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

TL;DR

This paper tackles position-blind ptychography, where both the object image and scan positions must be inferred from diffraction data. It develops a Bayesian variational framework that leverages score-based diffusion priors (and a surrogate RED-Diff approach) to regularize the ill-posed inverse problem, extended to joint inference over images and positions. Through a detailed 2D simulation study with realistic forward models, diverse probe structures, and both Gaussian and Poisson noise, the authors show that data-driven priors enable reliable reconstructions in most scenarios, with SSP (surrogate prior) delivering the best image quality and substantial, though not perfect, position recovery; the probe structure emerges as a crucial factor for success. The work demonstrates the potential of combining diffusion-based priors, variational inference, and structured illumination to make position-blind ptychography feasible, and outlines clear directions for extending to 3D, unknown rotations, and more realistic experimental settings with uncertainty quantification.

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.

Figures (13)

• Figure 1: The ptychographic SPI setup. Components from left to right: (a) a beam aperture, (b) an optional random phase mask, (c) a focusing optic, here illustrated as a Fresnel zone plate, (d) the interaction region at the beam focus, and (e) a detector. The photon beam is illustrated in transparent red. The particles move through the interaction region in an uncontrolled manner, and each particle generates a single diffraction pattern before disintegrating (diffraction before destructionneutzePotentialBiomolecularImaging2000chapman2014diffraction). This makes the particle position and orientation relative to the beam unknown in every measurement.
• Figure 2: Comparison of several probe functions $p$ used in this work. All three are based on the same random Zernike polynomial, with an optional random phase mask of block size $b$ applied as indicated. The dashed white square shows the extent of the imaged object $x$ for comparison. The diameter of the aperture is half a probe array size here, i.e., 256 pixels.
• Figure 3: Example image reconstructions of a single test object for the different optimization-based methods (Opt) and variational inference methods (VI), in (a) the non-blind baseline setting and (b) our position-blind setting. The images show complex magnitude as the brightness and complex phase as the hue.
• Figure 4: Reconstructed images for different probe functions with the SSP method. We compare (a) probes with different aperture diameters $d_\text{ap}$ and (b) optional random aperture phase masks of different block sizes $b$. The insets show the aperture-plane wavefront generating each respective probe.
• Figure 5: The loss landscape for an idealized position recovery problem. We plot summed squared errors between a noiseless measurement at the central position and simulated noiseless measurements at possible $(\Delta w, \Delta h)$ shifts relative to the center. We compare the three probe functions shown in \ref{['fig:probe-comparison']} with $d_\text{ap}=1/2$. The bottom row is zoomed in around (0,0) and of higher resolution.