The digital hologram reconstruction process has experienced significant improvements in recent years due to the rise of deep learning techniques. Unlike traditional reconstruction methods that primarily rely on complex optical setups and post-processing algorithms, deep learning-based methods provide the potential for faster, more efficient, and more accurate reconstructions. However, the effectiveness of deep learning models in digital holography is often constrained by the quality and quantity of available training data. High-quality and large-scale holographic datasets are difficult to obtain, with significant challenges in terms of both the complexity of data generation and associated costs. This creates a critical bottleneck in developing deep learning models capable of delivering high-performance hologram reconstructions. While deep learning techniques have demonstrated impressive results in holographic reconstruction with sufficient data, the problem becomes far more difficult when the available datasets are limited in size or quality. We investigate hologram reconstruction with small sample datasets and provide an innovative solution in the form of a graph neural network (GNN) model designed to enhance reconstruction performance by effectively capturing the physical relationships between amplitude and phase information in holograms.

We propose a GNN-based model for digital hologram reconstruction that addresses the limitations imposed by small sample datasets. The primary challenge in digital holography lies in the complex correlation between the amplitude and phase of the reconstructed light field. Traditional methods often struggle to capture these complex relationships accurately under scarce training data. By leveraging the capabilities of graph-based neural networks, our model can effectively encode these amplitude-phase correlations. Specifically, the GNN model constructs a graph structure that represents the physical relationships between pixels in the hologram, allowing it to learn the underlying patterns of light propagation more effectively than traditional convolutional neural network (CNN). To overcome the challenges of few-shot learning (FSL), we consider the intrinsic relationship between the amplitude and phase of the light field. The model takes the raw hologram as the input and performs joint modeling and inference of both amplitude and phase features by GNN. This approach allows the amplitude and phase to complement each other during the reconstruction process, enhancing the overall quality of the model’s output. In particular, the model first extracts initial amplitude and phase features from the input hologram. Then, by adopting the graph structure, GNN iteratively refines these features by considering the relationships between amplitude and phase during the inference process. This enables the model to restore both the amplitude and phase information of the light field accurately, even under limited data. To train the model, we employ a small dataset consisting of ten animal cell mitosis slices. Though small, this dataset provides sufficient labeled data for supervised training while adhering to the FSL scenario.

The proposed GNN model is evaluated by a series of experiments on both synthetic and real holographic datasets. The results indicate that the GNN model consistently outperforms traditional deep learning approaches in terms of both amplitude and phase reconstruction, especially in scenarios where the sample size is limited. In particular, the GNN model demonstrates exceptional performance in recovering the phase information, which is notoriously difficult to reconstruct by employing conventional methods. The ability of the model to accurately capture amplitude-phase correlations significantly improves the overall quality of the reconstructed holograms. Compared to other models, GNN shows better generalization capabilities when faced with small sample datasets, indicating that it can leverage the existing data more efficiently and avoid overfitting. Additionally, our experiments show that the model can reconstruct the light field with minimal detail loss, even in low-light conditions, which highlights its robustness. The improvements in both amplitude and phase reconstruction are particularly notable in complex holograms with high-frequency components, where traditional methods tend to fail or require extensive data preprocessing. Furthermore, the GNN model demonstrates the ability to generalize across different types of holograms, suggesting that the model’s effectiveness is not restricted to specific datasets but can be adapted to a variety of experimental conditions. The physical insights gained from the graph-based approach provide new perspectives on the interplay between the amplitude and phase, deepening the understanding of how light field information is encoded and reconstructed in digital holography.

We propose a novel approach to digital hologram reconstruction by GNNs, which significantly improves the reconstruction performance in small sample conditions. The ability of the GNN model to effectively model the complex physical relationships between amplitude and phase information is a key factor in its success. Experimental results demonstrate that GNN outperforms traditional deep learning models, particularly in terms of phase reconstruction, and provides a viable solution for hologram reconstruction even with limited training data. Our study lays a solid foundation for further advancements in digital holography and deep learning applications, particularly in situations where data acquisition is limited or expensive. By addressing the challenges of small sample datasets, the proposed model provides new possibilities for the practical implementation of digital holography in real-world applications, such as medical imaging, optical testing, and industrial inspections. Future research may explore further optimizations of the GNN architecture and its application to more diverse types of holographic data, potentially broadening its applicability and improving its robustness.