A physics-inspired deep learning framework for an efficient FPM reconstruction under low overlap conditions

2D observation of biological samples at hundreds of nanometers resolution or even below is of high-interest for many sensitive medical applications. Recent advances have been obtained with computational imaging and we consider here Fourier Ptychographic Microscopy (FPM). Although this technique has permitted to attain an impressive super-resolution factor up to 6 and to assess at the same time local optical thickness of samples, it suffers from low measurement cadence. This limits its applicability as a routine diagnostic tool. In this paper, we address the specific problem of FPM reconstruction when only few low resolution images are acquired. To this end, we introduce a physics informed optimization Deep Neural Network that is combined to statistical reconstruction learning. More precisely, the forward image microscope formation model is explicitly introduced in the model to optimize its weights starting from an initialization that is based on a statistical learning. This combination brings some robustness to the reconstruction process. The presented simulation results for an FPM configuration with very low overlap factor (Γ ∼ 10%) demonstrate the conceptual benefits of the approach in terms of image quality and resolution. The learning step is also shown to be mandatory.