Deep computational microscopy via physics-informed end-to-end learning with a learned forward model

Abstract Computational microscopy, which merges cutting-edge optical methods with intricate algorithms, offers significant potential for applications such as resolution improvement and quantitative phase retrieval. However, it faces challenges due to high computational demands and the need for precise algorithms. Recent advancements in data-driven deep-learning-based techniques have emerged to mitigate these challenges; however, incorporating physics-based constraints can further address the limitations. In this paper, we propose a deep-learning framework for image reconstruction in computational microscopy that combines the advantages of single-pass, end-to-end inversion and physics-informed learning approaches, while considering the challenges in obtaining exact physics-informed constraints. Our network learns the forward imaging process, which accurately estimates position-dependent optical aberrations and serves as an effective physical prior in the training of the reconstruction model. Validated on Fourier Ptychography (FP), our proposed framework demonstrates fast and robust FP reconstructions that outperform conventional model-based methods with significantly fewer input measurements and exhibits generalizability to unseen samples, as demonstrated by quantitative comparisons with existing methods. We evaluated our approach on various datasets, including human breast cancer pathology samples, the HeLA dataset, and the USAF phase target dataset, demonstrating that our method improves the practicality of computational microscopy by offering high-quality reconstructions with faster speeds over different sample types.