Constraint-Free Coherent Diffraction Imaging via Physics-Guided Neural Fields

CDI is a lensless imaging technique that enables atomic-resolution imaging of non-crystalline specimens and their dynamics. However, its broader implementation has been hindered by the instability and ill-posedness of its reconstruction process, known as phase retrieval, which relies heavily on handcrafted, object-specific constraints. To overcome the key limitations, we propose CDIP, a robust phase-retrieval framework that eliminates the need for such constraints by combining untrained coordinate-based neural fields for static and dynamic reconstructions and a physics-consistent forward model. We evaluate CDIP on simulated and experimental datasets that involve both static samples and dynamic processes, demonstrating that it substantially outperforms classical iterative algorithms and deep-learning baselines in terms of fidelity and stability. These results highlight a paradigm shift in both static and time-resolved CDI reconstruction, providing a broadly applicable framework for coherent imaging modalities such as ptychography and holography, across X-ray, electron, and optical probes.

💡 Research Summary

This paper introduces “CDIP” (Cross-Dimensional Implicit Priors), a novel phase-retrieval framework designed to overcome the long-standing limitations of Coherent Diffraction Imaging (CDI). CDI is a powerful lensless technique capable of atomic-resolution imaging but suffers from an ill-posed and unstable reconstruction process (phase retrieval), which traditionally relies heavily on accurate, handcrafted constraints like object support and positivity. These constraints are often unknown or inaccurate in practice, leading to reconstruction failures.

The core innovation of CDIP is the integration of an untrained, coordinate-based neural field with a physics-consistent forward model. Instead of optimizing a discrete 2D complex array, CDIP represents the object as a continuous 3D volumetric field parameterized by a neural network (specifically, a SIREN MLP). This network takes spatial (x, y, z) coordinates as input and outputs the corresponding complex amplitude and phase. This implicit representation acts as a powerful prior, restricting solutions to the space of smooth, continuous functions and inherently stabilizing the solution space.

A differentiable forward model projects this 3D neural field to 2D and applies a Fourier transform to generate a predicted diffraction pattern. The network parameters are then optimized by minimizing the discrepancy between these predictions and the measured diffraction intensities. Key to its success is the “progressive anchoring” strategy: optimization begins from a small central region of the field of view and gradually expands outward. This introduces a spatial bias that centers the object, resolving translational ambiguities and eliminating the need for an explicit support constraint. A perceptual loss based on a pre-trained VGG network is also incorporated to improve global structural coherence and robustness to Poisson noise.

The framework naturally extends to dynamic CDI by simply adding a temporal coordinate (t) to the neural field’s input, allowing it to model the entire spatiotemporal evolution of an object within a single continuous function, enabling coherent reconstructions without explicit temporal regularization.

The authors validate CDIP on experimental Bragg CDI data of static gold nanoparticles. Compared to conventional hybrid input-output (HIO) and error reduction (ER) algorithms with Shrinkwrap support refinement, CDIP produces smoother, more continuous phase reconstructions with fewer boundary artifacts, despite using no prior knowledge about the object’s support. The results demonstrate that CDIP substantially outperforms classical iterative methods and deep-learning baselines in reconstruction fidelity and stability.

In conclusion, CDIP represents a paradigm shift in CDI reconstruction, moving from reliance on explicit, object-specific constraints to a robust, constraint-free framework leveraging the implicit priors of neural fields and physical models. It provides a broadly applicable approach for both static and time-resolved coherent imaging across X-ray, electron, and optical domains.