Learnable reconstruction-based synthetic aperture imaging via Fourier ptychography

Fourier ptychography (FP), a synthetic aperture imaging technique, has made significant progress in recent years. This technique effectively overcomes the aperture limitations of imaging systems, enabling imaging at a resolution beyond the original system's capabilities. However, in far-field macroscopic FP imaging, high-quality image reconstruction often requires a large amount of sampling data, which not only increases system complexity but also limits practical applications. Additionally, the unavoidable speckle noise in far-field imaging presents an additional challenge for image reconstruction. To address these issues, we propose a model-constrained network called FPADMMNet, which combines the alternating direction method of multipliers (ADMM) with neural networks. This approach transforms the ADMM-based optimization algorithm into a trainable network structure, where each sub-problem is mapped to a specific network layer, and the iterative process is implemented through a series of stages. Experimental results show that FPADMMNet can still achieve high-quality image reconstruction under limited sampling conditions, reducing the amount of data required for reconstruction while maintaining reconstruction quality.