A Topological Loss Function for Low-Light Image Denoising

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, offering true features with resistance to noise across multiple scales. 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, 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 edges and complex structures and suppressing common artifacts.