Digital super-oscillation uniting residual dense network for super-resolution imaging

The convolutional neural networks (CNN) relying on the deep learning between the low-high resolution datasets have been demonstrated to achieve super-resolution (SR) imaging. However, most of the CNN-SR studies neglect the physical optical imaging model in the CNN learning. In this paper, we propose a digital super-oscillation (SO) principle uniting the residual dense network (RDN) to fully exploit the SR imaging. The digital SO principle regarded as a digital pupil filtering enables achieving the sub-diffraction shrinkage of the point spread function through the specific digital pupil modulating in the spatial spectrum domain. Numerical simulation shows that the spatial spacing ~ 0.67 diffraction limit of the objects could be resolved through the digital SO modulating of the diffraction-limited images. In the RDN training, the low-resolution dataset are the optical images proceeded by the digital SO principle. In compared with the optical images, the low-resolution dataset with more fine features attribute to a superior RDN model. Experiments on the RDN test datasets validate that the image fidelities of the super-resolution images approach the original objects and the statistical gradients of the super-resolution images possess at least two times enhancement in compared to the optical images. This study has potential applications in the computer vision, remote sensing, etc.