  Although image denoising algorithms have attracted significant research
attention, surprisingly few have been proposed for, or evaluated on, noise from
imagery acquired under real low-light conditions. Moreover, noise
characteristics are often assumed to be spatially invariant, leading to edges
and textures being distorted after denoising. Here, we introduce a novel
topological loss function which is based on persistent homology. The method
performs in the space of image patches, where topological invariants are
calculated and represented in persistent diagrams. The loss function is a
combination of $\ell_1$ or $\ell_2$ losses with the new persistence-based
topological loss. We compare its performance across popular denoising
architectures and loss functions, training the networks on our new
comprehensive dataset of natural images captured in low-light conditions --
BVI-LOWLIGHT. Analysis reveals that this approach outperforms existing methods,
adapting well to complex structures and suppressing common artifacts.
