Learning-based super interpolation and extrapolation for speckled image reconstruction.

Speckles arise when coherent light interacts with biological tissues. Information retrieval from speckles is desired yet challenging, requiring understanding or mapping of the multiple scattering process, or reliable capability to reverse or compensate for the scattering-induced phase distortions. In whatever situation, insufficient sampling of speckles undermines the encoded information, impeding successful object reconstruction from speckle patterns. In this work, we propose a deep learning method to combat the physical limit: the sub-Nyquist sampled speckles (~14 below the Nyquist criterion) are interpolated up to a well-resolved level (1024 times more pixels to resolve the same FOV) with smoothed morphology fine-textured. More importantly, the lost information can be retraced, which is impossible with classic interpolation or any existing methods. The learning network inspires a new perspective on the nature of speckles and a promising platform for efficient processing or deciphering of massive scattered optical signals, enabling widefield high-resolution imaging in complex scenarios.