measurement noise, in all except the most difficult evaluated imaging scenario.

Problem

• Reconstructs images without known scan positions
• Solves ptychographic phase retrieval with unknown positions
• Uses variational inference for position-blind reconstruction

Innovation

• Position-blind ptychography via variational inference
• Joint reconstruction using score-based diffusion priors
• Reliable imaging without scan position knowledge