  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.
