  Single-Photon Image Super-Resolution (SPISR) aims to recover a
high-resolution volumetric photon counting cube from a noisy low-resolution one
by computational imaging algorithms. In real-world scenarios, pairs of training
samples are often expensive or impossible to obtain. By extending Equivariant
Imaging (EI) to volumetric single-photon data, we propose a self-supervised
learning framework for the SPISR task. Particularly, using the Poisson unbiased
Kullback-Leibler risk estimator and equivariance, our method is able to learn
from noisy measurements without ground truths. Comprehensive experiments on
simulated and real-world dataset demonstrate that the proposed method achieves
comparable performance with supervised learning and outperforms
interpolation-based methods.
